Terms
What is ANOVA?
Analysis of variance (ANOVA) – a hypothesis testing procedure used to evaluate mean differences between two or more populations
• The purpose of ANOVA is similar to t-tests.
(True or False) All hypotheses in ANOVA are directional!
False: All hypotheses in ANOVA are non-directional.
Since F is a ratio of variances, we can never have a negative F.
• Variances can’t be negative.
• Therefore, there is only a single tail to the distribution.
What do we do after ANOVA?
Post hoc tests
Why use Two Factor ANOVA instead of One-Way ANOVA?
Two-Factor ANOVAs examine the effects of two independent variables on the dependent variable.
What is the F-ratio?
A ratio of two sample variances.
What is between group?
• Measures the size of mean differences between samples.
• obtained mean differences (including treatment effects)
• measures the size of the differences between each level’s sample mean.
(True or False) Even if one of the F-ratios isn't significant, we would still reject the null
False: If one or more of the F-ratios are not significant, we would fail to reject the null
Does ANOVA tell you which level has a significant difference?
No, ANOVA simply states that a difference exists
• It does not indicate which levels are different.
When do we use simple main effects? What does the simple main effect consider?
When explaining interactions
Descriptions of simple main effects always include info on both IVs and the DV
What if the between subjects and within subjects are equal?
In this case, we should expect an F-ratio near 1.00.
• When the F-ratio is near 1.00, we conclude that there is no significant effect of the IV.
• the F-ratio only measure random variance
• H0 is true and there are no differences between levels (AKA groups)
What is within group?
• Measures the magnitude of differences expected without any effects of the IV
• differences expected by chance (without treatment effects)
• measures the size of the differences that exist inside each of the treatment levels
(True or False) A large effect of the IV produces a large F-ratio.
True: When we get a large F-ratio (far from 1.00), we reject the null hypothesis and conclude there is at least one significant difference between groups.
What is the null and alternative hypothesis for an independent-measures (One-Way) ANOVA?
H0: μ1=μ2=μ3 (All μ’s are equal)
H1: There is at least one mean difference.
What do we need to consider for Two Factor ANOVA to determine if there is a significant difference?
The main effect of Factor A, the main effect of Factor B, the interaction effect of AxB, and within subjects
In an ANOVA degrees of freedom chart, what represents an alpha level of .05? An alpha level of .01?
Non-bolded number represent an alpha level of .05
Bolded numbers represent an alpha level of .01
What is an interaction?
Indicate when mean differences between individual treatment conditions, or cells, are different from what would be predicted from the main effects of the factors
• An interaction is when the two factors are not independent. The effect of one factor depends on the other.
(True or False) The post hoc test is done after ANOVA regardless of if we reject or fail to reject the null
False: The post hoc test is only done after an ANOVA where H0 is rejected
What does a post hoc test do?
• determine exactly which groups are different and which are not.
• The tests compare the treatments, two at a time, to test the mean differences while correcting for concerns about experiment-wise Type I error inflation.
What variables are used in Two Factor ANOVA? What are the differences between them?
Independent: IVs are manipulations used to group participants.
(Ex. assignment to treatment condition)
Quasi-independent variables: Quasi-IVs are preexisting variables used to group participants.
(Ex. participant gender)
What does η^2 do?
Compute the percentage of variance accounted for by the independent variable (group)
• most common technique for measuring effect size
What is a simple main effect?
Simple Main Effects: The impact of one factor on the dependent variable at a specific level of the other factor
(True or False) If there is a significant interaction, the main effects become useful
False: If there is a significant interaction the main effects become meaningless.
Why use ANOVA over multiple t-tests?
• Can examine more than two groups at the same time!
• Protects researchers from excessive risk of a Type I error in situations when comparing more than two population means
• It automatically adjusts for the effect testing multiple hypotheses has on Type I errors.
What is the null and alternative hypothesis for a Two-Factor ANOVA?
Hypothesis for Main Effect of Factor A
• Ho: μA1 = μA2
• H1: μA1 =/ μA2
Hypothesis for Main Effect of Factor B
• Ho: μB1 = μB2
• H1: μB1 =/ μB2
Interaction Hypothesis for Interaction Effect of AxB
• H0: There is no interaction between factors A and B
• H1: There is an interaction between factors A and B
What can cause the variance between means?
The differences (or variance) between means can be caused by two sources:
1. Effects of the IV: could cause the mean for one level to be higher (or lower) than the mean for another level.
2. Chance or Sampling Error: If there is no effect of the IV at all, we would still expect some differences in the DV values between levels due to random, unsystematic sampling error.