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Measurement

Assigning numbers or other symbols to characterisitics of objects being measured, accorind to predetermined rules. Characteristics of the time are measured rather thant he itme directly. Thus, this means that consumers are not meansured, only their perceptions, attitudes, preferences or other relevant characteristics.


Scaling

Can be considered a part of measurement
Scales place the objects being measured along a continuum Scaling is the process of placing consumer response along an attitudinal continuum from unfavorable, to neutral, to favorable. The scale is the set of values ranging from one to three 

Scale Characteristics

1. Description
2. Order 3. Distance 4. Origin **Together they define the level of measurement of a scale 

Description

Involves the unique labels or descriptors that are used to designate each value of the scale
Ex. 1= Female, 2= Male Ex. 1= Strongly Disagree, 2= Disagree, 3= Neutral, 4= Agree, 5= Strongly Agree 

Order

Refers to the relative sizes or positions of the descriptors
Order is denoted by descriptors such as greater than, less than, and equal to. Ex. A respondent's preference for three brands of athletic shoes is expressed by the following order wiht the most preferred brand being listed first and the least preferred brand last (Nike, Asics, Adidas). 

Distance

Means that absolute differences between the scale descriptors are known and can be expressed in units
Ex. A five person household has one person more than a four person household, which in turn has one more person than a three person househould. Thus, distance implies order, but the reverse may not be true 

Origin

Means that the scale has a unique or fixed beginning or true zero point. Thus, an exact measurement of income by a scale such as, "What is the annual income of our household before taxes?" has a fixed origin or a true zero point.
An answer of zero would mean that the household has no income at all A scale that has origin also has distance, order and description 

4 Primary Scales

1. Nominal
2. Ordinal 3. Interval 4. Ratio **The nominal scale is hte most limited, followed by the ordinal, the interval and the ratio scale. As the measurement level increases from nominal to ratio, scale complexity increases. 

Nominal Scale

Uses numbers as labels or tags for identifying and alssifying objects. The only characteristic possessed by these scales is description.
Each number is assigned to only one object and each object has only one number assigned to it. Common Examples: social security numbers and football player jersey numbers Marketing Examples: used for brands, attributes, stores, objects, and identifying participants in a study. 

Nominal Scale Continued

Used for classification purposes
They serve as labels for classes or categories. The classes are mutually exclusive and collectively exhaustive Mutually exclusive means that there is no overlap between classes; every object being measured falls into only one class Collectively exhaustive means that all the objects fall into one of the classes. For example, the numbers 1 and 2 can be used to classify survey respondents based on gender, with 1 denoting female and 2 denoting male. Each respondent will fal linto one of these two categories. 

Ordinal Scale

A ranking scale
In an ordinal scale, numbers are assigend to objects which allows researchers to determine whether an object has more or less of a scharacteristic than some other object. Objects ranked first have more of the characteristic of being measured than objects ranked second; however, it is not possible to determine whether the obeject ranked second is a close second or a distant second. Thus, ordinal scales possess descriptions and order characteristics, but not distance or origin. 

Ordinal Scale Continued

Common Example: quality rankings, rankings of teams in a tournament, and educational levels
Marketing Examples: used ot measure relative attitudes, opinions, perceptions and preferences In addition to the counting operation allowable for nominal scale data, ordinal scales also permit the use of statistics based on centiles. This means that if it is meaningufl to calculate percentile, media, or other summary statistics from ordinal data. 

Interval Scale

Numerically equal distances on teh scale represent equal values inteh characteristic being measured.
An interval scale contains all the informatin of an ordianl scale In addition, it allows you to compare the differences between objects. The difference between 1 and 2 is the same difference between 2 and 3, whihc is the same difference between 5 and 6. 

Interval Scale Continued

The interval scales possess the characterisitcs of description, order and distance.
In marketing research, data on attitudes, obtained from rating scales are often are treated as interval data. In an interval scale, the location of the zero point i snot fixed. Both teh zero point and the units of measurement are arbitrary; that is, these scales do not possess the origin characteristic. This is measured in teh measurement of temperature. 

Ratio Scale

Possess all the properties of the nominal, ordinal and interval scales.
In addition, a zero point is specified; that is, the origin of the scale is fixed. Thus, ratio scales possess the characteristic of origin. When measurement is taken using ratio scales, the researcher can identify or classifyu objects, rank the obejcts, adn compare intervals or differences Common Examples: height, weight, age, and income Marketing Examples: sales, costs, market share, and number of customers All statistical techniques can be applied ot ratio data. These include specialized statisitcs, such as the geometric mean. 

Comparative Scales

Involve the direct comparison of two or more obejcts
Ex. Respondents might be asked whtehr they prefer Coke or Pepsi Comparative scaling is sometimes referred to as nonmetric scaling The major benefit of comparative scaling is that small differences between objects under study can be detected. This makes them easy to understand and apply They also tend to reduce halo in which early judgements influence later judgements The major disadvantage of comparative scales is the limitation in term sof analyzing ordinal data. In additon, it is not possible to generalize beyond the objects under study. 

Noncomparative Scales

Also referred to as monadic or metric scales
Objects are scaled independently of each other. The resulting data are generally assumed to be interval scaled Ex. Respondents might be askedot evaluate Coke on a 1 to 7 preference scale. Similar evaluations would be then be obtained for Pepsi and RC Cola as well. 

3 Types of Comparative Scaling

1. Paired Comparison
2. Rank Order 3. Constant Sum Scaling 

Paired Comparison Scaling

Where a respondent is presented with a pair of alternatives and asked to select one. Data obtained in this way are ordinal in nature
Paired comparison scales are used when the research involves physical products Paired comparison is useful when the number of brands under consideration is limited to no more than five. When a larger number of brands is involved, the number of comparisons becomes unwieldy. Also problematic is the fact that poaired comparison bear little resemblance to the marketplace situation, which involves selection from multiple alternatives. Respondents might prefer one alternative to another; however, that does not imply that they like it in an absolute manner. 

Rank Order Scaling

Where respondents are simultaneously presented with several alternatives and asked to rank them accoriding to some criterion.
Ex. Consumer might be asked to rank brands of jeans according to preference Rankings typically are obtained by asking the respondents to assign a rank of 1 to the most preferred brand, 2 to the second most preferred, and so on, until each alternative is ranked down to the least preferred brand. However, it is possible that even the brand ranked 1 isnot liked in an absolute sense; that is, it might be the least disliked. Rank order scaling forces the respondent to discrimate among alternatives. It also takes less time than paired comparisons. Another advantage is that it is easily understood and the results are easy to communicate The major disadvantage is that it produces only ordinal level data 

Constant Sum Scaling

Where respondents allocate the sum of units, such as points, dollars, or chips among a set of alternatives according to some specified criterion.
The points are allocated to represent the importance attached to each attribute. If an attribute is unimportant, teh respondent assigns it zero points. IF an attribute is twice as important as some other attribute, teh respondent again assigns it twice as many points. All the points a respondent assigns must total 100. Hence, the name of the scale: constant sum. The main advantages of the constant sum scale are that it allows for discrimination among alternatives and does not requre too much time. Its one disadvantage is that respondents can allocate more or fewer units than those specified 

Noncomparative Scaling Techniques

Called a monadic scale because only one object is evaluated at a time
An object is not compared to another object or to some specified ideal, such as "the perfect brand." Respondents using a noncomparative scale apply their own rating standard 

Classification of Noncomparative Rating Scale

1. Continuous Rating Scales
2. Itemized Rating Scales Semantic Differential Stapel Likert 

Continuous Rating Scale Summary

Basic Characteristics: Place a mark on a continuous line
Ex.: Reaction to TV commercial Advantages: easy to construct Disadvantages: scoring can be cumbersome unless computerized 

Continuous Rating Scale

Allows the respondent to place a mark at any point along a line running between two extreme points rather than selecting from among a set of predetermined response categories
The scale points might be brief descriptions or numbers Continuous rating scales are sometimes referred to as graphic rating scales Because the distance between categories is constant and the zero point is arbitrary, this type of scale would produce interval data. Thus, this scale possesses the characteristics of description, order and distance 

Advantages and Disadvantages of a Continuous Rating Scale

Continuous scales are easy to construct
However, scoring themcan be difficult and unreliable unless they are presented on a computer screen or using computerized equipment Continuous rating scales can be easily implemented on the internet 

Itemized Rating Scales

Has a number of brief descriptions associated with each response category. The categories are typically arranged insome logical order, and the respondents are required to select the categories that best describe their reactions to whatever is being rated.
Itemized rating scales are the most widely used scales in marketing; the most commonly used are the likert, semantic differntial, and stapel scales Here, the data are treated as interval because the origin is arbitrary 

Likert Scale Summary

Basic Characteristics: degree of agreement on a 1 (strongly disagree) to 5 (strongly agree) scale
Ex. Measurement of attitudes Advantages: Easy to constuct, administer and understand Disadvantages: More timeconsuming 

Likert Scale

A measurement scale with five response categories ranging from strongly disagree to strongly agree, which requires the respondents to indicate a degree of agreement or disagreement with each of a series of statements related to the stimulus object


Advantages and Disadvantages of the Likert Scale

It is easy for the researcher to construct and administer, and it is easy for the respondent to understand. Therefore, it is suitable for mail, telephone, personal or electronic interviews.
The major disadvantage is that it takes longer to complete than other itemized rating scales. Respondents have to read the entire statement rather than a short phrase. Sometimes, it might be difficult to interpret the response to a Likert item, especially if it is an unfavorable statement 

Semantic Differential Scale Summary

Basic Characteristic: Seven point scale with bipolar labels
Ex. Brand, product and company images Advantages: Versatile Disadvantages: Difficult to construct appropriate bipolar adjectives 

Semantic Differential Scales

A sevenpoint rating scale with end points associated with bipolar labels that have semantic meaning
When using a semantic differential, a respondent is typically asked to rate a brand, store or some other object in terms of these bipolar adjectives, such as "cold" and "warm." To encourage careful consideration of each question, the negative adjective or phrase sometimes appears on the left side of the scale and sometimes on the right. This helps to control the tendency of some respondents, particularly those with very positive or negative attitudes, to mark the right or lefthand sides without reading the labels 

Advantages and Disadvantages of the Semantic Differential Scale

The semantic differential is a highly popular scale in marketing research because of its versatility. It is used to compare brand, product and company images to develop advertising and promotion strategies, and in new product development studies.
The major disadvantage is the difficulty in determining the appropriate bipolar adjectives to construct the scale. 

Stapel Scale Summary

Basic Characteristics: Unipolar 10point scale, 5 to +5, without a neutral point (zero)
Ex. Measurement of attitudes and images Advantages: Easy to construct and administered over telephone Disadvantages: Confusing and difficult to apply 

Stapel Scale

A scale for measuring attitudes that consists of a single adjective in the middle of an evennumbered range of values
The respondent is not allowed a neutral response, because no zero point is offered. Instead, respondents are asekd to indicate how accurately or inaccurately each term describes the object by selecting the appropriate number. The higher the number, the more accurately teh adjective describes the object. 

Advantages and Disadvantages of the Stapel Scale

Using only one adjective in teh Stapel scale has an advantage over semantic differentials, in that no pretest is needed to assure that the adjectives chosen are indeed opposites. The simplicity of hte scale also lends itself to telephone interviewing.
Some researchers believe the Staple scale to be confusing and difficult to apply 

6 Noncomparative Itemized Rating Scale Decisions

1. Number of Scale Categories
2. Balanced vs. Unbalanced 3. Odd vs. Even Number of Categories 4. Forced vs. Nonforced 5. Verbal Description 6. Physical Form 

Guidelines for the Number of Scale Categories

While there i sno single optimal number, traditional guidelines suggest there should be between five and nine categories


Guidelines for Balanced vs. Unbalanced

In general, the scale should be balanced to obtain objective data


Guidelines for Odd vs. Even Number of Categories

If a neutral or indifferent scale response is possible for at least some of the respondents, an odd number of categoreis should be used


Guidelines for Forced vs. Nonforced

In situations where the respondents are expected ot have no opinon, th accuracy of data may be imporved by a nonforced scale


Guidelines for Verbal Descriptions

An argument can be made for labeling all or many scale categoires. The ategory descriptions should be located as close to the response categories as possible


Guidelines for Physical Forms

A number of options should be tried and the best one selected


Number of Scale Categories

From teh researcher's perspective, the larger the number of categoreis contained ina scale, the finer the discrimination between the brands, alternatives, or other objects under study. The sensitivity of a sclae is the ability to detect subtle differences inthe attitudeor the characteristic being measure. Increasign the number of scael categoires increases sensitivity. The largerthe number of categories, however, the greatert he informationprocessing demands imposed ont eh respondents. Thus, the desire for more informatino must be balanced against the demand of the responddents.


Balanced vs. Unbalanced Scales

In a banalcned scale, the number of favorable nad unfavorable categories or scale points is equal. In an unbalanced scale, they are unequal.
Generally, balanced scales are desirable, ensuring the data collected are objective. IF the researcher sspects that the responses are likely to skew either negatively or positively, an unbalanced scale might be appropriate. Many researchers prefer to use an unbalanced scale with a larger number of satisfied categoires and fewer unsatisfied categoires when measuring customer satisfaction. When unbalanced scales are used, the nature and degree of unbalance in the scale hsould be taken into accoutn in data analysis. 

Odd or Even Numbers of Categories

When an oddnumber of categories are used in a scale, the midpoint typically representas a neutral category. The decision to use a neutral category and its labeling ahs a significant influence on teh response. The Likert scale is an example of a balanced rating scale wiht an odd number of cateogires and a neutral point.


Forced or Nonforced Choice

In a forced rating scale, the respondents are forced or required to express an opinion, because a "no opinion" option is not provided. When forced rating scales are applied to situation where a significant portion of the response population hold no opinion, the respondetns will tend to select an option at the midpoint of the scale. Marking a middle position when, in fact, "no opinion" is the desired response wil distort measures of central tendency and variance. In situations where the respondents holds no opinion rather than simply being reluctant to disclose that opinion, a nonforced scale that includes a "no opinion" cateogry can imporve the accuracy of data.


Nature and Degree of Verbal Description

Teh way a scale category is descirbed can have a considerable effect on teh response. Scale categories can have verbal, numerical or even pictorial descriptions. They might be provided for each category or only at the end points of the scale. Surprisingly, providing a verbal description for each category may not improve the accuracy or reliability of the data. Yet, an argument can be made for labeling all or many scale categories to reduce scale ambiguity.


Physcial Form or Configuration

The way a scale is presented can vary quite dramatically. Scales can be presented vertically or horizontally. Categories can be expressed by boxes, discrete liines, or units on a continuum and might or might not hvae numbers assigned to them. If numerical values are used they may be positive, negative or both.


MultiItem Scale

A scale consisting of multiple items where an item is a singel quesiton or statement to be evaluated. The Likert, semantic differential, and Stapel scales are all examples of multiitem scales.


Steps to Developing a MultiItem Scale

1. Develop the Construct
2. Develop a Theoretical Definition 3. Develop an Operational Definition 4. Develop a MultiItem Scale Generate a pool of scale items Reduce the pool of items based on judgment Collect data Purify the scale based on statistical analysis 5. Evaluate Scale Reliability and Validity 6. Apply the Scale and Accumulate Research Findings 

Scale Evaluation

A multiitem scale shold be evaluated for reliability and validity
To understand these concepts, it is useful to think of total measurement error as the sum of systematic error and random error. **Total Measurement Error= Systematic Error + Random Error 

Systematic Error

Affects the measurement in a constant way and represents stable factors that affect the observed score in the same way each time the measurement is made


Random Error

Measurement error that arises from random changes that have a different effect each time the measurement is made


Reliability

Refers to the extent to which a scale produces consistent results if repeated meaurements are made. Therefore, reliability can be defined as the extent to which measures are free from random error.


TestRetest Reliability

An approach for assessing reliability in which respondents are administered identical sets of scale items at two different times under as nearly equivalent conditions as possible


AlternativeForms Reliability

An approach for assessing reliability, which requires two equivalent forms of the scale to be constructed, adn then measures the same respondents at two different times using the alternate forms.


InternalConsistency Reliability

An approach used ot assess the reliability of a summated scale and refers to he consistency with which each item represents the constrcut of interest.


SplitHalf Reliability

A form of internal consistency reliability in which the items constituting the scale are divided into two halves, adn the resulting half scores are correlated.


Coefficient Alpha

A measure of internalconsistency reliability that is the average of all possible splithalf coefficients resulting form different splittings of the scale items.


Validity

The extent to which differences in observed scale scores reflect true differences in what is being measured, rather than systematic or random error.
A scale with perfect validity would contain no measurement error; that is, no systematic error and no random error. Researchers can assess validity in different ways: content validity, criterion validity, or construct validity. 

Content Validity

Involves a systematic but subjective assessment of how well a scale measures the construct or variable of interest.
For a scale to be content valid, it must address all dimensions of the construct. This is a commonsense evaluation of the scale. Content validity alone is not a sufficient meausre of the validity of a scale. It must be supplemented with a more formal evaluation of the scale's validty, namely criterion validity and construct validity. 

Criterion Validity

Reflects whether a scale performs as expected given other variables considered relevant to the construct. These variables are called criterion variables. They may include demographic and psychographic characteristics, attitudinal and behavioral measures, or scores obtained from other scales.


Construct Validity

Adresses the question of what construct or characterisitcs the scale is, infact measuring.
In order to assess constrcut validity, teh researcher msut have a strong understanding ofthe theory that provided the basis for constructing the scale. The researcher uses thoery to explain why the scale works and what deductions can be drawn from it. Construct validity includes convergent, discriminant, and nomological validity. 

Convergent, Discriminant and Nomological Validity

Convergent: The extent to which the scale correlates positively with other meausres of the same construct.
Discriminant: the extent to which a measure does not correlate wiht other constrcuts from which it is supposed to differ. Nomological: the extent to which the scale correlates in theoretically predicted ways with measures of different, but related, constructs. 

Relationship between Reliability and Validity

If a measure is perfectly valid, it also is perfectly reliable. In this case, neither systematic nor random error is present. Thus perfect validity implies perfect reliability.
If a measure is unreliable, it cannot be perfectly valid, because at a minimum, random error is present. Furthermore, systematic error might also be present. Thus unreliability implies invalidity. If a measure is perfectly reliable, it might or might not be perfectly valid, because systematic error might still be present. **Reliability is a necessary, but not a sufficient condition for validity. 

Questionnaire Design

A questionnaire is a formalized set of quesitons for obtaining information from respondents. It has three specific objectives:
1. The overriding objective is to translate the researcher's information needs into a set of specific questions that respondents are willing and able to answer. 2. A questionnaire should be written to minimize demands imposed on respondents. It should encourage them to participate in the entire interview, without biasing their responses. 3. A questionnaire should minimize response error. These errors can arise form respondents who give inaccurate answers or form researchers incorrectly recording or analyzing their answers. 

Questionnaire Design Process

1. Specify the information needed
2. Specifiy the type of interviewing method 3. Determine the content of individual questions 4. Design the questions to overcome the respondent's inability and unwillingness to answer 5. Decid on teh question structure 6. Determine the question wording 7. Arrange the questions in proper order 8. Choose the form and layout 9. Reproduce the questionnaire 10. Pretest the questionnaire 

1. Specify the Information Needed

The first step in questionnaire design is to specify the information needed. A continual review of the earlier stages of the research project particularly the specific components of the problem, the research questions, adn the hypotheses will help keep the questionnaire focused.


2. Specify the Type of Interviewing Method

Another important consideration in questionnaire design relates to how the data will be collected. An understanding of the various methods of conducting interviews provides quidance for questionnaire design.
Any type of intervieweradministered questionnaire should be written in a conversational style. The type of interviewing method also influences the content of individual questions. 

3. Determine the Content of Individual Questions

Once the information needed is specified adn the type of interviewing method is decided, the next step is to determine question content. First ask yourself, "Is the question necessary?" Then ask, "Are several questions needed instead of one?"
Before including a quesiton, teh researcher should ask, "How will I use these data?" Questions that might be nice to know, but that do not directly address the research problem should be eliminated. At times, certain questions can also be repeated for the purpose of assessing reliability and validity. 

DoubleBarreled Question

A single question that attempts to cover two issues. Such questions can be confusing ot respondents adn can result in ambiguous responses.


4A. Design the Questions to Overcome the Respondent's Inability to Answer

Respondents might not always be able to answer the questions posed to them. Researchers can help them overcome this limitation by keeping in mind the reasons people typically cannot answer a question: they might not be informed; they might not remember; or they might be unable to articulate certain types of responses


Is the Respondent Informed?

When teh research topic requires specialized experience or knowledge, filter questions that measure familiarity, product use, and past experience should be asked before questions about the topics themselves. Filter queistons enable the researcher to eliminate from the analysis those respondent's who are not adequately informed.
In addition, to filter questions, a "don't know" option to a question is helpful. This option has been found to reduce the number of uninformed responses wihtout reducing the overall response rate. 

Can the Respondent Remember?

People tend to remember events that are personally relevant or unusual or that occur frequently. The more recent the event occurred, the more readily an event will be recalled.
Questions can be designed to aid recall or they can be unaided, depending on teh research objectives. Unaided Ex.: "What brands of soft drinks do you remember being advertised on TV last night?" Aided Ex.: "Which of these brands were advertised on TV last night?" 

Can the Respondent Articulate?

When asked to provide answers that are difficult to articulate, respondents are likely to ignore that question and might refuse to complete the questionnaire.
Visual aids in the form of pictures, diagrams, or maps, as well as verbal descriptions, can help respondents to articulate responses. 

4B. Design the Questionnaire to Overcome the Respondent's Unwillingness to Answer

Even if respondents are able to answer a particular question, they might be unwiling to do so. Respondents might refuse to answer a question due to a variety of circumstances. The respondent might feel simply too much effort is involved, that the question serves no legitimate purpose, or that the information requested is too sensitive.


Effort Required of the Respondent

Although most individuals are willing to participate in a survey, this sense of cooperation might vanish if the questions require too much effort to answer.
The effort required of respondents can be reduced by asking easy quesitons for which the respondents merely have to check one of the response options. 

Legitimate Purpose

Respondents also object to questions that do no seem to serve a legitimate purpose.
A statement such as, "To determine how the consumption of cereal and preferences for cereal brand vary among people of different ages, incomes, and occupations, we need information on..." can make the request for information seem legitimate. 

Sensitive Information

It can be difficult to obtain information of a personal or highly sensitive nature from respondents.
To increase the likelihood of obtaining sensitive informaiton, such topics should be placed at the end of the questionnaire. By then, rapport has been created adn legitimacy of the project established, making respondents more willing to give information. 

5. Decide on the Question Structure

A question can be unstructured or structured.
Unstructured questions are openended questions that respondents answer in their own words. They are also referred to as freeresponse or freeanswer questions. Structured questions specify the set of responses as well as their format. A structured question might offer multiple choices, only two choices (dichotomous questions) or a scale. 

Advantages and Disadvantages of Unstructured Questions Summary

*Advantages:
good as first questions responses are less biased can provide rich insights *Disadvantages: potential for interviewer bias coding is costly and timeconsuming greater weight to articulate respondents unsuitable for selfadministered questions 

Advantages of Unstructured Questions

Openended quesiotns are good as first questions on a topic. THey enable the respondents to express general attitudes and opinion that can help the researcher interpret their responses to structured questions. Openended questions allow respondents to express their attitudes or opinion without the bias association with restricting responses to predefined alternatives. THsu, they can be useful in identifying underlying motivations, beliefs, adn attitudes.


Disadvantages of Unstructured Questions

The disadvantages of unstructured questions relate to recording error, data coding and the added complexity of analysis. Categorizing the recorded comments to openended questions introduces the second source of bias and another major disadvantage. Unstructured questions also are of limited value in selfadministered questionnaires (mail, CAPI, or electronic), because respondents tend to be more brief in writing than in speaking.


Unstructured Questions Summary

In general, openended questions are useful in exploratory research and as opening questions. However, in a large survey, the complexity of recording, tabulation, and analysis outweighs their advantages.


Advantages and Disadvantages of Multiple Choice Questions Summary

*Advantages:
interviewer bias is reduced easy to code and analyze improved respondent cooperation *Disadvantages: order or position bias difficult to design response options 

MultipleChoice Questions

In multiplechoice questions, the researcher provides a choice of answers, and respondents are asked ot select one or more of the alternatives given.
Two additional concerns in designing multiplechoice questions are the number of alternatives that should be included and order or position bias. 

Disadvantages of MultipleChoice Questions

Multiplechoice questions should include choices that cover the full range of possible alternatives. The alternatives hsould be mutually exclusive and collectively exhaustive. An "other (please specify)" category should be included where appropriate.
Order or position bias is the respondent's tendency to check and alternative merely because it occupies a certain position in a list. Alternatives that appear at the beginning and , to a lesser degree, at the end of a list have a tendency to be slected most often. When questions relate to numeric values (quantities or prices), there is a tendency to select the central value on the list. 

Advantages of MultipleChoice Questions

Multiplechoice questions are easier for respondents to answer. They also are easier to analyze and tabulate than openended quetions. Interviewer bias also is reduced, given that these types of questions work very well in selfadministered conditions.


Advantages and Disadvantages of Dichotomous Questions Summary

*Advantages:
interviewer bias is reduced easy to code and analyze improved respondent cooperation *Disadvantages: Wording can bias responses 

Dichotomous Questions

A dichotomous question has only two response alternatives: yes or no, agree or disagree, and so forth. Sometimes, multiplechoice questions can be dichotomous.
Dichotomous questions have many of hte same strenghts and weaknesses of multiplechoice questions. They have one serious flaw, however. The direction of question wording can have a significant effect on the responses given. To overcome this directional bias, the question should be framed in one direction on onehalf of the questionnaires and in the opposite direciton on the other half. This is referred to as the splitballot technique. 

Disadvantages and Advantages of Scales Summary

*Advantages:
interviewer bias is reduced easy to code and analyze improved respondent cooperation *Disadvantages: difficult to design multiitem scales 

Scales

Questions making use of scales are easy to answer, and therefore, are popular.


6. Determine the Question Wording

Translating the informaiton needed into clearly worded quesiotns that are easily understood is the most difficult aspect of questionnaire development. Poorly worded questions can confuse or mislead respondents, leading to nonresponse or response error. Poorly worded questions can also frustrate the respondents to teh point that they refuse to answer those questionsor items. This is referred to as item nonresponse and leads to nonresponse error. If respondents interpret questions differently than intended by the researcher, serious bias can occur, leading to response error.
To avoid problems in question wording, consider the following five guidelines: define the issue, use ordinary words, avoid ambiguous words, avoid leading questions, and use positive and negative statements. 

Define the Issue

Questions should always clearly define the issue being addressed. These particularly who, wha, when and where can also serve as guidelines for defining the issue in a question.


Use Simple Words

Simple, ordinary words that match the vocabulary level of the respondent should be used in a questionnaire.
When choosing words, keep in mind that the average person in teh U.S. has a high school, not a college education. Simplicity in wording and a conscious effor tto avoid technical jargon should guide questionnaire development. 

Use Unambiguous Words

When selecting words for a questionnaire, the questionnaire designer should choose words with only one meaning. This is not an easy task given that a number of words that appear unambiguous can have different meanings to different people. these include usually, normally, frequently, often, regularly, occasionally, and sometimes.


Avoid Leading or Biasing Questions

A leading question is one that clues the respondent to what the answer should be.
Some respondents have a tendency to agree with whatever way the question is leading them to answer. This tendency is known as yeasaying and results in a bias called acquiescence bias. 

Balance Dual Statements

Many questions, particularly those measuring attitudes and lifestyles, are worded as statements to which respondents indicate their degree of agreement or disagreement using Likert scales. The statements in these types of questions can be worded either positively or negatively. Evidence shows that the responses obtained often depend on the direction of the wording of the questions: that is, whether they are stated positively or negatively.
Two different questionnaires that reverse the direction of the questions could also be used to control for any bias introduced by the positive or negative nature of the statements. 

7. Arrange the Questions in Proper Order

When arranging questions in a proper order, the researcher should consider the opening questions, the type of information sought, question difficulty, adn the effect on subsequent questions.
Questions should be arranged in a logical order, organized around topic ideas. 

Opening Questions

Opening questions set the stage for the remainder of the questionnaire.
They can introduce the topic, attempt to gain the confidence and cooperation of respondents, or establish the legitimacy of the study. The openign quesitons should be interesting, simple and nonthreatening. Questions that ask respondents for their opinions are always good openers, because most people like to express their opinions. 

Types of Information

Three types of information are obtained from a questionnaire:
1. Basic Information: information that relates directly to the marketing research problem. 2. Classification Information: scoioeconomic and demographic characteristics used to classify respondents. 3. Identification Number: a type of informaiton obtained in a questionnaire that includes name, postal address, email address, and phone number. 

Question Difficulty

Respondents can perceive questions as difficult for a variety of reasons. They might relate to sensitive issues or be embarrassing, complex, or dull.
Questions that could be perceived as difficult should be placed late in the sequence, after a relationsihip has been established and the respondent is involved in teh process. 

Effect on Subsequent Questions

Initial questions can influence questions asked later in a questionnaire. As a rule, a series of questions should start with a general introduction to a topic, followed by specific questions related to teh topic. THis prevents specific quesitons from biasing response to the general problem.
Going from general to specific is called the funnel approach, becuase it beign with broader (more general) questions adn tehn asks narrower (more specific) questions, reflecting the shape of a funnel. Although the funnel appraoch is more commonly used, sometimes an inverted funnel approach is used when teh respondents do not ahve clearly formulated views about a topic or when they lack a common frame of reference in responding to general questions on the topic. 

Logical Order

Quesitns should be aske din a logical order, organized around topic areas.
When switching topics, brief transitional phrases or sentences should be used to help respondents switch their train of thought. Branching questions direct respondetns or interviewers to different places in the questionnaire based ontehir response to eh question at hand. Branches enable respondents to skip irrelevant questions or elaborate in areas of specific interest. 

8. Choose the Form and Layout

The physical characteristics of a questionnaire, such as the format, spacing, and positioning can have a significant effect on the results. This is particularly true for selfadministered questions.
Dividng a questionnaire into sections with separate topic areas for each section is a good practice. The questions in each part should be numbered, particularly when branching question are used. Preferably, the questionnaires should be precoded. In precoding, a code should be assigned to every conceivable response before data collection. 

9. Reproduce the Questionnaire

The quality of the paper and print process used for the questionnaire also influences response. For example, if the questionnaire is reproduced on poorquality paper or is otherwise shabby in appearance, the respondetns might conclude that he project is unimportant, and this perception will be reflected in the quality of the responses. Therefore, the questionnaire shoudl be reproduced on goodquality paper and have a professional appearance. Multipage questionnaires should be presented in booklet form rather than simply stapled or clipped.


Reproducing the Questionnnaire Continued

The tendency to crowd questions together to make the questionnaire look shorter should be avoided. Overcrowding leave little space for responses, which results in shorter answers. It also increases errors in data tabulation. In addition, crowded questionnaires appear more complex, resulting in lower cooperation and completion rates.


10. Pretest the Questionnaire

Pretesting refers to testing the questionnaire on a small sample of respondents, usually 15 to 30, to identify and eliminate potential problems.
All aspects of the questionnaire, including question content, wording, sequence, form and layout, quesitn difficulty, and instrcutions should be tested. Additionally, pretesing should be conducted with a subset of the respondent group. The pretest groups hsould be similar to the survey respondents in terms of their backgournd characteristics, familiarity with the topic, and attitudes and behaviors of interest. 

Pretesting Continued

After the necessary changes have bene made, another pretest could be admionistered using the actual data colleciton appraoch, if it is mail, telephone, or electronic. This stage of the pretest will reveal any potential probelms int eh interviewign method to be used in the actual survey.
Pretesting should be continued unitl no further changes are needed. As a final step, the responses obtained during the pretest shoudl be coded and analyzed. The analysis of pretest responses can serve as a check on the adequacy of the problem definition, and provdie insight into the nature of the data as well as analytic techniques. 

Sample or Census

In sampling, an element is the object (or person) about which or from which the information is desired. In survey research, the element is usually the respondent.
A population is the total of all the elements that share some comon set of characteristics. Each marketing research project has a uniquely defined population that is described in terms of its parameters. The objective of most marketing research projects is to obtain information about the characteristics or parameters of a population. 

Sample vs. Census

A census involves a complete count of each element in a population.
A sample is a subgroup of the population. 

Samples

Budget= small
Time available= short Population size= large Variance in teh characterisitc= small Cost of sampling error= low Cost of nonsampling errors= high Nature of measurement= destructive Attention ot individual cases= yes 

Census

Budget= large
Time available= long Population size= small Variance in teh characterisitc= large Cost of sampling error= high Cost of nonsampling errors= low Nature of measurement= nondestructive Attention ot individual cases= no 

The Sampling Design Process

1. Define the Population
2. Determine the Sampling Frame 3. Select Sampling Technique(s) 4. Determine the Sample Size 5. Execute the Sampling Process 

1. Define the Population

Sampling design begins by specifying the targe population. The target population is the collection of elements or objects that possess the information the researcher is seeking. It is essentail that hte resercher preisely define the target population if the data generated are to address the marketing research problem.
The target population should be defined in terms of elements, sampling units, extent, and time frame. As stated earlier, the element is the object (or person) about which or from which the information is desired. A sampling unit might be the element itself or it might be a more readily available entity containing the element. 

2. Determine the Sampling Frame

A sampling frame is a representation of the elements of hte target population. It consists of a list or set of directions for identifying the target population. A sampling frame can come from the telephone book, a computer program for generating telephone numbers, an association directory listing the firms in an industry, a mialing list purchased form a commercial orgnaization, a city directory, or a map.


3. Select a Sampling Technique

Selecting a sampling tehcnique involves choosing nonprobability or probability sampling.
Nonprobability sampling relies on teh personal judgement of the researcher, rather than chance in selecting sample elements. THe researcher might select the sample arbitrarily based on convenience or make a conscious decision about which elements ot include int eh sample. Examples of nonprobability sampling include interviewing people at street corners, in retail stores, or in malls. In probability sampling, elements are selected by chance, that is, randomly. The probability of selecting each potential sample from a population can be prespecified. Although every potential sample need not have the same probability of selection, ti is possible to specify the probability of selecting a particular sample of a given size. 

4. Determine the Sample Size

Sample size refers to the number of elements to be included in the study. Determining the sample size invovles both qualitative and quantitative considerations.
As a general rule, the more important the decision, the more precise the informaoitn must be. THis implies the need for larger samples. The nature of the research also has an impact on teh sample size. Exploratory research, such as a focus group, employes qualitative techniques that are typically based on small samples. Conclusive research, such as a descriptive survey, requires large samples. As teh number of variables in a study increases, teh sample size must grow accordingly. 

5. Execute the Sampling Process

Execution of the sampling process refers to implementing the various details of the sample design. The population is defined, teh sampling frame is complied, and hte sampling units are drawn using the appropriate sampling technique needed to achieve the required sample size.


Nonprobability Sampling Techniques

1. Convenience Sampling
2. Judgmental Sampling 3. Quota Sampling 4. Snowball Sampling 

Convenience Sampling

Convenience sampling invovles obtaining a sample fo elements based on the convenience of the researcher. The selection of sampling units is left primarily to the interviewer. Respondents often are selected because they happen to be in the right place at the right time.
Convenience samples are not appropriate for descriptive or causal research wehre the aim is to draw population inferences. Convenience samples are useful, however, in exploratory research where the objective is to generate ideas, gain insight 

Advantages and Disadvantages of Convenience Sampling

Convenience sampling has advantages of being both inexpensive and fast. Additionally, the sampling usits tend to be accessible, easy to meausre, adn cooperative.
However, the resulting sample is not always representative of any definable target population. This sampling process also sufferes from selection bias, which means the individuals who participate in a convenience sample might have characteristics that are systematically different than the characterisitcs that define the target population. 

Judgmental Sampling

Judgmental sampling is a form of convenience smapling in which the population elements are selected basedon teh researcher's judgment. The researcher chooses the sampling elements because she or he believes htey represent the population of interest.


Advantages and Disadvantages of Judgmental Sampling

Judgment sampling has appeal because it is low cost, convenient and quick. It is subjective, however, relying largely on the expertise adn creativity of the researcher. Therefore, generalizations to a specific population cannot be made, usually becuase the population is not defined explicitly. This sampling technique is most appropriate in research when braod population generalizations are not required.


Quota Sampling

Quota sampling introduces two stages to the jugmental sampling process. The first stage consists of developing control categories or quotas of population elements. Using judgment to identify relevant categories such as age, sex or race, the researcher estimates the distribution of these characteristics in the target population.
Quotas are used to ensure that the composition of the sample is the same as the composition of the population with respect to the characteristics of interest. Once the quotas have been assigned, the second staage of the sampling process takes place. Elements are selected using a convenience or judgment process. Considerable freedom exists in selecting the elements to be included int eh sample. The only requirement is that the elements that are selected fir the control characteristics. 

Advantages and Disadvantages of Quota Sampling

A number of potential problems are associated with this sampling technique. Relevant characteristics might be overlooked in the quotasetting process, resulting in a smaple that does not mirror the population on relevant control characteristics. Because the elements within each quota are selected based on convenience or judgment, many sources of selection bias are potentially present. Quota sampling also is limited in that it does not permit assessment of sampling error.
Quota sampling attempts ot obtain representattive samples at a relatively low cost. Quota samples are also relatively convenient to draw. With adequate controls, quota sampling obtains results close to those for conventional probability sampling. 

Snowball Sampling

In snowball sampling, an initial group of respondents are selected usually at random. After being interviewed, these respondents are asked to identify others who belong to the target population of interest. This process is continued, resulting in a snowball effect, as one referral is obtained from another.
Although this sampling technique begins with a probability sample, it results in a nonprobability sample. This is because referred respondents tend to have demographic and psychographic characterisitcs that are more similar to the person referring them than would occur by chance. Snowball sampling is used when studying characteristics that are relatively rare or difficutl to identify in the population. 

Advantages and Disadvantages of Snowball Sampling

The major advantage of snowball sampling is that it substantially increases the likelihood of locating the desired characteristic in the population. It also results in relatively low sampling variance and costs.


Probability Sampling Techniques

1. Simple Random Sampling
2. Systematic Sampling 3. Stratified Sampling 4. Cluster Sampling 

Simple Random Sampling

In simple random sampling (SRS), each element in the population has a known and equal probability of selection. Furthermore, each possible sample of a given size *n) has a known and equal probability of being the sample actually selected. The implication in a random sampling procedure is that each element is selected independently of every other element.


Advantages and Disadvantages of Simple Random Sampling

Simple random smapling is easilty understood and produces data that are representative of a target population. Most statistical inference approaches assume that random sampling was used.
However, SRS suffers from at least four limitations: 1. Constructing a sampling frame for SRS is difficult 2. SRS can be expensive and timeconsuming because the sampling frame might be widely spread over a large geogrpahical area 3. SRS often results in lower precision, producing samples wiht large standard error 4. Samples generated by this technique might not be represnetative of the target population, particularly if the sample size is small. 

Systematic Sampling

In systematic sampling, the sample is chosen by selecting a random starting point and then picking every ith element in succession from the sampling frame. The frequency with which the elements are drawn, i, is called the sampling interval. It is determined by dividing the population size N by the sample size n adn round ing to the nearest integer.


Advantages and Disadvantages of Systematic Sampling

Systematic sampling is less costly and easier than SRS because random selection is done only once. Systematic sampling can also be applied without knowledge of the makeup of the sampling frame.


Stratified Sampling

Stratified sampling involves a twostep sampling process, producing a probability rather than a convenience or judgment sample. First, the population is divided into subgroups called strata. Every population element should be assigned to on e adn only one stratum, and no population elements should be omitted. Second, elemetns are then randomly selected from each stratum.


Stratified Sampling Continued

A major objective of stratified sampling is to increase precision witout increasing cost. The population is partitioned using stratification variables. The strata are formed based on four criteria: homogeneity, heterogeneity, relatedness, adn cost. The following guideline should be observed:
1. Elements wihtin strata must be similar or homogeneous 2. Elements between strata must differ or be heterogeneous 3. The stratification variables must be related to the characteristic of interest 4. The number of strata usually varies between two and six. Beyond six strata, any gain in precision is more than offest by the increased costs. 

Advantages and Disadvantages of Stratified Sampling

Stratification offers two advantages. Sampling variation is reduced when the research follows these listed criteriea. Sampling costs can alos be reduced when the stratification variables are selected in a way that is easy to measure and apply. Variables commonly used for stratification include demographic characteristics, type of consumer, size of firm, or type of industry. Stratified sampling improves the precision of SRS.


Cluster Sampling

In cluster smapling, the target population is first divided into mutually exclusive and collectively exhaustive subpopulations, or clusters. Then a random sample of clusters is slected based on a probability sampling technique, such as SRS. For each selected cluster, either all the elements are included int ehsample or a sample of elements is drawn probabilistically.
If all the elements in each selected cluster are inclued in the sample, teh procedure is called onestage cluster sampling. If a sample of elements is drawn probabilistically from each selected cluster, the procedure is twostage cluster sampling. Cluster sampling increases sampling effieciency by decreasing cost. One common form of cluster sampling is area sampling, which relies on clustering basedon geographic aras, such as counties, housing tracts, or blocks. 

Advantages and Disadvantages of Cluster Sampling

Cluster sampling has two major advantages: feasibility and low cost. Because sampling frames often are available in terms of clusters rather than population elements, cluster smapling might be the only feasible approach.
Lists of geographical areas, telelphone exchanges, and other clusters of consumers can be constrcuted relatively easily. Cluster sampling is the most costeffective probability sampling technique. This advantage must be weighed against several limitations. Cluster sampling produces imprecise samples in which distinct, heterogeneous clusters are difficult to form. 

Cluster Sampling Versus Stratified Sampling

*Cluster Sampling:
Only a sample of the subpopulations (clusters) is selected for sampling Within a cluster, elements should be different, whereas homogeneity or similarity is maintained between different clusters. A sampling frame is needed only for the clusters selected for the sample. Increases sample efficiency by decreasing cost *Stratified Sampling: All of the subpopulations (strata) are selected for sampling Within a strata, elements should be homogeneous with clear differences (heterogeneity) between the strata. A complete sampling frame fo the entire stratified subpopulations should be drawn Increases precision 

Frequency Distribution

In a frequency distribution, one variable is considered at a time. The objective is to obtain a count of the number of responses associated with different values of hte variable. The relative occurrence, or relative frequency, of different values of the variable is expressed in percentages.
A frequency distribution helps determine the extent of illegitimate responses. The presence of outliers, cases iwth extreme values, can also be detected. A frequency distribution also indicates the shape of the empirical distribution of the variable. 

Statistics Associated with Frequency Distribution

A frequency table is easy to read and provides baisc information, but sometimes this information might be too detailed adn the researcher must summarize it by teh use of descriptive statistics. The most commonly used statistics associated with frequencies are measures of location (mean, mode, and median) and measures of variability (range and standard deviation).


Measures of Location and of Central Tendency

The measures of location are meausres of central tendency, because they tend to describe the center of the distribution. If the entire sample is changed by adding a fixed constant to each observation, then the mean, mode, and median changes by the same fixed amount.


Mean

The mean is the AVERAGE value and is the most commonly used meausre of central tendency or center of a distribution.
It is used to estimate the average whent he data have been collected using an interval or ratio scale. 

Mode

The mode is the value that occurs MOST FREQUENTLY.
It represents the highest peak of the distribution. The mode is a good measure of location when the variable is inherently categorical or has otherwise been grouped into categories. 

Median

The median of a sample is the MIDDLE VALUE when the data are arranged in ascending or descending rank order.
If the number of data points is even, the median is usually estimated as the midpoint between the two middle values by adding the two middle values and dividing their sum by 2. The middle value is the value where 50 percent of the vluaes are greater than that value, and 50 percent are less. Thus, the median is the 50th percentile. 

The 3 Measures of Central Tendency Summary

The three values are equal only when the distribution is symmetric. In a symmetric distribution, the values are equally likely to plot on either side of the center of the distribution, adn the mean, mode, and median are equal.
If the variable is measured on a nominal scale, the mode should be used. If the variable is measured on an ordinal scale, the median is appropriate. If the variable is measured on an interval or ratio scale, the mode is a poor measure of central tendency and should not be used. When there are outliers in the data, the mean is not a good measure of central tendency, adn it is useful to consider both the mean and the median. 

Measures of Variability

The measures of variability indicate the dispersion of a distribution. The most common, which are calculated on interval or ratio data, are the range, variance, and standard deviation.


Range

The range measures the SPREAD of the data. It is simply the difference between the largest and the smalled values in the sample.
As such, the range is directly affected by outliers. 

Variance

The difference between teh mean and an observed value is called the deviation from the mean.
The variance is the mean squared deviation from the mean; that is, the average of the squareof teh deviations from teh mean for all the values. The variance can never be negative. When the data points are clustered around the mean, the variance is small. When the data points are scattered around the mean, the variance is large. 

Standard Deviation

The standard deviation is the square root of the variance. Thus, the standard deviation is expressed in teh same units as the data, whereas the variance is expressed in squared units.
The standard deviation serves the same purpose as the variance in helping us to understand how clustered or spread the distribution is around the mean value. We divide by n1 instead of n, because the sample is drawn from a population and we are trying to determine how much the responses vary from teh mean of the entire population. However, the population mean is unknown; therefore, the sample mean is used instead. 

Hypothesis Testing

Hypotheses are unproven statements or propositions of interest to the researcher. Hypotheses are declarative and can be tested statistically. Often, hypotheses are possible answers to research questions.


General Procedure for Hypothesis Testing

Step 1: Formulate the null and alternative hypotheses
Step 2: Select the appropriate test Step 3: Choose the level of significance Step 4: Collect data and calculate the test statistic Step 5: Determine probability associated wiht the test statistic OR determine the critical value of the test statistic Step 6: Compare with the level of significance OR determine if the test statistic falls into the nonrejection region Step 7: Reject or fail to reject the null hypothesis Step 8: Draw marketing research conclusion 

Step 1: Formulating the Hypothesis

A null hypothesis is a statemetn of the status quo, one of no difference or no effect. If the null hypothesis is not rejected, no changes will be made.
An alternative hypothesis is one in which some difference or effect is expected. Accepting the alternative hypothesis will lead to changes in opinions or actions. The null hypothesis is always the hypothesis that is tested. The null hypothesis refers ot a specified values of hte population parameter, not a sample statistic. A null hypothesis may be rejected, but i can never be accepted based on a single test. A onetailed test is a test of the null where the alternative is expressed directionally (x>0.4, x<0.4). A twotailed test is a test of the null where teh alternative is not expressed directionally (x=0.4, x/= 0.4). The onetailed test is more powerfrul than the twotailed test 

Step 2: Selecting an Appropriate Test

The test statistic measures how close the sample has come to the null hypothesis. The test statistic often follows a wellknown distribution, such as the normal, t, or chisquare distributions.


Step 3: Choosing Level of Significance

Whenever an inference is made about a population, there is a risk that an incorrect conclusion will be reached. Two types of error can occur.


Type I Error

Type I Error: occurs when the sample results lead to the rejection of the null hypothesis, when it is in fact true. The probability of typeI error also is called the level of significance (a), and is equal to 100 minus the confidence level.


Type II Error

Type II Error: occurs when the null hypothesis is not rejected when it is in fact false. The probability of typeII error is denoted by B. Unlike a, the magnitude of B depends on the actual value of hte population parameter. The complement (1B) of the probability of a typeII error is called the power of a statistical test.


The Power of a Test

The power of a test is the probability (1B) of rejecting the nul hypothesis when it is false and should be rejected. Although B is unknown, it is related to a. The level of a, along with the sample size, will determine the level of B for a particular research design. The risk of both a and B can be controlled by increasing the sample size.


Step 4: Data Collection

Sample size is determined after taking into accoutn the desired a and B erros, incidence and completion rates, and other qualitative considerations, such as budget constraints. Then, the required data are collected and the value of the test statistic is computed.


Step 5: Determining the Probability (Critical Value)

Using standard normal tables, the probability of obtaining a z value can be calculated. The area to the right of z is called the pvalue, which is the probability of observing a value of the test statistic as extreme as, or more extreme than, the value actually observed, assuming that the null hypothesis is true.
Note that in determining the critical value of the test statistic, theh area to teh right of the critical value is either a or a/2. It is a for a onetail test and a/2 for a twotail test. 

Steps 6 and 7: Comparing the Probability (Critical Value) and Making the Decision

If the probability associated with the calculated or observed value of the test statistic is less than teh level of significance (a), the null hypothesis is rejected.
Hwever, if the absolute value of the calculated value of the test statistic is greater than the absolute value of the critical value of the test statistic, the null hypothesis is rejected. he critical value is the value of the test statistic that divides the rejection and nonrejection regions. 

Step 8: Marketing Research Conclusion

The conclusion reached by hypothesis testing must be expressed in terms of the marketing research problem and the managerial action that should be taken.


CrossTabulation

Whereas a frequency distribtution describes one variable at a time, a crosstabulation describes two or more variable simultaneously.
Crosstabulation results in tables that reflect teh join distribution of two or more variables with a limited number of categories or distinct values. The categories of one variable are crossclassified withthe categoreis of one or more other variables. Cross tabulation tables are also called contingency tables. 

CrossTabulation Continued

Crosstabulation is widely used in commercial marketing research because:
1. crosstabulation analysis and results can be easily interpreted and understood by managers who are not statistically oriented 2. The clarity of interpretation provides a stronger link between research results and managerial action 3. Crosstabulation analysis is simple to conduct an dmore appealing to less sophisticated researchers. Crosstabulation with two variables also is known as bivariate crosstabulation. 

Statistics Associated wiht CrossTabulation

The statistical significance of the observed association is commonly measured by the chisquare statistic.
Generally, the strength of an association is of interest only if the association is statistically significant. The strength of the association can be measured by the phi correlation coefficient, the contingency coefficient, and Cramer's V. 

ChiSquare

The chisquare statistic (x2) is used to test the STATISTICAL SIGNIFICANCE of the observed association in a crosstabulation. It can be used in determining whether a systematic association exists between two variables.
An important characteristic i sthe number of degrees of freedom associatioed with it. In general the number of degrees of freedom is equal to the number of observations less the number of constraints needed ot calculate a statistical term. In the case of a chisquare statistic association wiht a crosstabulation, the number of degrees of freedom is equal to the product of number of rows (r) less one and the number of columns (c) less one. 

ChiSquare Continued

Unlike the normal distribution, the chisquare distribution is a skewed distribution, the shape of which depends solely on the number of degrees of freedom. As the number of degrees of freedom increases, the chisquare distribution becomes more symmetrical.
The chisquare statistic can also be used in goodness of fit tests to determine whether certain models fit the observed data. These tests are conduced by calculating teh significance of sample deviations from assumed theoretical (expected) distributions adn can be performed on crosstabulations as well as on frequencies (oneway tabulations). 

PhiCoefficient

The phi coefficient (phi symbol) is used as a measure of the STRENGTH of association in the special case of a TABLE WITH 2 ROWS and 2 COLUMNS (2 X 2 Table).
The phi coefficient is proportional to the square root of the chisquare statistic. It takes the value of 0 when there is no association, which would be indicated by a chisquare value of 0 as well. 

Contingency Coefficient

The contingency coefficient (C) can be used to assess the STRENGTH of a table of ANY SIZE.
The contingency coefficent varies between 0 and 1. The 0 value occurs in the case of no association, but the maximum value of 1 is never achieved. Rather, the maximum value of the contingency coefficient depends on the size of the table. 

Cramer's V

Cramer's V is a modified version of the phi correlation coefficient, and is used in TABLES LARGER THAN 2X2.
Cramer's V is obtained by adjusting phi for either the number of rows or the number of columns in teh table, based on which of the two is smaller. The adjustmetn is such that V will range from 0 to 1. A large value of V merely indicates a high degree of association. It does not indicate how the variables are associated. 

Parametric Tests

Hypothesistesting procedures that assume the variables of interest are measured on at least an interval scale.


The tTest

Parametric tests provide inferences for making statements about the means of parent populations. A ttest is commonly used for this purpose.
A tstatistic is calculated by assuming that the variable is normally distributed, the mean is known, and the population variance is estimated from the sample. 

The t Distribution

The tdistribtution is similar to the normal distributin in appearance. Both distributions are bell shaped and symmetric. However, the t distribution has more area in the tails and less in the center than the normal distribution. This is because population variance is unknonw and is estimated by the sample variance. Given the uncertaintiy in the value of the sample variance, the observed vlaues of t are more variable than those of z. Thus, we must go a larger number of standard deviations from zero to encompass a certain percentage of values from the t distribution than is the case with the normal distribution. As the number of degrees of freedom increases, however, the t distribution approaches the normal distribution.


Conducting tTests

Step 1: Formulate the null and alternative hypotheses
Step 2: Select appropriate ttest Step 3: Choose level of significance Step 4: Collect data and calculate tstatistic Step 5: Determine probability associated with tstatistic OR determine the critical value of tstatistic Step 6: Compare with level of significance OR determine if the tstatistic falls into the (non)rejection region Step 7: Reject or do not reject the null Step 8: Draw marketing research conclusion 

The zTest

A univariate hypothesis test using the standard normal distribution


Two Independent Sample tTest

Samples drawn randomly from different populations are termed independent samples.
For the purpose of analysis, data pertaining to different groups of respondents (i.e. males and females) are generally treated as independent samples even though the data may pertain to the same survey. 

Fdistribution

A frequency distribution that depends upon two sets of degrees of freedom; the degrees of freedom in the numerator and the degrees of freedom in the denominator.
If the probability of F is greater than the significance level (a), the null is not rejected and t based on teh pooled variance estimate can be used. However, if the probability of F is less than or equal to a, the null is rejected and t based ona separate variance estimate is used. 

Paired Sample tTest

In many marekting research applicantions, the observations for the two groups are not selected from independent samples. Rather, the observations relate to paired samples in that the two sets of observations relate to the same respondents.


ANOVA

A statistical technique fo examing teh differences among means for two or more populations. The null hypothesis is taht all means are equal and the alternative hypothesis is that at least one mean is not equal to another.


ANOVA Continued

In its simplest form, ANOVA must have a dependent variable that is metric (measured using an interval or ratio scale) and one or more independent variables. The independent variables must be categorical (nonmetric). The differences in independent variables would be examined by a oneway analysis of variance, which involves only one categorical variable, or a single factor that defines the different samples or groups. These groups also are called treatment conditions. Thus, the different independent samples are treated as categories of a single independent variable.


Summary of Hypothesis Testing

1. One Sample
Means: ttest, if variance is unknown; ztest if variance is known. Proportions: ztest 2. Two Independent Samples Means: twogroup ttest; Ftest for equality of variances; ztest Proportions: ztest; Chisquare test 4. Paired Samples Means: paired ttest Proportions: Chisquare test 4. More Than Two Samples Means: oneway analysis of variance Proportions: Chisquare test 