Descriptives

tadaa_nom(ngo$geschl, ngo$abschalt, print = "markdown")
\(\chi^2\) Cramer’s V \(\lambda_x\) \(\lambda_y\) \(\lambda_{xy}\) c
5.35 0.15 0.15 0.03 0.09 0.15



tadaa_ord(ngo$urteil, ngo$leistung, print = "markdown")
\(\gamma\) \(D_x\) \(D_y\) \(D_{xy}\) \(\tau_A\) \(\tau_B\) \(\tau_C\)
0.65 0.51 0.51 0.51 0.39 0.51 0.43



Omnibus Tests

tadaa_aov

One-Way

tadaa_aov(deutsch ~ jahrgang, data = ngo, type = 1, print = "markdown")

Table 1: One-Way ANOVA: Using Type I Sum of Squares

Term df SS MS F p \(\eta^2\) Cohen’s f Power
jahrgang 2 52.57 26.28 6.54 < 0.01 0.05 0.23 0.91
Residuals 247 993.23 4.02
Total 249 1045.8 30.3



tadaa_aov(deutsch ~ jahrgang, data = ngo, type = 2, print = "markdown")

Table 2: One-Way ANOVA: Using Type II Sum of Squares

Term df SS MS F p \(\eta^2\) Cohen’s f Power
jahrgang 2 52.57 26.28 6.54 < 0.01 0.05 0.23 0.91
Residuals 247 993.23 4.02
Total 249 1045.8 30.3



tadaa_aov(deutsch ~ jahrgang, data = ngo, type = 3, print = "markdown")

Table 3: One-Way ANOVA: Using Type III Sum of Squares

Term df SS MS F p \(\eta^2\) Cohen’s f Power
jahrgang 2 52.57 26.28 6.54 < 0.01 0.05 0.23 0.91
Residuals 247 993.23 4.02
Total 249 1045.8 30.3



Two-Way

tadaa_aov(deutsch ~ jahrgang * geschl, data = ngo, type = 1, print = "markdown")

Table 4: Two-Way ANOVA: Using Type I Sum of Squares

Term df SS MS F p \(\eta_\text{part}^2\) Cohen’s f Power
geschl 1 66.56 66.56 18.09 < 0.001 0.07 0.27 0.99
jahrgang 2 52.57 26.28 7.14 < 0.001 0.06 0.24 0.93
jahrgang:geschl 2 28.85 14.42 3.92 < 0.05 0.03 0.18 0.71
Residuals 244 897.82 3.68
Total 249 1045.8 110.95



tadaa_aov(deutsch ~ jahrgang * geschl, data = ngo, type = 2, print = "markdown")

Table 5: Two-Way ANOVA: Using Type II Sum of Squares

Term df SS MS F p \(\eta_\text{part}^2\) Cohen’s f Power
geschl 1 66.56 66.56 18.09 < 0.001 0.07 0.27 0.99
jahrgang 2 52.57 26.28 7.14 < 0.001 0.06 0.24 0.93
jahrgang:geschl 2 28.85 14.42 3.92 < 0.05 0.03 0.18 0.71
Residuals 244 897.82 3.68
Total 249 1045.8 110.95



tadaa_aov(deutsch ~ jahrgang * geschl, data = ngo, type = 3, print = "markdown")

Table 6: Two-Way ANOVA: Using Type III Sum of Squares

Term df SS MS F p \(\eta_\text{part}^2\) Cohen’s f Power
geschl 1 71.4 71.4 19.41 < 0.001 0.07 0.28 0.99
jahrgang 2 52.57 26.28 7.14 < 0.001 0.06 0.24 0.93
jahrgang:geschl 2 28.85 14.42 3.92 < 0.05 0.03 0.18 0.71
Residuals 244 897.82 3.68
Total 249 1050.63 115.79



Testing term sort order

Table 7: Factorial ANOVA: Using Type III Sum of Squares

Term df SS MS F p \(\eta_\text{part}^2\) Cohen’s f Power
G 1 0 0 0 > 0.99 0 0 0.05
G:R 3 188.62 62.87 0.84 0.48 0.03 0.17 0.23
G:R:Z 3 277.6 92.53 1.24 0.3 0.04 0.21 0.33
G:Z 1 3.79 3.79 0.05 0.82 0 0.02 0.06
R 3 34.5 11.5 0.15 0.93 0.01 0.07 0.08
R:Z 3 243.15 81.05 1.08 0.36 0.04 0.2 0.3
Z 1 17.89 17.89 0.24 0.63 0 0.05 0.08
Residuals 84 6288 74.86
Total 99 7053.55 344.5



Kruskal-Wallis

tadaa_kruskal(stunzahl ~ jahrgang, data = ngo, print = "markdown")

Table 8: Kruskal-Wallis Rank Sum Test

\(\chi^2\) df p
20.89 2 < 0.001



Two-Sample Tests

tadaa_chisq

tadaa_chisq(ngo, abschalt, geschl, print = "markdown")

Table 9: Pearson’s Chi-squared test with Yates’ continuity correction

\(\chi^2\) p df Odds Ratio \(\phi\)
4.77 < 0.05 1 0.55 0.15



tadaa_t.test

tadaa_t.test(data = ngo, response = deutsch, group = geschl, print = "markdown")

Table 10: Two Sample t-test with alternative hypothesis: \(\mu_1 \neq \mu_2\)

Diff \(\mu_1\) Männlich \(\mu_2\) Weiblich t SE df \(CI_{95\%}\) p Cohen's d Power
-1.03 7.09 8.12 -4.11 0.25 248 (-1.53 - -0.54) < 0.001 -0.52 0.98



tadaa_t.test(data = ngo, response = deutsch, group = geschl, paired = TRUE,
             print = "markdown")

Table 11: Paired t-test with alternative hypothesis: \(\mu_1 \neq \mu_2\)

Diff \(\mu_1\) Männlich \(\mu_2\) Weiblich t SE df \(CI_{95\%}\) p Cohen's d Power
-1.03 7.09 8.12 -4.21 0.25 124 (-1.52 - -0.55) < 0.001 -0.38 0.99



tadaa_t.test(data = ngo, response = deutsch, group = geschl, var.equal = FALSE,
             print = "markdown")

Table 12: Welch Two Sample t-test with alternative hypothesis: \(\mu_1 \neq \mu_2\)

Diff \(\mu_1\) Männlich \(\mu_2\) Weiblich t SE df \(CI_{95\%}\) p Cohen's d Power
-1.03 7.09 8.12 -4.11 0.25 247.43 (-1.53 - -0.54) < 0.001 -0.52 0.98



tadaa_t.test(data = ngo, response = deutsch, group = geschl, 
             direction = "less", print = "markdown")

Table 13: Two Sample t-test with alternative hypothesis: \(\mu_1 < \mu_2\)

Diff \(\mu_1\) Männlich \(\mu_2\) Weiblich t SE df \(CI_{95\%}\) p Cohen's d Power
-1.03 7.09 8.12 -4.11 0.25 248 (-Inf - -0.62) < 0.001 -0.52 0.99



tadaa_t.test(data = ngo, response = deutsch, group = geschl, 
             direction = "greater", print = "markdown")

Table 14: Two Sample t-test with alternative hypothesis: \(\mu_1 > \mu_2\)

Diff \(\mu_1\) Männlich \(\mu_2\) Weiblich t SE df \(CI_{95\%}\) p Cohen's d Power
-1.03 7.09 8.12 -4.11 0.25 248 (-1.45 - Inf) > 0.99 -0.52 0



tadaa_wilcoxon

tadaa_wilcoxon(ngo, deutsch, geschl, print = "markdown")

Table 15: Wilcoxon rank sum test with continuity correction with alternative hypothesis: \(M_1 \neq M_2\)

Difference \(M_1\) Männlich \(M_2\) Weiblich W p
-1 7 8 5620.5 < 0.001



Table 16: Wilcoxon rank sum test with continuity correction with alternative hypothesis: \(M_1 < M_2\)

Difference \(M_1\) Männlich \(M_2\) Weiblich W p
-1 7 8 5620.5 < 0.001



tadaa_wilcoxon(ngo, deutsch, geschl, paired = TRUE, print = "markdown")

Table 17: Wilcoxon signed rank test with continuity correction with alternative hypothesis: \(M_1 \neq M_2\)

Difference \(M_1\) Männlich \(M_2\) Weiblich W p
-1 7 8 1527 < 0.001



tadaa_wilcoxon(ngo, deutsch, geschl, paired = TRUE, 
               direction = "less", print = "markdown")

Table 18: Wilcoxon signed rank test with continuity correction with alternative hypothesis: \(M_1 < M_2\)

Difference \(M_1\) Männlich \(M_2\) Weiblich W p
-1 7 8 1527 < 0.001



One-Sample Tests

z-Test

# z: known sigma
tadaa_one_sample(data = ngo, x = deutsch, mu = 7.5, sigma = 2, print = "markdown")

Table 19: z-Test with alternative hypothesis: \(\mu_1 \neq\) 7.5

\(\mu_1\) deutsch SE z \(CI_{95\%}\) p Cohen's d Power
7.6 0.13 0.82 (6.59 - 8.62) 0.41 0.05 0.13



tadaa_one_sample(data = ngo, x = deutsch, mu = 8, sigma = 2, 
                 direction = "less", print = "markdown")

Table 20: z-Test with alternative hypothesis: \(\mu_1 <\) 8

\(\mu_1\) deutsch SE z \(CI_{95\%}\) p Cohen's d Power
7.6 0.13 -3.13 (6.59 - 8.62) < 0.001 -0.2 0.93



tadaa_one_sample(data = ngo, x = deutsch, mu = 7, sigma = 2, 
                 direction = "greater", print = "markdown")

Table 21: z-Test with alternative hypothesis: \(\mu_1 >\) 7

\(\mu_1\) deutsch SE z \(CI_{95\%}\) p Cohen's d Power
7.6 0.13 4.78 (6.59 - 8.62) < 0.001 0.3 1



t-Test

tadaa_one_sample(data = ngo, x = deutsch, mu = 7.5, print = "markdown")

Table 22: One Sample t-test with alternative hypothesis: \(\mu_1 \neq\) 7.5

\(\mu_1\) deutsch df SE t \(CI_{95\%}\) p Cohen's d Power
7.6 249 0.13 0.8 (7.35 - 7.86) 0.42 0.05 0.13



Table 23: One Sample t-test with alternative hypothesis: \(\mu_1 <\) 8

\(\mu_1\) deutsch df SE t \(CI_{95\%}\) p Cohen's d Power
7.6 249 0.13 -3.06 (7.35 - 7.86) < 0.01 -0.19 0.92



Table 24: One Sample t-test with alternative hypothesis: \(\mu_1 >\) 7

\(\mu_1\) deutsch df SE t \(CI_{95\%}\) p Cohen's d Power
7.6 249 0.13 4.66 (7.35 - 7.86) < 0.001 0.29 1



Assumptions

Levene

tadaa_levene(ngo, deutsch ~ jahrgang, print = "markdown")

Table 25: Levene's Test for Homogeneity of Variance (Brown-Forsythe Adaption)

Term df F p
jahrgang 2 0.41 0.66
Residuals 247



tadaa_levene(ngo, deutsch ~ jahrgang, center = "mean", print = "markdown")

Table 26: Levene's Test for Homogeneity of Variance

Term df F p
jahrgang 2 0.27 0.76
Residuals 247



tadaa_levene(ngo, deutsch ~ jahrgang * geschl, print = "markdown")

Table 27: Levene's Test for Homogeneity of Variance (Brown-Forsythe Adaption)

Term df F p
jahrgang:geschl 5 0.61 0.69
Residuals 244