Download Research Variables Measurement Scales of Measurement

Chapter 4: Data & the Nature of
Measurement
• 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.
Measurement
• 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
Scales of Measurement
• 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.
– 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.
– 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‐ Measurement 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.
Nominal
Ordinal
Interval
Ratio
Examples:
Diagnostic
Socioeconomic IQ test scores;
categories; brand class; ranks
personality and
names; political
attitude scales
affiliation
Weight; length;
reaction time;
number of
responses
Properties:
Identity
Identity;
Magnitude
Identity;
Magnitude;
Equal Intervals
Identity;
Magnitude;
Equal Intervals;
True Zero
Mathematical None
Operations:
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
• 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.”
Measuring & Controlling Variables
• Measurement 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.
– 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
Measurement
• 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.
Individual Differences & Statistical
Procedures
•
Depend on variability or differences in responses among subjects.
– Example: Pseudo‐data for a memory test administered to subjects who had been trained,
versus subjects not trained.
Group A (trained)
Group B (non‐trained)
98
94
93
88
90
82
89
77
Median
91.5
85
Mode
None
None
Mean
92.5
85.25
– 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.
– Example:
• Symmetric Distribution‐ Bell shaped curve. Most
Subjects are near middle of distribution.
– Normal Distribution‐ Curve defined by an equation.
– Example:
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.
– Example: Categorizing on the basis of gender & political
affiliation.
• Univariate‐ One variable frequency distribution.
– Example: Total number of males or females.
• 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.
– Example:
• 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.)
– 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)
– 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.