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Statistics

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is the science of conducting studies to collect,organize, summarize, analyze, and draw conclusions from data.

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Sample

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Consist of few or more members of the populations.

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Parameters

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Measures of the population

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Uses of Statistics

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a. Statistics can give a precise description of data.

b.Statistics can predict the outcome of experiment or the behavior of an individual.

c.Statistics can be used to test a hypothesis

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Descriptive statistics

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concerned with collecting, organizing, presenting, and analyzing numerical data.

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Inferential statistics

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analyze the organized data leading to prediction or inferences.Here it implies that before carrying out an inference, appropriate and correct descriptive measures or methods are employed to bring out good results.

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Descriptive Statistics Examples

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a.According to the Census Bureau, 20% of all Filipino workers get to work via carpool. b. According to the Court Administration of the Philippines, 14% of trial-ready civil actions and equity cases in Metro Manila during 1993 were decided in less than six months.

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Inferential statistics examples

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a.The National Eye Institute has halted a clinical trial on a type of eye surgery, calling it ineffective and possibly harmful to a person’s vision.

b.Drinking decaffeinated coffee can raise cholesterol levels by 7%.

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Population

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refers to the groups or aggregates of people, objects, materials, events, or things of any form. This is the totality of all the samples.

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“estimates”or“statistics.”

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Measures of the samples

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interviewing people, observing or inspecting items, using questionnaires and checklists.

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Statistical data or information can be gathered through

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variable

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The characteristic that is being studied•is a characteristic that takes two or more values which varies across individuals.

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qualitative or quantitative

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Variables can be

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discrete or continuous

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Quantitative variables are further classified as

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dependent or independent

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variable can be

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independent variable

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To predict the value of variable on the other ; is the predictor

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dependent variable

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variable whose value is being predicted.

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set of data

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•collection of values for a particular variable.

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data

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Observing the values of a variable yields

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qualitative,quantitative, discrete, and continuous

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used to describe data

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measurement.

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Assigning a numerical value to a variable is a process called

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scale or level of measurement

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•relates to the rules used to assign scores and is an indicator of the kind of information that the scores provide.

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Nominal data

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use numbers for the purpose of identifying name or membership in a group or category. ;observations can be classified and counted without particular order or ranking imposed on the data.

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nominal scale

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All qualitative variables are measured on

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Ordinal data

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connote ranking or inequalities

One category is higher than the other one. In this type of data, numbers represents“greater than” or “less than” measurements, such as preferences or rankings.

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Interval scales

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indicate an actual amount and there is equal unit of measurement separating each score, specifically equal intervals.

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Ratio data

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are similar to interval data, but has an absolute zero and multiples are meaningful.;include all the usual measurements of length,height, weight, area, volume, density, velocity, money, and duration. These are the highest level of measurement.

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Summation

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denoted by , is defined as where 1 and n are called the lower and upper limits respectively.

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primary data

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refer to facts and figures coming directly from an original source and based on first-hand experiences.

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secondary data

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1.come from published or unpublished materials previously collected by other investigators.

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Survey method

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1.is a manner of collecting data by asking the participants questions either through interview or questionnaire.

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Questionnaire

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a.is the most widely used technique for obtaining information. This is a list of questions which intend to answer the problem being investigated.

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Interview

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a.involves direct interaction or person-to-person exchange of views between the interviewee and interviewer.

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Experimental method

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1.is usually being applied to situations which are planned and controlled. Examples are data collection from an experiment done in laboratories and green houses.

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Observation method

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3.allows the possibility of recording the behavior of the participants on the time of conduct.

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Existing records or hard data

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3.are data sourced from reports,published and unpublished manuscripts from various organizations. Examples are annual reports and student's transcript of records.

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Registration method

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5.is being used to gather data enforced by certain laws. Examples are registration of birth, death or other licenses.

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Sampling

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is the act of studying only a segment or subset of the population representing the whole.

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target population

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•is the group from which representative information is desired and to which inferences will be made.

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Sampling population

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is the population from where the samples are actually taken

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sampling frame

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•the list of units or members of the sampling population.

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sampling unit

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•each member of the sampling population

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•objective of the study, nature of the variables to be collected, the population understudy and the availability of the relevant information.

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choice of sampling design depends upon

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probability and non-probability sampling designs:

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Sampling design is categorized into

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Probability sampling

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1.is the process where each unit in the population has a known nonzero probability of being included in the sample. This probability is used not only in sample selection but also in estimation. The concept of randomness eliminates the bias in drawing samples.

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Simple Random Sample

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•This is the process of selecting a sample by giving each sampling unit an equal chance of being drawn as sample. This may be done by assigning a number to each sampling unit, like 1 to N, and selecting n (sample size) samples using the table of random numbers.

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Systematic Sampling (with a random start)

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b.This is a variation of random sampling. This may be applied even when a sampling frame is not available or there are too numerous sampling units.

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Stratified Random Sampling

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c. This is a method of selecting simple random sample from each of the sub-population (Strata) into which the population has been divided.

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Cluster sampling

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is a method of selecting a sample of distinct groups,or clusters, of smaller units called elements. The sample clusters may be chosen by random sampling or systematic sampling with random start.Cluster sampling is being used when a sampling frame is not readily available or when cost considerations are important.

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Multistage Sampling

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e.the selection of the sample is accomplished in two or more steps. The population is divided into a set of primary sampling units(first stage). After selecting the primary units, these are further divided into secondary sampling units, (second stage) and the second level sampling is applied. This process goes on until desired stage is reached.

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Non-probability Sampling

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2.in using this sampling design, it is difficult to determine the probability of a unit to be chosen as sample. This results to uncertainty in assessing the reliability of the sample results.

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Judgment or Purposive Sampling

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a.the samples are selected based on expert's subjective judgment or based on some specified criteria.

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Snowball Sampling

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d.This is a technique where an initial sample will be asked to identify other members of the population. Those identified will be considered as samples and will also be asked to identify other members of the population.

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Accidental or Convenience Sampling

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b.in this design, units which are available at hand are being used as samples.

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Quota Sampling

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c.Data collectors may consider a quota to meet as sample. Data enlisters may be given a specific number of samples to be collected.

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Presentation of data

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also needs planning and presentation.

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raw data

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If the data gathered are in their original form, they are called.;They are unarranged and ungrouped.

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1.Textual presentation

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This type of presentation incorporates data in set of narrative sentences or paragraph.Researchers usually use this form when the data have only a few numerical figures. This kind of presentation emphasizes and compares important figures.

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2.Tabular presentation

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This is a systematic way of categorizing related data in rows and columns. This methodical arrangement called statistical table presents data in a more concise and greater detail than in textual or graph forms.

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3.Graphical Presentation

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This is a method of presenting quantitative data in pictorial form produces a device which is often referred to as graph or chart.

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Line Graph

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This is a graphical device that is'effective in showing a trend over a period of time.

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Bar Graph

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a.It is a useful tool in showing the relationship between two or more sets of data.

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Pie Chart

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a.This is a circular graph that presents the component divisions of the whole.Each division or part is proportional to the size or percentage it represents.

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Pictograph

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a.this kind of graph which is also known as picture-graph or pictogram makes use of symbols that represent standard value. The symbols drawn for this kind of charting tool should be self-explanatory and should fit the data being symbolized.

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Raw data

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are data collected in an investigation and they are not organized systematically.

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Frequency distribution

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is the tabular arrangement of numerical data showing its classes and the frequency (denoted by the symbol f) or times of occurrence of the given values belonging to these classes.

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interval or ratio scale.

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Data arranged in a frequency distribution table are those

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grouped data.

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Raw data that are presented in the form of a frequency distribution are called

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array or stem-and-leaf diagram

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Raw data must first be organized either by setting up an

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array.

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An ordering of the observations from smallest to the largest or vice versa is an

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stem position

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Distributing the data by setting a stem(usually the first digit in the numerical value) and leaf (the succeeding digits). Each row represents a ___ and each digit to the right of a vertical line is a leaf.