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Chapter 11

Testing for Differences

Differences betweens groups or categories of the independent variableStatistical tests of difference reveal whether the differences observed are greater than differences that might occur by chance Chi-square t-test ANOVA

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Inferential Statistics

Statistical test used to evaluate hypotheses and research questionsResults of the sample assumed to hold true for the population if participants are Normally distributed on the dependent variable Randomly assigned to categories of the IV

Caveats of application

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Alternative and Null Hypotheses

Inferential statistics test the likelihood that the alternative hypothesis is true and the null hypothesis is notSignificance level of .05 is generally the criterion for this decision If p .05, then alternative hypothesis accepted If p > .05, then null hypothesis is retained

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Degrees of Freedom

Represented by dfSpecifies how many values vary within a statistical testCollecting data always carries errordf help account for this errorRules for calculating df or each statistical test

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Four Analytical Steps

1. Statistical test determines if a difference exists

2. Examine results to determine if the difference found is the one predicted

3. Is the difference significant?4. Evaluate the process and procedures of

collecting data

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Chi-Square

Represented as χ2

Determines if differences among categories are statistically significant Compares the observed frequency with the

expected frequency The greater the difference between observed

and expected, the larger the χ2

Data for one or more variables must be nominal or categorical

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One-Dimensional Chi-Square

Determines if differences in how cases are distributed across categories of one nominal variable are significantSignificant χ2 indicates that variation of frequency across categories did not occur by chanceDoes not indicate where the significant variation occurs – only that one exists

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Example of One-Dimensional Chi-Square

Types of Persuasive Strategies Simple offers

Statement of

benefits

Availability of alcohol

Appeal to group

minimization

Norms Facilitation Total n = 532

46.4% n = 247

14.7% n = 78

17.3% n = 92

7.3% n = 39

11.5% n = 61

2.8% n = 15

100%

χ2 = 3.29.86 (df = 5), p < .001

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Contingency Analysis

Also known as two-way chi-square or two-dimensional chi-squareExamines association between two nominal variables in relationship to one another Columns represent frequencies of 1st variable Rows represent frequencies of 2nd variable Frequency of cases that satisfy conditions of

both variables inserted into each cell

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Example of Contingency Analysis

Ritual Type Marital Relationships

Friendships Totals

Enjoyable activities 154 150 304 Escape 31 17 48 Communication 50 43 93 Patterns/habits/mannerisms 38 6 44 Idiosyncratic/symbolic favorites

48 7 55

Play rituals 27 16 43 Celebration 13 22 35 Totals 361 261 622 χ2 (df = 6) = 46.77, p < .001

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Limitations of Chi-Square

Can only use nominal data variablesTest may not be accurate If observed frequency is zero in any cell, If expected frequency is < 5 in any cell

Cannot directly determine causal relationships

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t-Test

Represented by tDetermines if differences between two groups of the independent variable on the dependent variable are significant IV must be nominal data of two categories DV must be continuous level data at interval or

ratio level

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Commons Forms of t-Test

Independent sample t-test Compares mean scores of IV for two different

groups of people

Paired comparison t-test Compares mean scores of paired or matched IV

scores from same participants

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Types of t-Tests

Two-tailed or nondirectional t-test Hypothesis or research question indicates

that a difference in either direction is acceptable

One-tailed or directional t-test Hypothesis or research question specifies

the difference to be found

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Limitations of t-Test

Limited to differences of two groupings of one independent variable on one dependent variableCannot examine complex communication phenomena

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Analysis of Variance

Referred to with acronym ANOVARepresented by FCompares the influence of two or more groups of IV on the DVOne or more IVs can be tested -- must be nominal -- can be two or more categoriesDV must be continuous level data

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ANOVA Basics

Planned comparisons Comparisons among groups indicated in

the hypothesis

Unplanned comparisons, or post hoc comparisons Not predicted by hypothesis -- conducted

after test reveals a significant ANOVA

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ANOVA Basics

Between-groups variance – differences between groupings of IV are large enough to distinguish themselves from one anotherWithin-groups variance – variation among individuals within any category or groupingFor significant ANOVA, between-groups variance is greater than within-groups variance

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ANOVA Basics

F is calculated to determine if differences between groups exist and if the differences are large enough to be significantly differentA measure of how well the categories of the IV explain the variance in scores of the DV The better the categories of the IV explain

variation in the DV, the larger the F

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ANOVA Design Features

Between-subjects design Each participant measured at only one level of

only one condition

Within-subject design Each participant measured more than once,

usually on different conditions Also called repeated measures

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One-Way ANOVA

Tests for significant differences in DV based on categorical differences of one IV One IV with at least two nominal categories One continuous level DV

Significant F Difference between groups is larger than

difference within groups

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Two-Way ANOVA

Determines relative contributions of each IV to the distribution of the DV Two nominal IVs One continuous level DV

Can determine main effect of each IVCan determine interaction effect -- if there is a simultaneous influence of both IVs

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Example of Two-Way ANOVA

Male Female

One-sided news report

Males viewing one-sided news report

Females viewing one-sided news report

Two-sided news report

Males viewing two-sided news report

Females viewing two-sided news report

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Main and Interaction Effects

Main EffectUnique contribution of each IVOne IV influences scores on the DV and this effect is not influenced by other IV

Interaction EffectOne IV cannot be interpreted without acknowledging other IVIf interaction effect exists, main effects are ignored

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Factorial ANOVA

Accommodates 3 or 4 IVs Still determines main effects of each IV Determines all possible interaction effects

3 x 2 x 2 ANOVA First IV has 3 categories Second IV has 2 categories Third IV has 2 categories

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Limitations of ANOVA

Restricted to testing IV of nominal or categorical data

When 3 or more IVs used, can be difficult and confusing to interpret

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Tests of Differences