Part IV Significantly Different: Using Inferential Statistics Chapter 13  Two Groups Too Many? Try Analysis of Variance (ANOVA)

What you will learn in Chapter 13 What Analysis of Variance (ANOVA) is and when it is appropriate to use How to compute the F statistic How to interpret the F statistic How to use SPSS to conduct an ANOVA single factor design

Analysis of Variance (ANOVA) Used when more than two group means are being tested simultaneously Group means differ from one another on a particular score / variable Example: DV = GRE Scores & IV = Ethnicity Test statistic = F test R.A. Fisher, creator

Path to Wisdom & Knowledge How do I know if ANOVA is the right test?

Different Flavors of ANOVA ANOVA examines the variance between groups and the variances within groups These variances are then compared against each other Similar to the t Test…only in this case you have more than two groups One-way ANOVA Simple ANOVA Single factor (grouping variable)

More Complicated ANOVA Factorial Design More than one treatment/factor examined Multiple Independent Variables One Dependent Variable Example – 3x2 factorial design Number of Hours in Preschool G e n d r Male 5 hours per week 10 hours 20 hours Female

Computing the F Statistic Rationale…want the within group variance to be small and the between group variance to be large in order to find significance.

Hypotheses Null hypothesis Research hypothesis

Source Table Source SS df MS F Between 1,133.07 27 566.54 8.799 Within 1,738.40 29 64.39 Note: F value for two group is the same as t2

Degrees of Freedom (df) Numerator Number of groups minus one k-1 3 groups --- 3 – 1 = 2 Denominator Total number of observations minus the number of groups N-1 100 participants --- 30 – 3 = 97 Represented: F (2, 27)

How to Interpret F (2,27) = 8.80, p < .05 F = test statistic 2,27 = df between groups & df within groups {Ah ha…3 groups and 30 total scores examined} 8.80 = obtained value Which we compared to the critical value p < .05 = probability less than 5% that the null hypothesis is true Meaning the obtained value is GREATER than the critical value

Omnibus Test The F test is an “omnibus test” and only tells you that a difference exists Must conduct follow-up t tests to find out where the difference is… BUT…Type I error increases with every follow-up test / possible comparison made 1 – (1 – alpha)k Where k = number of possible comparisons

Using the Computer SPSS and the One-Way ANOVA

SPSS Output What does it all mean?

Post Hoc Comparison

Glossary Terms to Know Analysis of variance Omnibus test Simple ANOVA One-way ANOVA Factorial design Omnibus test Post Hoc comparisons Source table

Part IV Significantly Different: Using Inferential Statistics Chapter 17     What to Do When You’re Not Normal: Chi-Square and Some Other Nonparametric Tests

What you will learn in Chapter 17 A brief survey of nonparametric statistics When they should be used How they should be used

Introduction Parametric statistics have certain assumptions Variances of each group are similar Sample is large enough to represent the population Nonparametric statistics don’t require the same assumptions Allow data that comes in frequencies to be analyzed…they are “distribution free”

One-Sample Chi-Square Chi-square allows you to determine if what you observe in a distribution of frequencies is what you would expect to occur by chance. One-sample chi-square (goodness of fit test) only has one dimension Two-sample chi-square has two dimensions

Computing Chi-Square What do those symbols mean?

More Hypotheses H0: P1 = P2 = P3 H1: P1 P2 P3 Null hypothesis Research hypothesis H1: P1 P2 P3

Computing Chi Square C2 = 20.6 For 23 30 7 49 1.63 Maybe 17 13 169 Category O E D (O-E)2 (O-E)2/2 For 23 30 7 49 1.63 Maybe 17 13 169 5.63 Against 50 20 400 13.33 Total 90 C2 = 20.6

So How Do I Interpret… x2(2) = 20.6, p < .05 x2 represents the test statistic 2 is the number of degrees of freedom 20.6 is the obtained value p < .05 is the probability

Using the Computer One-Sample Chi Square using SPSS

SPSS Output What does it all mean?

Other Nonparametric Tests

Glossary Terms to Know Parametric Nonparametric One-sample Chi Square