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42 Cards in this Set
- Front
- Back
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Analysis of Variance (ANOVA) |
procedure for testing variation among the means of more than two groups |
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Within-Groups estimate of the population variance |
- average of estimates figured entirely from the scores within each of the samples - not affected by whether the null hypothesis is true |
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What determines the level of within group variation? |
-chance factors |
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Between-groups estimate of the population variance |
- based on the variation between the means of the samples - if null is true, the between groups estimate of the population variance is influenced by chance factors - if null is false, between groups variance influenced by chance factors and treatment effects |
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True or False: When the null hypothesis is true, the ratio of the between-groups population variance estimate to the within-groups population variance should be about 1. |
True |
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True or False: When the research hypothesis is true, this ratio should be greater than 1. If you figure this ratio and it comes out much greater than 1, you can reject the null hypothesis |
True |
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Analogy for F-ratio |
signal-to-noise |
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MSwithin |
= |
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Estimated Variance of the distribution of means |
= |
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Grand Mean |
overall mean of all your scores |
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MSbetween |
- estimate of population variance based on the variation between the means = |
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F |
= |
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True or False: An F distribution cannot be lower than 0 and can rise quite high but most F ratios pile up near 1 |
True |
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Between groups degrees of freedom |
numerator degrees of freedom |
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Within-groups degrees of freedom |
denominator degrees of freedom |
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Hypothesis Testing with ANOVA |
1. Restate question as research and null about populations 2. Determine characteristics of comparison distribution 3. Determine cutoff 4. Determine your sample's score on the comparison distribution 5. Decide whether to reject null |
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ANOVA assumptions |
- cutoff F ratio from table is strictly accurate only when populations follow a normal curve and have equal variances - all scores in groups are independent from each other |
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What is considered equal variances? |
if the variance estimate of the group with the largest estimate is no more than four or five times that of the smallest and the sample sizes are equal, the conclusions using the F-distrubtion should be adequately accurate |
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True or False: In practice, the real interest is not in an overall, or omnibus, difference among the several groups, but rather in more specific comparisons |
True |
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Planned contrasts |
- also called a priori comparisons, planned comparisons, or linear contrasts |
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True or False: The within-groups population variance estimate will be the same as for the overall analysis of variance |
True |
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True or False: The between groups population variance estimate in a planned contrast is different from the between-groups variance estimate in the overall analysis |
True |
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Procedure for determining the between-groups population variance estimate |
1. Estimate the variance of the distribution of means 2. Figure the estimated variance of the population of individual scores |
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Bonferroni procedure |
- ex. 2 planned contrasts = 0.05/2=0.025 - ex. 3 planned contrasts= 0.05/3= 0.017 - if there are only two planned contrasts (or even three), it is common for researchers not to correct at all |
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Post hoc comparisons |
researcher fishing through results to see which groups differ from each other |
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True or False: The Scheffe test and Tukey test are the most widely used, with the Neuman-Keuls and Duncan procedures almost as common |
True |
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Scheffe Test |
- most widely applicable - most conservative - F/dfbetween |
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Proportion of variance accounted for ( ) |
- proportion of total variation of scores from the grand mean that is accounted for by the variation between the means of the groups = |
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Another common name for R squared is |
- eta squared, correlation ratio, |
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R squared has a minimum of ____ and a maximum of ____ |
0 1 |
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Effect sizes for R squared |
small = 0.01 medium= 0.06 large= 0.14 |
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What does a power of 0.56 mean? |
Even if the research hypothesis is in fact true and has a large effect size, there is 56% chance that the study will come out significant |
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What is the main concern of using planned contrasts instead of an overall analysis of variance? |
we lose out on finding unexpected differences not initially planned and we put too much control of what is found in the hands of the researcher (versus nature) |
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What do the small letters next to the means mean? |
means with same letter are not significantly different from each other; those with different letter are |
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SStotal |
= |
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SSwithin |
= |
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SSbetween |
= |
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MSbetween |
= |
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MSwithin |
= |
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Analysis of Variance table |
lays out results of an analysis of variance based on the structural model method |
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Other names for Between-groups variance in ANOVA table |
between, group, model, treatment |
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Other names for within-groups variance in ANOVA table |
error |
