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28 Cards in this Set
- Front
- Back
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What are the hypotheses for an independent samples t-test?
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H0: both means are equal
HA: the means are not equal (possibly directional) NB: only two groups! |
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What are the hypotheses for Levene's test?
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H0: variances are equal (sigma squared)
HA: variances are not equal |
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What are the hypotheses for one-way ANOVA?
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H0: all means are equal
HA: not all means are equal |
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What are the hypotheses for two-way ANOVA?
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H01: no main effect of factor A
H02: no main effect of factor B H03: no interaction effect |
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What are the hypotheses for multiple linear regression testing?
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H0: all coefficients are 0 (except for intercept)
HA: at least one isn't 0 => check with t-tests |
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What are the assumptions of one-way ANOVA?
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MINE:
Measurement level of DV Independent observations Normally distributed DV in each group Equal error variances (aka homogeneity) |
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What are the assumptions of ANCOVA?
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IVR:
Independence of factor and covariate => ANCOVA with covariate as DV Variance is homogeneous => Levene's test Regression slopes are homogeneous => Run ANCOVA with interaction effects No interaction between factor and covariate? |
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Total sum of squares
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Model sum of squares + Residual sum of squares
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Model sum of squares
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For each group: ( n ( group_mean - grand_mean)) ^2
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Residual sum of squares
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For each group: sum (value - group_mean)^2
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How to get a "mean" sum of squares
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Divide by (appropriate) degrees of freedom
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What are the df's in one-way ANOVA?
(and ANCOVA) |
dfr = total sample size - number of groups
dfm = number of groups -1 dfc = 1 |
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What are the df's in two-way ANOVA?
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dfa = a-1
dfb = b-1 dfr = n-ab db(axb) = (a-1)(b-1) |
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What are the df's in multiple linear regression testing?
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dfm = number of predictors
dfr = n - dfm - 1 |
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Formula for F-test in one-way ANOVA
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F = MSm / MSr
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Which measure is used for effect size and how to calculate it
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R^2 = eta^2 = SSm / (SSm + SSr) = SSm / SSt
.01 is small .09 is medium .25 is large |
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Ordinal variable = interval variable?
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When number of groups is more than 6
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Rule of thumb for Levene's test (homogeneity assumption)
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Samples sizes not too different? 1:4
Sample variances not too different? 1:10 => okay |
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Steps in one-way ANOVA
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AFEPI:
1. Assumption of homogeneity 2. F-test for effect of factor 3. Effect size 4. Post-hoc comparisons if F-test significant and more than 2 groups 5. Indicate which group scores higher if significant |
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Steps in two-way ANOVA
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AFEIPI:
1. Assumption of homogeneity 2. F-test for main & interaction effects 3. Check effect size 4. Interaction effect: if significant, plot means; if not, leave out of model and run with main effects only 5. Post-hoc if main effects significant 6. Indicate which group scores higher if significant |
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Steps in regression analysis
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FETBA:
1. F-test significant? 2. Effect size large enough? 3. T-tests significant? 4. Sign and size of b-parameters 5. Absolute value of standardized coefficients |
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Steps in ANCOVA
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IRAFPIC:
1. Independence covariate/factor 2. Regression lines homogeneous? 3. Assumption of homogeneity 4. F-test significant? 5. Post-hoc if factor is significant and more than 2 groups 6. Indicate which group scores higher 7. Covariate significant in F-test? => plot |
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Steps in sequential analysis
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Same as for regression analysis:
FETBA |
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When to use one-way ANOVA
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Differences between two or more groups
=> how DV is different in several groups DV = interval/ratio IV = categorical |
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When to use two-way ANOVA
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Differences between groups based on different factors
=> how DV is different in several groups DV = interval/ratio IVs = categorical |
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When to use multiple linear regression
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Predict DV from several factors
DV = interval/ratio IVs = interval/ratio |
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When to use ANCOVA
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Differences in groups based on different factors while controlling for a covariate
DV = interval/ratio IVs = categorical Covariate = interval/ratio |
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What are the hypotheses for sequential analysis?
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H0: R2-change = 0 (adding predictors does not improve model)
HA: adding predictors does improve the model |
