Research Design & Statistics V: Two-way Between Ss (Independent measures) ANOVA

What would cause a bigger F-test statistic?

A smaller within number

Which tests are used for Nominal IV and Nominal DV?

Chi-square test of independence

In a Two-Way ANOVA what are the two IVs called?

Factors

What is the whole point of the F-Ratio Statistic?

How much variance is due to the factor in question (A, B, or AxB), compared to how much variance we'd expect due to chance. If it's a lot bigger than we'd expect due to chance, we'll get a big F value and reject the null hypothesis.

What are the specifics of a One-way between subjects ANOVA?

One independent variable An independent variable that has multiple levels One dependent variable

Which test has One IV with 3+ levels?

One-way ANOVA

Which test has Three IVs?

Three-way ANOVA

For a 2 x 2 completely within-subjects design, The 2-way ANOVA reduces to just 3 within-Ss t-tests

•IV1 main effect: run a within-Ss t-test on the difference score between the two conditions of IV1 •IV2 main effect: run a within-Ss t-test on the difference score between the two conditions of IV2 Interaction: run a within-Ss t-test on the difference of difference scores!

In order to conduct a study to determine whether meditation affects body weight, Brian plans to have one group participate in different lengths of meditation time. After each length of meditation time, Brian will measure the body weight of each individual in the group, which is _____ form of ANOVA.

repeated measure

Which test has One IV with 2 levels?

t-test

What does Factor stand for in a Two-way ANOVA?

•= independent variable •Factor A, Factor B: two different IVs in the same experiment •A1 = the first condition (level) of Factor A

What are Main Effects in Two-Way between Ss ANOVA?

•Mean differences among levels of one factor •Differences are tested for statistical significance •Each factor (factor A and factor B) is evaluated independently of the other factor(s) in the study

Two- way between Ss ANOVA symbols

•Two-way between-subjects ANOVA (assuming equal n in all cells) •F = (aka F ratio) = test statistic (various) •df = degrees of freedom (various) •SS = Sum of squared deviations of raw scores from the mean (various) •MS = Mean of squared deviations (various)

Which tests are used for NOMINAL independent variable(s) and interval/ratio DV?

•t-test (within-Ss or between-Ss): conducted on 1 IV with 2 levels (aka conditions) •One-way ANOVA: conducted on 1 IV that has 3 or more levels •Two-way ANOVA: conducted on 2 IVs (that each have 2 or more levels) •Three-way ANOVA: conducted on 3 IVs (that each have 3 or more levels)

What is the denominator in the F-ratio?

Denominator will be the same. MSwithin is always going to be our estimate of variance in DV expected due to chance.

The purpose of running an ANOVA is to find the _____ .

Differences between means

What are the 3 F-statistics that a Two-way ANOVA produce?

1)One for the first IV/Factor (main effect) 2)One for the second IV/Factor (main effect) 3)One for the interaction between the IVs/Factors

Brian is conducting a study to determine whether meditation affects body weight. Brian plans to have three different groups, where each group will be assigned a different length of meditation time. When Brian gathers his data, he will compare the body weights of the participants between groups. Which type of ANOVA is Brian using?

Between subject

What are the specifications for a Two-Way ANOVA?

Both variables are between-subjects (aka independent measures) •2 x 2 factorial design (both variables have only 2 conditions) (assuming equal n in each cell)

Brian plans to have one group participate in different lengths of meditation time for his study to determine whether meditation affects body weight. After each length of meditation time, he will measure the body weight of each individual in the group. Brian's assistant, Barney, is worried that they will not see a big difference in the body weight of the participants from the first post-meditation weigh-in to the subsequent weigh-ins. What phenomenon is Barney worried about?

Carryover effect

What does Cell stand for in a Two-way ANOVA?

Combination of conditions of 2 factors

Brian wants to know if there is a significant difference between the means in the study he is conducting. What value does Brian need to examine?

F-Ratio

Two-way ANOVA sampling distribution?

Fcritical = critical value that our test statistic must be greater than to reject H0. Distribution of F ratios

What is Total Variance?

How far spread out from each other are all the scores.

What is the idea behind the ANOVA?

If the samples are truly not all from the same population, then the BETWEEN-GROUPS VARIANCE of the samples should be bigger than the WITHIN-GROUPS VARIANCE of the samples.

Why would we run an ANOVA instead of several t-tests?

It is unethical to run multiple statistical tests on the same data because you will eventually find something due to the sheer probability and not an actual relationship. You'll be able to examine a large amount of data and look for interactions without having to do a whole lot more statistical analyses.

What are the specifics of a Two-way ANOVA

TWO independent variables Each independent variable has multiple levels ONE dependent variable

What does ANOVA measure?

The degree to which levels or groups of an independent variable differ from each other

What are Interactions in a Two-Way between Ss ANOVA?

The mean differences between individual treatment conditions, or cells, are different from what would be predicted from the overall main effects of the factors

How many F-Ratios are there?

Three

What will the Two-way ANOVA show us?

Two main effects: •Does Factor A have a (statistically significant) overall effect on the DV? •Does Factor B have a (statistically significant) overall effect on the DV? One Interaction: •Does the effect of one factor vary depending on the other factor? •Do the two factors combined have an effect on the DV that we wouldn't understand from just looking at each factor by itself?

Which test has Two IVs, both between-subjects?

Two-way between-subjects ANOVA

Which test has Two IVs, one between-subjects and one within-subjects?

Two-way mixed ANOVA

Which test has Two IVs, both within-subjects?

Two-way within-subjects ANOVA

What is the Numerator in the F-ratio?

Variance in DV due to one of the 3 effects. Numerator will vary across the 3 F-tests. •MSA •MSB MSAxB