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23 Cards in this Set
- Front
- Back
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One Way Analysis of Variance
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Analytic technique that is used when you have a single (nominal) independent variable with three or more levels, and a single interval-level dependent variable.
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The F statistic is a variance ratio.
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Numerator = Between groups variance
Denominator = Within groups variance. |
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Whereas t-tests evaluate mean differences against a measure of standard deviation
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F-tests evaluate mean differences against a measure of variance.
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We now are interested in testing three or more group differences simultaneously
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Allows for multiple comparisons among means while controlling for protection to the Type I error rate – more on this later.
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ANOVA can be used for between groups designs or repeated measures designs.
BTWN: |
Between groups design: each individual is exposed to only one level of the independent variable of interest.
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ANOVA can be used for between groups designs or repeated measures designs.
REPEATED |
Repeated measures design: each individual is exposed to each level of the independent variable of interest (often the repeated measure is time: 3 or more waves of data collection).
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The variance estimates that make up the F-ratio are called “Mean Squares.” So the F ratio is actually:
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MS BTWN/MS Within
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as the # of samples increases
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the number of t tests necessary to compare every possible pair of means increases at an even greater rate
probability of a type i error becomes far larger than .05 |
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ANOVA as a technique allows us to first test whether or not there is an overall difference (AKA, an “omnibus difference”) between means.
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If F is significant, it means that at least one of the means is significantly different from the rest – but we don’t know which ones.
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The One-Way Between-Groups ANOVA: Applying the Six Steps of Hypothesis Testing
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1. Identify the populations, the comparison distribution, and the assumptions.
2. State the null and alternative hypotheses 3. Define the characteristics of the comparison distribution 4. Determine the critical values 5. Calculate the observed F (the test statistic) 6. Reject/fail to reject the Null, and interpret the results. |
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The F distribution is NOT symmetrical, it is positively skewed.
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Thus, all tests are one-tailed.
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Critical values are defined by the degrees of freedom between groups and the degrees of freedom within groups.
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DF between groups = degrees of freedom for the numerator.
DF within groups = degrees of freedom for the denominator. Total DF = DF between + DF within. |
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Tukey’s HSD Test
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“Honestly significant difference”
We evaluate a specific mean difference and divide it by the standard error |
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HSD Critical Value
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Critical value for the HSD test: the q-statistic.
The HSD value is compared to the q-critical value. If observed is beyond critical, comparison is significant. |
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Bonferroni correction.
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Uses the original .05, and divides it by the number of comparisons we’re making. If the comparisons are significant at that new alpha level, comparison is significant.
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Two-Way ANOVA: When the Outcome Depends on More than One Variable
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Factorial analysis of variance
One interval dependent measure and two or more nominal independent measures Each independent measure is called a factor |
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Why use a two-way ANOVA?
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A three-for-one design
Main effects for each independent variable Plus an interaction effect – that is how one variable behaves based on the level of the other variable Cell: a box that depicts one unique combination of levels of the independent variable Arrangement of cells: e.g., 2 x 3 ANOVA |
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A 2 X 3 Design
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The Number of numbers refers to the number of independent variables in the design.
The value of each number refers to the number of levels each variable has. Multiply the values of the design together to identify the number of experimental conditions (i.e., cells). Thus, a 2 X 3 Design has two independent variables, one with two levels and another with three levels. How many “cells” in the design? How many mean comparisons? |
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Main effect
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The effect of one independent variable “collapsing” (i.e., ignoring) the other variable.
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Interaction
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When the effect of one independent variable “depends on” the level of the other independent variable.
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Understanding Interactions
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Effect of one independent variable varies as a function of the level of the other independent variable
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Quantitative interaction
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strengthening or weakening of the effect, but the direction of the initial effect is unchanged
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Qualitative interaction
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effect of one independent variable is reversed depending on the level of the other independent variable
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