7
Experimental Research Methods (Fach) / L4 (Lektion)
After this lecture and studying the materials, students are able to:
• Explain the assumptions of ANOVA and when ANOVA is robust to violations of these assumptions
• Specify simple and complex contrasts
• Specify contrasts in case of equal and unequal sample sizes
• Interpret the output of SPSS when a hypothesis using a planned contrast is tested
Diese Lektion wurde von tklmn erstellt.
Diese Lektion ist leider nicht zum lernen freigegeben.
- ANOVA vs. t-test vs. regression The hypothesis tested in ANOVA, independent samples t-test, and regression analysis is the same if K = 2 The hypothesis tested in ANOVA, independent samples t-test, and regression analysis is the same if K = 2 t-value is the same as in the independent samples t-test, F-value is the same as in the ANOVA
- Assumptions of a statistical test • The result of a statistical test is valid if all assumptions of the test are met• If an assumption of a test is violated, then the test is: (i) robust or (ii) not robust to a violation of thatassumption• A test is robust to the violation if the true p-value is approximately equal to the reported p-value (whichyou can find in the SPSS-output)• A test is not robust if the true p-value of the test is not equal to the reported p-value• If (i) the test is robust to the violation, then the results of the test (the reported p-value) is still consideredto be valid• If (ii) the test is not robust to the violation, the results of the test (the reported p-value) is not valid usea different testLec
- Assumptions ANOVA 1. Independent observations (methodological assumption) • Violated in case of repeated measures of the same person • ANOVA not robust to violation! use Repeated Measures ANOVA as a different test2. Residuals are normally distributed for each group • ANOVA robust to violation if sample size per group ?? ≥ 30 • If ?? < 30 use different test that is not discussed in this course3. The variance of the residuals is the same across groups; this property is known as the homogeneity of variance assumption • Tested using the Levene’s test in SPSS • ANOVA robust to violation if the highest ?? is not more than 1.5 times as high as the lowest ?? • If variances within groups are unequal and highest ?? is more than 1.5 times as high as the lowest ?? use different test that is not discussed in this course
- Recap ANOVA • Technique used to compare multiple groups in one Omnibus test• Tests the following null hypothesis: H0: “all K groups have the same mean” H1: not H0• In ANOVA, we can split the total Sum of squares (SST) into the Sums of squares between (SSB) and the Sums of squares within (SSW)• We can calculate the F-statistic using the Mean squares between (MSB) and the Mean squares within (MSW)
- Testing contrasts : a specific comparison between group means. For example, we can contrast themean of Therapy I to Therapy II
- specific groups comparisons To better understand the nature of the group-mean differences, we need a way to decidewhich individual means do indeed differ from each other
- Experiment-wise Type I error level The probability of finding at least one Type I error
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