One-Way ANOVA Workshop: Homogeneity and Post Hoc Tests

Workshop One-way Between Subjects ANOVA Test for Homogeneity Post Hoc Test  ANOVA – analysis of variance  Used to if there is determine significant difference in the DV (means) between levels of the IV  One-way (one IV variable)  Between subjects (difference subject in each level)  ANOVA tell us if there is a difference – require a post hoc to determine which groups are significantly different.  Assumption – Homogeneity – check the variances to determine if they are similar across the levels  Assumption of Normality – check across levels to determine if they are normally distributed  As with a t-test we can only infer causation if we are using a true experiment otherwise association are inferred (quasi- experiment)  When to use a non-parametric test – assumptions violated, unequal n  Non Parametric -Between Subject - Krusall Wallis H Test- post hoc MWU

Workshop One-way Between Subjects ANOVA Test for Homogeneity Post Hoc Test Example 3 – use PETREND Example Question: Participants were divided into the following 5 groups (ADJUSTGP) according to their ADJUST score: LOW1 (scores from the 35 to 59), LOW2 (60 to 69), MEDIAN (70 to 79), HIGH1 (80 to 89), and HIGH2 (scores greater than 90). Are SCST scores different for the ADJUSTGPs? If so, which groups are more resourceful? DV = _________________________ IV =______________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _________________________________________________________________________________ Sub-setting and Grouping is done for this question 1. Anaylsis -----Descriptives-----ADJUST and SCST -----include Min and Max ---use min, max for subset if required

Descriptive Statistics -Place SCST, and ADJUST , into the Variable Box -Means, SD, min, max for SCST and ADJUST -Place ADJUSTGP into variable box -Tables- Frequency tables – ADJUSTGP WARDDescriptive Statistics jaspDescriptives::Descriptives( version = "0.17.2", formula = ~ SCST + ADJUST + ADJUSTGP, frequencyTables = TRUE) Descriptive Statistics SCST ADJUST ADJUSTGP Valid 161 161 161 Missing 0 0 0 Mean 17.530 76.129 Std. Deviation 25.522 13.775 Minimum -69.000 35.000 Maximum 76.000 104.000 Note. Not all values are available for Nominal Text variables Frequency Tables Frequencies for ADJUSTGP ADJUSTGP Frequency Percent Valid Percent Cumulative Percent high1 41 25.466 25.466 25.466 high2 29 18.012 18.012 43.478 low1 20 12.422 12.422 55.901 low2 29 18.012 18.012 73.913 median 42 26.087 26.087 100.000 Missing 0 0.000 Total 161 100.000 Note. The following variables have more than 10 distinct values and are omitted: SCST, ADJUST.

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ADJUST has been split into 5 groups , LOW1 (scores from the 35 to 59), LOW2 (60 to 69), MEDIAN (70 to 70), HIGH1 (80 to 89), and HIGH2 (scores greater than 90). Testing Assumptions: Normality  Go to Descriptives in tool bar  Place SCST in variable box and ADJUSTGP in Split box  Click on Distribution Descriptive Statistics jaspDescriptives::Descriptives( version = "0.17.2", formula = ~ SCST, shapiroWilkTest = TRUE, splitBy = "ADJUSTGP") Descriptive Statistics SCST high1 high2 low1 low2 median Valid 41 29 20 29 42 Missing 0 0 0 0 0 Mean 19.589 33.315 -0.743 7.425 20.300 Std. Deviation 21.173 20.931 26.307 26.985 23.748 Shapiro-Wilk 0.976 0.971 0.933 0.984 0.979 P-value of Shapiro-Wilk 0.516 0.589 0.174 0.934 0.640 Minimum - 38.000 -4.000 -69.000 -54.000 -34.000 Maximum 55.000 76.000 45.000 65.000 69.000  Check the p values for Shapiro-Wilk test and the p values

 All the groups are normally distributed therefore we can use a One-way between subjects ANOVA – we still need to check homogeneity of variance One- way between ANOVA Analysis ---- Linear Model - Go the the ANOVA icon in the top tool bar - DV (ATTITUDE) goes in the variable box - IV (grouped) SCSTSP goes in the Fixed Factors box - Display o Descriptive Stats o Estimates of effect size eta square η 2 - Model - type 11 - Homogeneity tests -Levene’s - Post Hoc o move ADJUSTGP to empty box o Standard o Tukey ANOVA jaspAnova::Anova( version = "0.17.2", formula = SCST ~ ADJUSTGP, contrasts = list(list(contrast = "none", variable = "ADJUSTGP")), descriptives = TRUE, effectSizeEstimates = TRUE, homogeneityTests = TRUE, postHocTerms = ~ ADJUSTGP, sumOfSquares = "type2")

ANOVA - SCST Cases Sum of Squares df Mean Square F p η² ADJUSTGP 17360.651 4 4340.163 7.795 9.408×10 -6 0.16 7 Residuals 86860.853 156 556.800 Note. Type II Sum of Squares Descriptives Descriptives - SCST ADJUSTGP N Mean SD SE Coefficient of variation high1 4 1 19.589 21.173 3.307 1.081 high2 2 9 33.315 20.931 3.887 0.628 low1 2 0 -0.743 26.307 5.882 -35.422 low2 2 9 7.425 26.985 5.011 3.634 median 4 2 20.300 23.748 3.664 1.170 Assumption Checks Test for Equality of Variances (Levene's) F df1 df2 p 0.946 4.000 156.000 0.439 Post Hoc Tests Standard Post Hoc Comparisons - ADJUSTGP Mean Difference SE t p tukey high1 high2 -13.726 5.72 5 -2.397 0.121 low1 20.332 6.43 6 3.159 0.016 low2 12.164 5.72 5 2.125 0.215 median -0.711 5.18 1 -0.137 1.000

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Post Hoc Comparisons - ADJUSTGP Mean Difference SE t p tukey high2 low1 34.058 6.85 9 4.966 1.745×10 -5 low2 25.890 6.19 7 4.178 4.642×10 -4 median 13.015 5.69 7 2.284 0.155 low1 low2 -8.168 6.85 9 -1.191 0.757 median -21.043 6.41 1 -3.282 0.011 low2 median -12.875 5.69 7 -2.260 0.164 Note. P-value adjusted for comparing a family of 5 Interpreting the above results Testing Assumptions - Homogeneity of Variance 1. Test for Homogeneity of Variance  Levene’s test  Assumption Checks Test for Equality of Variances (Levene's) F df1 df2 p 0.946 4.000 156.000 0.439  Levene’s test for homogeneity is _________________________________________  We can therefore use ___________________________________________________  Remember we test for normality and found it ____________________

Descriptive Statistics SCST high1 high2 low1 low2 median Valid 41 29 20 29 42 Missing 0 0 0 0 0 Mean 19.589 33.315 -0.743 7.425 20.300 Std. Deviation 21.173 20.931 26.307 26.985 23.748 Shapiro-Wilk 0.976 0.971 0.933 0.984 0.979 P-value of Shapiro-Wilk 0.516 0.589 0.174 0.934 0.640 Minimum - 38.000 -4.000 -69.000 -54.000 -34.000 Maximum 55.000 76.000 45.000 65.000 69.000  Check the p values for Shapiro-Wilk test and the p values Interpret the ANOVA results ANOVA - SCST Cases Sum of Squares df Mean Square F p η² ADJUSTGP 17360.651 4 4340.163 7.795 9.408×10 -6 0.16 7 Residuals 86860.853 156 556.800 Note. Type II Sum of Squares  F (______) = _____, p _______ , η 2 = _______  I s it significant? ________________________________ LOW1 LOW2 MEDIAN HIGH1 HIGH2 Mean SCST Mean SCST Mean SCST Mean SCST Mean SCST

Statistical Results and Interpretation - -------------------------------------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------- - What must we do now? ______________________________________________________ - JASP uses Tukey-Kramer Method not Tukey Honestly significant difference. This takes into account the _____________________ Interpreting the Post Hoc Tests Standard Post Hoc Comparisons - ADJUSTGP Mean Difference SE t p tukey high1 high2 -13.726 5.72 5 -2.397 0.121 low1 20.332 6.43 6 3.159 0.016 low2 12.164 5.72 5 2.125 0.215 median -0.711 5.18 1 -0.137 1.000 high2 low1 34.058 6.85 9 4.966 1.745×10 -5 low2 25.890 6.19 4.178 4.642×10 -4

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Post Hoc Comparisons - ADJUSTGP Mean Difference SE t p tukey 7 median 13.015 5.69 7 2.284 0.155 low1 low2 -8.168 6.85 9 -1.191 0.757 median -21.043 6.41 1 -3.282 0.011 low2 median -12.875 5.69 7 -2.260 0.164 Note. P-value adjusted for comparing a family of 5 Descriptives - SCST ADJUSTGP N Mean SD SE Coefficient of variation high1 4 1 19.589 21.173 3.307 1.081 high2 2 9 33.315 20.931 3.887 0.628 low1 2 0 -0.743 26.307 5.882 -35.422 low2 2 9 7.425 26.985 5.011 3.634 median 4 2 20.300 23.748 3.664 1.170

Chart made from JASP Output to help with the interpretation ( do not put in formal report) Pr(>|t|) 1 st Mean SCST 2 nd Mean SCST Compare the two SCST means LOW2 - LOW1 0.757NS 7.425 -0.743 No difference in the two SCST means MEDIAN - LOW1 0.011* 20.3 -0.743 Median Adjust group SCST mean score is significantly higher than LOW1 Adjust group SCST mean score HIGH1 - LOW1 0.0016* 19.589 -0.743 HIGH1 Adust group SCST score is significantly higher than the LOW1 Adjust group SCST mean score HIGH2 - LOW1 1.745x10 -5 * 33.315 -0.743 HIGH2 SCST significantly higher LOW1 SCST MEDIAN - LOW2 0.164NS 20.3 7.425 Median SCST is not significantly differentLOW2 SCST HIGH1 - LOW2 0.215NS 19.589 7.425 HIGH1 SCST mean is not significantly difference thatn LOW2 SCST mean HIGH2 - LOW2 4.642x10 -4* 33.315 7.425 HIGH2 SCST mean significantly higher than Low 2 SCST mean HIGH1 - MEDIAN 1.00NS 19.589 20.3 No difference in the two SCST means HIGH2 - MEDIAN 0.155NS 33.315 20.3 High 2 SCST mean is not significantly different than Median SCST mean HIGH2 - HIGH1 0.121NS 33.315 19.589 High 2 SCST mean is not significantly different than High1 SCST mean

What to write  LOW1 ( M =______, SD =_____) and LOW2( M = _____, SD = ____) are _________________  MEDIAN ( M =____, SD =______) is ________significantly different LOW2 ( M = ____, SD = ____), HIGH1 ( M =_____, SD = _____) and HIGH2 ( M = ___, SD = _____) adjustment groups  HIGH1 ( M =____, SD = ____)and HIGH2 ( M = ____, SD = ____) are ___ significantly different  LOW1 ( M =____, SD = _____) adjustment groups were significantly ______resourceful than MEDIAN ( M =_____, SD =______) HIGH1 ( M =_____, SD =_____) and HIGH2 ( M = _____, SD = ____) adjustment groups.  LOW2 ( M =____, SD =____) ____significantly ________than HIGH2 ( M =_____, SD = ____)  Do we have an effect of adjustment level on learned resourcefulness? __________________________________________  students in the higher adjustment group ___________________________  middle adjustment groups are _____________having an effect on SCST Write up

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Student one way between ANOVA instructions Jasp version

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