Research Variables. Measurement. Scales of Measurement. Chapter 4: Data & the Nature of Measurement

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1 Chapter 4: Data & the Nature of Graziano, Raulin. Research Methods, a Process of Inquiry Presented by Dustin Adams Research Variables Variable Any characteristic that can take more than one form or value. Examples: Anxiety, intelligence, height, reaction time. Independent Variable May or may not be manipulated by researcher. Dependent Variable Observed and measured by researcher. Usually depends on independent variable. Purpose is to accurately represent the research variables numerically. Abstract number scale: 4 concepts Identity Each number has a particular meaning. Magnitude Numbers have an inherent order from smaller to larger (ex: 5 is a greater magnitude than 3.) Equal Intervals The difference between units is the same anywhere on the scale (the difference between 2 & 3 is the same as the difference between 99 & 100.) True Zero Zero of the abstract number scale, represents none of the concept being measured Goal of Abstract Number Scale is to match characteristics of the variables as they are measured and the characteristics of real numbers. Otherwise one is limited on the mathematical operations one can perform on data. Ex: # of questions a child asked in a week. Scales of 4 levels/scales of measurement to help identify closeness of match to real number system. Nominal Scales Lowest level of measurement, scales least matching to the real number system. Differences between categories is qualitative, not quantitative. No zero point; cannot be ordered from high to low; no assumption of equal units of measurement. Nominal Data/Categorical Data Chi Square most commonly used statistical tests. Examples: Number on an athlete s jersey, social security number, telephone number. Ordinal Scales Measure variables in order of magnitude. Property of magnitude, numbers are assigned to categories. Do not indicate anything about intervals. Ordered Data. Example: Rank in class/class standing. Interval Scales conveys information about orderings of magnitude. No true zero. Score Data. Examples: IQ test, Fahrenheit/Celsius scale. Ratio Scales Contain all properties of Abstract Number Scale. Score Data. Example: Weight, Length, etc.

2 Examples: Nominal Ordinal Interval Ratio Diagnostic categories; brand names; political affiliation Socioeconomic class; ranks Properties: Identity Identity; Magnitude Mathematical Operations: IQ test scores; personality and attitude scales Identity; Magnitude; Equal Intervals Weight; length; reaction time; number of responses Identity; Magnitude; Equal Intervals; True Zero None Rank Order Add; subtract Add; subtract; Multiply; Divide Type of Data: Nominal Ordered Score Score Typical Statistics Used: Chi square Sign test; Mann Whitney U Test T test; ANOVA T test; ANOVA Measuring & Controlling Variables Error Can distort the scores so that the observations no longer reflect reality. Response set bias Any tendency for a subject to distort their response to a dependent measure. Social Desirability Tendency to respond in what one believes to be most socially acceptable. Operational Definitions Definition of a variable in terms of the procedures used to measure or manipulate variable. Reliability, effective range, validity. Reliability The reproducibility factor. Interrater reliability Both raters must be blind to the ratings of the other (when reproducing results.) Perfect interrater reliability two raters results always agree. Zero interrater reliability two unrelated raters. Correlation Coefficient usually used (ch. 5) Test retest reliability Internal consistency reliability Test same subject multiple times. the more observations we make to obtain a score for a person, the greater will be the reliability of that score. Effective Range Abstract number scale appropriate for what is being measured Example: A mouse and elephant would use two different ranges for weight measurement. Validity Readings are accurate reflections of what is being measured. Not the same as reliability. Example: If a person weighs 170 lbs, the scale should say so, otherwise, the reading is not valid. Scale Attenuation effects Attenuation Restricting the range of a scale Ceiling Effect No chance to show higher scores Floor Effect No chance to show lower scores The Need for Objective Objective measures Measures that do not change regardless of how or when it is being measured, and by whom. Statistical Analyses Powerful tools for accurately describing phenomena. Provide objective ways of evaluating patterns of events by computing the probability of observing such patterns by chance alone. Chapter 5: Statistical Analysis of Data Statistics Powerful tools for organizing and understanding large sets of data. Describe groups Summarize results Evaluate data Integral part of research design Descriptive Statistics Simplify & Organize data (no conclusions drawn.) Inferential Statistics Go beyond simple description to help us make inferences about data.

3 Individual Differences & Statistical Procedures Depend on variability or differences in responses among subjects. Pseudo data for a memory test administered to subjects who had been trained, versus subjects not trained. Group A (trained) Median Mode None None Group B (non trained) Descriptive Statistics Frequency Counts & Distributions Nominal & Ordinal Data Compute Frequencies Cross tabulation categorizing subjects on the basis of more than one variable at the same time. Categorizing on the basis of gender & political affiliation. Univariate One variable frequency distribution. Total number of males or females. Mean Graphical Representation of Data Often use histograms & frequency polygons Histograms Frequency of a given score is represented by the height of a bar above that score. Frequency Polygon Frequency is indicated by the height of a point above each score in the abscissa. Completed by connecting adjacent points. Advantage: Two frequency distributions can be evaluated. Symmetric Distribution Bell shaped curve. Most Subjects are near middle of distribution. Normal Distribution Curve defined by an equation. Skewed Distribution Scores tend to pile up at one end of distribution; indicated by tail of curve. Positively skewed Most scores pile up near bottom (tail points toward high end of scale.) Negatively skewed Most scores pile up near top (tail points toward low end of scale.)

4 Distributions can be defined by location on x axis (central tendency) and horizontal spread (variability of distribution) Summary Statistics Describe data with one or two numbers, and provide a basis for later analyses in which inferential statistics will be used. Measures of central tendency Provide an indication of the center of distribution where most scores tend to cluster Mode most frequently occurring score in distribution.» Bimodal Data contain 2 modes» Trimodal Data contain 3 modes Median Middle score in a distribution where scores are arranged lowest highest.» 50th percentile (50% of subjects scored above median/50% of subjects scored below median.) Inferential Statistics Statistical analyses used to draw inferences about a population. Only Tested if Null Hypothesis is true. Populations and Samples Population (in people) larger group of all the people of interest from which the sample is selected. Sample Subset of people drawn from the population. Sampling error variation among different samples drawn from the same population. Refers to small variability among samples due to chance.» With odd number of n scores, median is the value at score (n + 1)/2» With even number of n scores, median is the average between score at n/2 and n/2 + 1» Only used in score data, not in nominal or ordinal. Mean Average of all scores.» Xbar = ( X)/N, where X is the sum of all data, and N is the number of data. Measures of variability: range, variance, & standard deviation. Range Distance from the lowest to the highest score. Variance Variance(s2) = (Sum of Squares)/(Degrees of Freedom)» s2 = ( (X Xbar)2)/(N 1) Null Hypothesis general hypothesis that can be applied to many types of comparisons. There is not any statistical difference between the population means. Rejected if the observed sample means are very different. Population parameter Characteristic computed by testing everyone in population. Sample Statistic Characteristic computed by testing a sample drawn from population. Statistical Decisions and Alpha Levels Alpha Level somewhat arbitrary cutoff point of determining whether Null Hypothesis is true. (usually small)

5 Type I and Type II Errors Type I Error Occurs when null hypothesis is rejected when it in fact should have been accepted. Probability of this happening is equal to set alpha level. Type II Error Occurs when we fail to reject the null hypothesis when it is false. Testing for Mean Differences Inferential statistics most frequently used to evaluate mean differences between groups. Simple t test typically used with score data from two independent samples of subjects. Samples are independent if different subjects appear in each sample and if subjects in two samples are not matched in any way. Null hypothesis is that there is no difference in two population means Correlated t test Within subjects design Same subjects appear in each group. Matched subjects design all subjects are matched in pairs then randomly assigned so that one member of the pair goes into one group and the other member goes into another. Correlated t test would be the appropriate test to use to analyze the results of the study. Analysis of Variance (ANOVA) When we have more than two groups and want to test for mean differences among the groups, ANOVA is the appropriate test. Test compares means of various groups (not variance.) Useful for analyzing results of studies that use one independent variable AND more than one independent variable.

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