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Assumptions for independent-measures (1)

The observations within each sample must be independent


Assumptions for independent-measures (2)

The two populations from which the samples are selected
must be normal


Assumptions for independent-measures (3)

The two populations from which the samples are selected
must have equal variances (i.e., homogeneity of variance)


What is a repeated-measures design?

A repeated-measures design or within-subjects design, is one in
which the dependent variable is measured two or more times for
each individual in a single sample. The same group of subjects is
used in all of the treatment conditions.

Examples of conditions: pre-survey, post-survey; before treatment,
after treatment; treatment 1, treatment 2

ud = 0


What is an independent-measures design?

A research design that uses a separate group of participants for
each treatment (or for each population) is called an
independent-measures design or between-subjects design.

Examples of groups: smoker, non-smoker; undergraduate,

u1 - u2 = 0


Assumptions for repeated-measures

The observations within each treatment condition must be


Assumptions for repeated-measures

 The population distribution of difference scores must be


What is a correlation?

A correlation describes and measures three characteristics of
the relationship between two variables:
 Direction
 Form
 Strength or consistency
Examples: age and agility
shoe size and height
amount of rainfall and umbrella sales


Characteristics of a Relationship (Correlation)

Positive (+)
Negative (-)
Linear (i.e., straight line)
Strength or consistency of relationship
Numerical value of correlation
How well data fits a straight line


What is the Pearson Correlation?

Measures degree and direction of the linear relationship
between two continuous variables
 Most common correlation
 Also known as Product-moment correlation
ρ - represents correlation for a population
r - represents correlation for a sample


Why Use Pearson Correlation?

Prediction - two variables related in some systematic
way can be used to make predictions (e.g., X predicts
 Validity - does an instrument measure what it’s suppose
to measure
 Reliability - does a measurement procedure produce a
consistent score
 Theory verification - theories usually make claims about
the relationship between variables (e.g., personality
type and achievement)


What is an outlier?

An outlier is a nonrepresentative value (larger or
smaller than those in the data)


What is Coefficient of determination?

r² measures the proportion
of variability in one variable that can be determined
from the relationship with the other variable.
 Example: A correlation of r = 0.70 between X and Y
means that r² = 0.49 or 49% of the variability in Y can be
predicted from its relationship with X.

Small effect: r2 = .01
Medium effect: r2 = .09
Large effect: r2 = .25


What is Spearman Correlation?

Spearman correlation can be used in two situations:
 to measure relationship between two variables measured
on an ordinal scale
 to measure the consistency of a relationship between two
variables, independent of the specific form of the


WHat is the Phi Coefficient?

The phi coefficient is used when both variables are
The calculation proceeds as follows:
 Convert each of the dichotomous variables to numerical
values by assigning a 0 to one category and a 1 to the
other category for each of the variables.
 Use the regular Pearson formula with the converted


What is the Chi Square Test for Goodness of Fit?

Chi-square test for goodness of fit uses sample data to test hypotheses
about the shape or proportions of a population distribution.
Of the four leading brands of computers, which is preferred by
undergraduate students?

Null: There is no preference
Alternate: There is a preference


What are Observed and Expected Frequencies?

Chi-square goodness of fit tests uses frequencies to test
Observed frequency, fo, is the number of individuals from the
sample who are classified into a particular category.
Expected frequency, fe, for each category is the frequency value
that is predicted if the null hypothesis is true.
expected frequency, fe = pn
where p is the proportion stated in the null hypothesis and n is the
sample size


What is the Chi-Square Test of Independence?

Chi-square test of independence uses frequency data from a sample to
evaluate the relationship between two variables in the population.
Relationship between political party affiliation (liberal, conservative) and
intention to vote (yes, no).
Note: Two variables are independent if there is no consistent, predictable
relationship between them.


Effect size for chi-square test for goodness of fit and independence?

Cohens W
Interpretation: 0.10 small effect; 0.30 medium effect; 0.50 large effect
Note: The Cohen’s w can be used with both chi-square tests but there are
two special effect size measures that are more highly recommended for the
chi-square test of independence.


Effect Size
Effect size for chi-square test of independence only?

Phi Coefficient
Interpretation: 0.10 small effect; 0.30 medium effect; 0.50 large effect
Note: Is used only when we are testing for independence with a 2x2

2x2 matrix


Chi-Square Test Assumptions

Independence of observations
Size of the expected frequencies: A chi-square test works
best with a minimum expected frequency of 5 in each cell