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1

Assumptions for independent-measures (1)

The observations within each sample must be independent

2

Assumptions for independent-measures (2)

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

3

Assumptions for independent-measures (3)

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

4

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

5

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,
graduate

u1 - u2 = 0

6

Assumptions for repeated-measures

The observations within each treatment condition must be
independent

7

Assumptions for repeated-measures

 The population distribution of difference scores must be
normal

8

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

9

Characteristics of a Relationship (Correlation)

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

10

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

11

Why Use Pearson Correlation?

Prediction - two variables related in some systematic
way can be used to make predictions (e.g., X predicts
Y)
 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)

12

What is an outlier?

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

13

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

14

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
relationship

15

WHat is the Phi Coefficient?

The phi coefficient is used when both variables are
dichotomous.
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
scores.

16

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.
Examples:
Of the four leading brands of computers, which is preferred by
undergraduate students?

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

17

What are Observed and Expected Frequencies?

Chi-square goodness of fit tests uses frequencies to test
hypotheses
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

18

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.
Example:
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.

19

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.

20

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
matrix

2x2 matrix

21

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