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29 Cards in this Set
- Front
- Back
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Hypothesis testing procedure that is used to evaluate mean differences between two or more treatments (or populations). Uses sample data as the basis for drawing general conclusions about populations. |
Analysis of Variance
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the variable that designates the groups being compared (IV)
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Factor
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individual conditions or values that make up a factor
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Levels
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The variance in the numerator provides a single number that measures the differences among all of the sample means. The variance in the denominator measures the mean differences that would be expected if there were no treatment effect.
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F-Ratio
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The risk of a Type I error, or alpha level, for an individual hypothesis test
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Test wise Alpha level
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Total probability of a type I error that is accumulated from all of the individual tests in the experiment
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Experiment-wise alpha level
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As the number of separate tests increases...
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so does the experiment-wise alpha level
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How does ANOVA avoid the problem of an inflated experiment-wise alpha level?
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ANOVA uses one test with one alpha level to evaluate the mean differences
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ANOVA divides the total variability into what two basic components?
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Between Treatment Variance and Within-Treatment Variance
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Measures the differences between the sample means
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Between Treatment Variance
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Provides a measure of variability inside each treatment condition
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Within-Treatment Variance
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Between-Treatments Variance explains what two differences
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Differences that are a result of sampling error (naturally occurring) and Differences between treatments (caused by treatment effects)
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Within Treatment Variance explains
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Differences that exist within a treatment that represent random and unsystematic differences that occur when there are no treatment effects causing the scores to be different. Provides a measure of how big the differences are when the null hypothesis is true
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What does the F-Ratio compare?
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Compares between treatment and within treatment variances.
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What does the value obtained from the f-ratio help determine?
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Whether any treatment effects exist.
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What is the denominator of the F-ratio called?
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The error term
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Observed Score = Grand Mean + Treatment Effect + Random Error [SSt = SSa +SSs/a]
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One-Way Between ANOVA
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Degrees of Freedom for One-Way Between ANOVA
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1. df(SSt) = N - 1 / 2. df(SSa) = J - 1 / 3. df(SSs/a) = N-J
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One-Way Between ANOVA: Mean Square Between Group
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MSa = SSa/dfa
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One-Way Between ANOVA: Mean Square Within Group
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MSs/s = SSsa/dfsa
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One-Way Between ANOVA F-test
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F = MSa/MSsa
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The F-value can never be
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NEGATIVE
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One-Way Between ANOVA Distributed Assumptions
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Independence. Identical Within-Group Error Distribution. Random Sampling/Random Assignment. Normal Distribution. Identical Between-Group Error Distribution.
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One-Way Between ANOVA Effect Size when there are only two groups
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Cohen's d
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The proportion of the total variance that is attributed to the treatment effect. Only talks about one factor, doesn't matter the number of levels. Biased estimate (inflated when sample size is large)
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One-Way Between ANOVA Effect Size Eta Squared
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How much difference in the ratio of the proportion explained by treatment and proportion of variance not explained by treatment
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One-Way Between ANOVA Effect Size Cohen's F
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The proportion of the total variance accounted for by the treatment effect in the population. More unbiased measure than eta squared.
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One-Way Between ANOVA Effect Size Omega squared
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Quantitative index of the sensitivity of an experiment. Probability of correctly rejecting a false null hypothesis.
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Power
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Power increases when:
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alpha level increase; size of the treatment effect increases; size of error variance decreases; sample size increases |
