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Module 1: Introduction to Statistics

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Module 1 Overview

  • The Role of Statistics
  • The Research Process
  • Threats to Validity
  • Statistical Terminology
  • Scales of Measurement
  • Introduction to Descriptive and Inferential Statistics

The Role of Statistics

  • The goal of virtually all quantitative research studies is to identify and describe relationships among constructs, or variables.
  • Data, or observations, are collected in a very systematic manner, and conclusions are drawn based on the data.
  • At a basic level, statistical techniques allow us to aggregate and summarize data in order for researchers to draw conclusions from their study.

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The Typical Research Process

  • The typical quantitative study involves a series of steps, one of which is statistical analysis.
  • NOTE: These are steps in the research process and not sections of the dissertation.

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Step 1: Research Questions

  • Research questions reflect the problem that the researcher wants to investigate.
  • Research questions can be formulated based on theories, past research, previous experience, or the practical need to make data-driven decisions in a work environment.
  • Research questions are vitally important because they, in large part, dictate what type of statistical analysis is needed as well as what type of research design may be employed.

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Examples of Research Questions

  • How is financial need related to retention after the freshman year of college?
  • What types of advertising campaigns produce the highest rates of inquiries among prospective applicants at NSU?
  • How do males and females differ with respect to statistics self-efficacy?
  • How does a body image curriculum improve body image in college females?

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Hypotheses

  • While research questions are fairly general, hypotheses are specific predictions about the results, made prior to data collection.
  • As financial need increases, the likelihood of retention decreases.
  • Personalized letters result in more inquiries than brochures.
  • Males have higher levels of self-efficacy than females.
  • Body image will improve as a result of the new curriculum.

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Step 2: Operationalize & Choose Measures

  • Many variables of interest in education and psychology are abstract concepts that cannot be directly measured.
  • This doesn’t preclude us from studying these things, but requires that we clearly define the specific behaviors that are related to the concept of interest.

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Measuring Abstract Concepts

  • How does one measure retention, inquiry rate, statistics self-efficacy, and body image?
  • The process of defining variables and choosing a reliable and accurate measurement tool is called operationalizing your variables.
  • Good measurement is vital to the trustworthiness of your results!

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Step 3: Choose a Research Design

  • In Step 3, we develop a plan for collecting the data we need (i.e., a “blueprint” for the study)
  • This is called research design, and includes things such as:
  • Who will participate in the study?
  • Who will receive the intervention?
  • Will there be a “control group”?
  • Will data be collected longitudinally?
  • What instrument will be used to collect data?
  • What type of data will be collected?

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Threats to Validity

  • Internal Validity
  • Problems associated with the experimental procedures or experiences of participants
  • External Validity
  • Problems that affect the generalizability of the results

  • The choice of design impacts the validity of your final results

Step 4: Analyze The Data

  • Once the data have been collected, the results must be organized and summarized so that we can answer the research questions.
  • This is the purpose of statistics
  • The choice of analysis at this stage depends entirely on two prior steps:
  • The research questions
  • How the variable is measured

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Step 5: Draw Conclusions

  • After analyzing the data, we can make judgments about our initial research questions and hypotheses.
  • Are these results consistent with previous studies?
  • The conclusions drawn from a study may provide a starting point for new research.

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The Role of Statistics

  • Despite the anxiety usually associated with statistics, data analysis is a relatively small piece of the larger research process.
  • There is a misconception that the trustworthiness of statistics is independent of the research process itself
  • This is absolutely incorrect!
  • A statistical analysis can in no way compensate for a poorly designed study!!!!

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Statistical Terminology

Population

  • A population is the entire set of individuals that we are interested in studying.
  • This is the group that we want to generalize, or apply our results to.
  • Although populations can vary in size, they are usually quite large.
  • Thus, it is usually not feasible to collect data from the entire population.

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Sample

  • A sample is simply a subset of individuals selected from the population.
  • In the best case, the sample will be representative of the population.
  • That is, the characteristics of the individuals in the sample will mirror those in the population.

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Parameters vs. Statistics

  • In most studies, we wish to quantify some characteristic of the population.
  • Example:
  • The retention rate, inquiry rate, average level of self-efficacy, average level of body image
  • This is the population parameter
  • Parameters are generally unknown, and must be estimated from a sample
  • The sample estimate is called a statistic

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Variables

  • A characteristic that takes on different values for different individuals in a sample.
  • Examples:
  • Retention (yes/no)
  • Inquiry about NSU (yes/no)
  • Self-efficacy (score on self-efficacy questionnaire)
  • Body image (score on body image questionnaire)
  • In statistical formulas, variables are usually referred to generically as X or Y

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Independent Variables (IV)

  • The “explanatory” variable
  • The variable that attempts to explain or is purported to cause differences in a second variable.
  • Some texts refer to the IV as the one manipulated by the investigator.
  • Example:
  • Does a new curriculum improve body image?
  • The curriculum is the IV

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Dependent Variables (DV)

  • The “outcome” variable
  • The variable that is thought to be influenced by the independent variable
  • Example:
  • Does a new curriculum improve body image?
  • Body image is the DV

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Confounding Variables

  • Researchers are usually only interested in the relationship between the IV and DV.
  • Confounding variables represent unwanted sources of influence on the DV, and are sometimes referred to as “nuisance” variables.
  • Example:
  • Does a new curriculum improve body image?
  • Such things as heredity, family background, previous counseling experiences, etc. can also impact the DV.

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Controlling Confounding Variables

  • Typically, researchers are interested in excluding, or controlling for, the effects of confounding variables.
  • This is generally not a statistical issue, but is accomplished by the research design.
  • Certain types of designs (e.g., experiments) better control the effects of confounding variables (because they use a control group).
  • If an experiment or an equivalent control group is not possible ANCOVA

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Examples

  • Do students prefer learning statistics online or face to face?
  • What is the IV? DV?

  • Are there differences in the anxiety levels of students who have had statistics before versus students who have never had statistics?
  • What is the IV? DV?

Scales of Measurement

Variable Measurement Scales

  • For any given variable that we are interested in, there may be a variety of measurement scales that can be used:
  • What is your annual income? _________
  • What is your annual income?

a. 10,000-20,000 b. 20,000-30,000 c. 30,000-40,000 d. 40,000-50,000 e. 50,000 or above

  • Variable measurement is the second factor that influences the choice of statistical procedures (research question is the first).

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Scales of Measurement

  • Nominal
  • Ordinal
  • Interval
  • Ratio

Nominal Scale

  • Observations fall into different categories or groups.
  • Differences among categories are qualitative, not quantitative.
  • Examples:
  • Gender
  • Ethnicity
  • Counseling method (cognitive vs. humanistic)
  • Retention (retained vs. not retained)

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Ordinal Scale

  • Categories can be rank ordered in terms of amount or magnitude.
  • Categories possess an inherent order, but the amount of difference between categories is unknown.
  • Examples:
  • Class standing
  • Letter grades (A,B,C,D,F)
  • Likert-scale survey responses (SD, D, N, A, SA)

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Interval Scale

  • Categories are ordered, but now the intervals for each category are exactly the same size.
  • That is, the distance between measurement points represent equal magnitudes (e.g., the distance between point A and B is the same as the distance between B and C).
  • Examples:
  • Fahrenheit scale of measuring temperature
  • Chronological scale of dates (1997 A.D.)
  • Standard scores (z-scores)

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Ratio Scale

  • Same properties as the interval scale, but with an additional feature
  • Ratio scale has an absolute 0 point.
  • Absolute 0 point permits the use of ratios (e.g., A is “twice as large” as B).
  • Examples:
  • Number of children
  • Weight
  • Annual income

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Categorical vs. Continuous Variables

  • In practice, it is not usually necessary to make such fine distinctions between measurement scales.
  • Two distinctions, categorical and continuous are usually sufficient.
  • Categorical variables consist of separate, indivisible categories (i.e., men/women).
  • Continuous variables yield values that fall on a numeric continuum, and can (theoretically) take on an infinite number of values.

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Level of Measurement Summary

  • In practice, the four levels of measurement can usually be classified as follows:

  • Continuous variables are generally preferable because a wider range of statistical procedures can be applied

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Examples

  • What is the level of measurement of
  • Temperature OC?
  • Color?
  • Income of professional baseball players?
  • Degree of agree (1 = Strongly Disagree,
    5 = Strongly Agree)?

Descriptive Statistics

  • Procedures used to summarize, organize, and simplify data (data being a collection of measurements or observations) taken from a sample (i.e., mean, median, mode).
  • Examples:
  • The average score on the Rosenberg Self-Esteem Scale was 7.5
  • 63% of the sample described themselves as Caucasian

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Inferential Statistics

  • Techniques that allow us to make inferences about a population based on data that we gather from a sample.
  • Study results will vary from sample to sample strictly due to random chance (i.e., sampling error).
  • Inferential statistics allow us to determine how likely it is to obtain a set of results from a single sample.
  • This is also known as testing for “statistical significance.”

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Module 1 Summary

  • The Role of Statistics
  • Statistical Terminology
  • Scales of Measurement
  • Introduction to Descriptive and Inferential Statistics

Step 1:

Research

Questions &

Hypotheses

Step 2:

Operationalize

& Choose

Measures

Step 3:

Choose a

Research

Design

Step 4:

Analyze

Data

Step 5:

Draw

Conclusions

The Research Process

Nominal

Ordinal

Categorical Variables

Interval

Ratio

Continuous Variables