All levels checked simultaneously two outcomes iv had

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Unformatted text preview: sence of any difference due to IV levels. All levels checked simultaneously Two outcomes: IV had no effect, or some level of the IV had an effect on the DV. Hypothesis testing H0: m1=m2=m3=....=mk Ha: not (H0: m1=m2=m3=....=mk) When you reject the null hypothesis, H0, you do not know which of the means were different from which others Post hoc tests required Conceptually - how it works Check if between-group variance is larger than within-group variance similar to checking if total variance is larger than error variance within-group variance is an estimate of error variance between-group variance is error variance + a function of systematic variance **BOOK ERROR ABOVE** harken back to project 1 To test if the difference is significant, one uses an F-test F = between group / within group Note the effect of error variance. 3 REMINDER: We’re dealing with inferential statistics here rather than the descriptive stats used in Project 1 Calculations Sums of squares SStotal = S(xi - GM)2 Note that total variance = SStotal / n-1 The total sum of squares = between group SS and within-group SS Within group variance is an estimate of error variance SSwg = S (x1 - x-bar1) 2 + S(x2 - x-bar2) 2 + ... (xk-x-bark) 2 To get an index of average error variance, divide this quantity by the dfwg = n - k This is an estimate of the error variance - variance not accounted for by the IV Between group variance - what does it estimate? There will be some between group variance simply due to error variance If there is no systematic variance, between group variance is an estimate of error variance. SSbg = n1 (x-bar1-GM) 2 + n2 (x-bar2-GM) 2 + nk (x-bark-GM) 2 dfbg = k - 1 MSbg = SSbg / k -1 So the goal is to determine whether the between group variance, MSbg, is very similar to MSwg, thus making it = to the estimate of the error variance OR whether it is greater than MSwg, thus meaning that the group variable, the IV, is causing additional variance. Use an F-test to compare the two: To determine if the F is significant, you look up a critical F in an F-table (Appendix A3). Must know the degrees of freedom and choose an alpha level. So, the steps are: 1. Find SSwg, divide by n - k to get MSwg 2. Find SSbg, divide by k - 1 to get MSbg 3. Calculate F = MSbg / MSwg 4. Look up Fcritical 5. Compare calculated F to F critical Anticipated sizes of F values Note, if you have two groups, F is = t^2 t’s are analogous to ‘std. deviations’ so 2 s.ds above the mean is unusual, i.e. t=2 is a bit unusual. Hence an F of 4 would be considered large See 1st column of A3, p. 275 4 Look at table A3 to get an idea of the sizes of F values that are considered significant. Also, note that the .01 table has higher F values - larger effects are needed if...
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This note was uploaded on 06/30/2012 for the course PSY 211 taught by Professor Chance during the Spring '11 term at University of Phoenix.

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