James _01_ Statistics Ch. 1

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Statistics

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the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. Is about providing a measure of confidence in any conclusion

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Data

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Information obtained; can be numerical, or nonnumerical (or, list of observed values for a variable)

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Lurking Variable

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an explanatory variable that was not considered in a study, but that affects the value of the response variable in the study

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Population

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Entire group to be studied

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Individual

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a person or object that is a member of the population

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Sample

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a subset of the population that is being studied

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Statistic

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A numerical summary of a sample that summarizes information about a sample

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Descriptive Statistics

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Describe data using tables, charts, graphs, numerical summaries

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Inferential Statistics

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(conclusion from subset applied to entire population)
Uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result.

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Parameter

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A numerical summary of a population. Ex. 95% of

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The Process of Statistics (steps)

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1) Identify the research objective
2) Collect the data needed to answer the question(s) posed in 1
3.) Describe the data
4.) Perform inference (extend to population)

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Variables

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characteristics of the individuals within the population; ex. weight, height, etc.

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Qualitative Variables

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* Allow for classification of individuals based on some attribute or characteristic.
(Classification, category)
Ex. Class divided by colors of shoes wearing; Dr. looking through files and finds what kind problems they have

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Quantitative Variable

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Provide numerical measures of individuals. The values of a quantitative variable can be added or subtracted an provide meaningful results (we can count them)

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Approach

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A way to look at and organize a problem so that it can be solved

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Discrete Variable

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a quantitative variable that either has a finite number of possible variables or a countable number of possible variables. (If you count to get the value of quantitative variable it is discrete)

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Continuous Variable

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A quantitative variable that has an infinite number of possible values that are not countable. (Infinite # of variables depending on precision of instrument, ie. speed, weight, time, volume)

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Nominal level of measurement

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(Nominal = to name) if the values of the variable name, label, or categorize. The naming scheme does not allow for the values of the variable to be arranged in a ranked or specific order.
Ex. Gender

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Ordinal level of measurement

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(Ordinal = order) if it has the properties of the nominal level of measurement, however the naming scheme allows for the values of the variable to be ranked in a specific order.
Ex. Letter grade earned in your statistics class

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Interval level of measurement

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If it has the properties or the ordinal level of measurement and the differences in the values of the variable have meaning (adding and subtracting can be performed). A value of 0 does not mean absence of quantity
Ex. Temperature

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Ratio level of measurement

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If it has the properties of the Interval level of measurement and the ratios of the values of the variable have meaning. A value of 0 means the absence of the quantity (multiplication and division can be performed)
Ex. Number of days during the past week that a college student studied

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2 Methods of Collecting Data

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1) Observational studies

2) Designed experiments

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explanatory variable; response varible

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In an research, we wish to determine how varying the amount of an _____________ ______________ affects the value of a _______________ _____________.

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Response Variable

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What we want to see that happens in a research

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Explanatory Variable

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What affects the Response variable in research

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Observational Study

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measures the value of the response variable without attempting to influence the value of either the response or explanatory variables. Ex. "do you like coke or coke zero?"

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Designed experiment

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When a researcher assigns the individual in a study to a specific group, intentionally changes the value of an explanatory variable, and then records the value of the response variable for each group

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Confounding

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occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study
(often cause is lurking variable)

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3 Types of Observational Studies

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1.) Cross-sectional Studies

2.) Case-control studies

3.) Cohort studies

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Cross-sectional studies

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These observational studies collect information about individuals at a specific point in time or over a very short period of time.

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Case-control studies

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These studies are retrospective, meaning that they require individuals to look back in time or require the researcher to look at existing records.
(Individuals with one characteristic may be matched with those who do not, is. smoking vs. non-smoking)

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Cohort studies

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First identifies a group of individuals to participate in the study (the ________ ). The __________ is then observed over a long period of time. During this period, characteristics about the individuals are recorded and some individuals will be exposed to certain factors (not intentionally) and others will not. At the end of the study the value of the response variable is recorded for the individuals.

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Prospective

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When data are collected over time (Cohort studies)

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Equation of a line:

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* y = mx + b
m = slope
x = explanatory variable
b = response (y-intercept)

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Retrospective

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they require individuals to look back in time or require the researcher to look at existing records (Case-control studies)

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Census

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a list of all individuals in a population along with certain characteristics of each individual.

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Random Sampling

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Process of using chance to select individuals from a population to be included in the sample. Or use random number generator - in doing this we must set the SEED: initial point for generator to start creating random #'s

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Simple Random Sampling

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When a sample size from a population is obtained and every possible sample has an equally likely chance of occurring

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N =

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Letter in equation to represent population size

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n =

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Letter in equation to represent sample size of population

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a Frame

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A list of all the individuals within the population

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Random number table

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computer generated; rows on left - columns on top
Remember when reading: read two numbers or more including between the gap!

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Stratified Sample

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Obtained by separating the population into non-overlapping groups called strata = groups; (ex. rep, dem, ind) and then obtaining a simple random sample from each stratum; individuals in each strata should be homogeneous (or similar) in some way

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* - Cain's Fav!

Systematic Sampling

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* - Cains Fav!
Obtained by selecting every kth individual from the population. Ex. grocery store manager wants to survey Wed's customers

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Steps in Systematic Sampling

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1) Population size (N) needed
2) Sample size (n) needed
3.) Compute N/n = # (round down) Ex. 523/40 = 13.075 = 13 ( this number is k)
4.) Select number between 1-k(13)- call this # p (say 5)
5.) Sample consists of: 1st person 5, next 18, etc;
p, p+k, p+2k..., p+(n-1)k; last part of equation gives you last person (total - first person)

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Cluster Sample

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Obtained by selecting all individuals with a randomly selected collection or group of individuals; (get cluster and check all individuals in cluster) (you can have a cluster in a cluster as well)

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Convenience Sampling

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A sample in which the individuals are easily obtained and not based on randomness.

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Self-selected

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In convenience sampling - individuals themselves decide to participate in survey
AKA (Voluntary response)

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Multistage Sampling

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Most large-scale surveys obtain samples using a combination the techniques; an ex. of this is the Nielsen ratings - use Census data then divide country into geographical divisions (strata) then study individuals

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Bias

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If the results of the sample are not representative of the population, then the sample has a _______

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Bias in Sampling ; 3 Types

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(To question in own mind statistics you are given)
1.) Sampling Bias
2.) Non-Response Bias
3.) Response Bias

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Sampling Bias

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Means that the technique used to obtain the sample's individuals tends to favor one part of the population over the other; also results in UNDERCOVERAGE, which occurs when the proportion of one segment of pop is lower in a sample than it is in the population

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Nonresponse Bias

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___________________ _______ exists when individuals selected to be in the sample who do not respond to the survey have different opinions from those who do.

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Response Bias

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(Calling into radio/tv show; polls online - individuals who respond have their own opinions)
Exists when the answers on a survey do not reflect the true feelings of the respondent.

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Open Question

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allows the respondent to choose his or her response (not from a list)

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Closed Question

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Requires the respondent to choose from a list of predetermined responses

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Nonsampling errors

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result from undercoverage, nonresponse bias, response bias, or data-entry error. Such errors could also be present in a complete census of the population

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Sampling error

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results from using a sample to estimate information about a population. This type of error occurs because a sample gives incomplete information about a population.

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Experiment

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a controlled study determining affect of varying one or more explanatory variables or factors (x on # line) has on a response variable. Any combination of the values of the factors is called a TREATMENT

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Experimental unit

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In an experiment, this is the person, object, or some other well defined item upon which a treatment is applied

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Subject

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We often refer to the experimental unit as a __________ when he or she is a person.

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Control Group

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Serves as a baseline treatment that can be used to compare to the other treatments.

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Placebo

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An innocuous (not harmful) medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication.

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Blinding ; 2 types of Blinding

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Refers to nondisclosure of the treatment an experimental unit is receiving.
2 types:
1.) Single blinding
2.) Double blinding

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Single blinding

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In experiments, when the experimental unit (or subject) does not know which treatment he or she is receiving.

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Double blinding

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In experiments, when neither the experimental unit (or subject) nor the researcher in contact with the experimental unit knows which treatment the experimental unit is receiving

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Design

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To __________ an experiment means to describe the overall plan in conducting the experiment.

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Steps for Conducting an Experiment

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1.) Identify the problem to be solved
2.) Determine the factors that affect the response variable
3.) Determine the number of experimental units
4.) Determine the level of each factor
5.) Conduct the Experiment
6.) Test the Claim

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Completely Randomized Design

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One in which each experimental unit is randomly assigned to treatment.

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Matched-pairs design

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An experimental design in which the experimental units are paired up. The pairs are selected so that they are related in some way (same person before and after treatment). Ie, 2 females, twins, husband & wife, same geographical location, etc.