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 5: One-Way ANOVA: Using Type I Sum of Squares

Term	df	SS	MS	F	p	\(\eta^2\)	Cohen’s f
jahrgang	2	52.57	26.28	6.54	< .01	0.05	0.23
Residuals	247	993.23	4.02
Total	249	1045.8	30.3

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

Table 6: One-Way ANOVA: Using Type II Sum of Squares

Term	df	SS	MS	F	p	\(\eta^2\)	Cohen’s f
jahrgang	2	52.57	26.28	6.54	< .01	0.05	0.23
Residuals	247	993.23	4.02
Total	249	1045.8	30.3

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

Table 7: One-Way ANOVA: Using Type III Sum of Squares

Term	df	SS	MS	F	p	\(\eta^2\)	Cohen’s f
jahrgang	2	52.57	26.28	6.54	< .01	0.05	0.23
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 8: Two-Way ANOVA: Using Type I Sum of Squares

Term	df	SS	MS	F	p	\(\eta_\text{part}^2\)	Cohen’s f
geschl	1	66.56	66.56	18.09	< .001	0.07	0.27
jahrgang	2	52.57	26.28	7.14	< .001	0.06	0.24
jahrgang:geschl	2	28.85	14.42	3.92	< .05	0.03	0.18
Residuals	244	897.82	3.68
Total	249	1045.8	110.95

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

Table 9: Two-Way ANOVA: Using Type II Sum of Squares

Term	df	SS	MS	F	p	\(\eta_\text{part}^2\)	Cohen’s f
geschl	1	66.56	66.56	18.09	< .001	0.07	0.27
jahrgang	2	52.57	26.28	7.14	< .001	0.06	0.24
jahrgang:geschl	2	28.85	14.42	3.92	< .05	0.03	0.18
Residuals	244	897.82	3.68
Total	249	1045.8	110.95

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

Table 10: Two-Way ANOVA: Using Type III Sum of Squares

Term	df	SS	MS	F	p	\(\eta_\text{part}^2\)	Cohen’s f
geschl	1	71.4	71.4	19.41	< .001	0.07	0.28
jahrgang	2	52.57	26.28	7.14	< .001	0.06	0.24
jahrgang:geschl	2	28.85	14.42	3.92	< .05	0.03	0.18
Residuals	244	897.82	3.68
Total	249	1050.63	115.79

Testing term sort order

set.seed(0)
data.frame(A = rnorm(100, mean = c(25, 30, 45)),
           G = c(rep("a", 50), rep("b", 50)),
           R = sample(letters[3:6], size = 100, TRUE),
           Z = sample(letters[7:8], size = 100, TRUE)) %>%
  tadaa_aov(data = ., formula = A ~ G * R * Z, type = 3, print = "markdown")

## Warning in tadaa_aov(data = ., formula = A ~ G * R * Z, type = 3, print =
## "markdown"): Some independent variables are not factors, auto-converting...

## Warning in tadaa_aov(data = ., formula = A ~ G * R * Z, type = 3, print =
## "markdown"): Converting G to factor, please check your results

## Warning in tadaa_aov(data = ., formula = A ~ G * R * Z, type = 3, print =
## "markdown"): Converting R to factor, please check your results

## Warning in tadaa_aov(data = ., formula = A ~ G * R * Z, type = 3, print =
## "markdown"): Converting Z to factor, please check your results

Table 11: Factorial ANOVA: Using Type III Sum of Squares

Term	df	SS	MS	F	p	\(\eta_\text{part}^2\)	Cohen’s f
G	1	66.51	66.51	0.88	.35	0.01	0.1
G:R	3	184.97	61.66	0.82	.488	0.03	0.17
G:R:Z	3	22.77	7.59	0.1	.959	0	0.06
G:Z	1	7.73	7.73	0.1	.75	0	0.03
R	3	687.47	229.16	3.04	< .05	0.1	0.33
R:Z	3	137.54	45.85	0.61	.612	0.02	0.15
Z	1	0.68	0.68	0.01	.925	0	0.01
Residuals	84	6336.13	75.43
Total	99	7443.79	494.59

Kruskal-Wallis

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

Table 12: Kruskal-Wallis Rank Sum Test

\(\chi^2\)	df	p
20.89	2	< .001

Two-Sample Tests

`tadaa_chisq`

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

## Warning: Unknown or uninitialised column: `cramers`.

Table 13: Pearson’s Chi-squared test with Yates’ continuity correction

\(\chi^2\)	p	df	Odds Ratio	\(\phi\)
4.77	< .05	1	0.55	0.15

`tadaa_t.test`

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

Table 14: 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
-1.03	7.09	8.12	-4.11	0.25	247.43	(-1.53 - -0.54)	< .001	-0.52

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

Table 15: 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
-1.03	7.09	8.12	-4.21	0.25	124	(-1.52 - -0.55)	< .001	-0.38

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

Table 16: 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
-1.03	7.09	8.12	-4.11	0.25	247.43	(-1.53 - -0.54)	< .001	-0.52

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

Table 17: Welch 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
-1.03	7.09	8.12	-4.11	0.25	247.43	(-Inf - -0.62)	< .001	-0.52

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

Table 18: Welch 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
-1.03	7.09	8.12	-4.11	0.25	247.43	(-1.45 - Inf)	> .99	-0.52

`tadaa_wilcoxon`

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

Table 19: 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	< .001

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

Table 20: 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	< .001

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

Table 21: 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	< .001

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

Table 22: 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	< .001

One-Sample Tests

z-Test

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

Table 23: z-Test with alternative hypothesis: \(\mu_1 \neq\) 7.5

\(\mu_1\) deutsch	SE	z	\(CI_{95\%}\)	p	Cohen's d
7.6	0.13	0.82	(6.59 - 8.62)	.411	0.05

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

Table 24: z-Test with alternative hypothesis: \(\mu_1 <\) 8

\(\mu_1\) deutsch	SE	z	\(CI_{95\%}\)	p	Cohen's d
7.6	0.13	-3.13	(6.59 - 8.62)	< .001	-0.2

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

Table 25: z-Test with alternative hypothesis: \(\mu_1 >\) 7

\(\mu_1\) deutsch	SE	z	\(CI_{95\%}\)	p	Cohen's d
7.6	0.13	4.78	(6.59 - 8.62)	< .001	0.3

t-Test

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

Table 26: One Sample t-test with alternative hypothesis: \(\mu_1 \neq\) 7.5

\(\mu_1\) deutsch	df	SE	t	\(CI_{95\%}\)	p	Cohen's d
7.6	249	0.13	0.8	(7.35 - 7.86)	.423	0.05

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

Table 27: One Sample t-test with alternative hypothesis: \(\mu_1 <\) 8

\(\mu_1\) deutsch	df	SE	t	\(CI_{95\%}\)	p	Cohen's d
7.6	249	0.13	-3.06	(7.35 - 7.86)	< .01	-0.19

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

Table 28: One Sample t-test with alternative hypothesis: \(\mu_1 >\) 7

\(\mu_1\) deutsch	df	SE	t	\(CI_{95\%}\)	p	Cohen's d
7.6	249	0.13	4.66	(7.35 - 7.86)	< .001	0.29

Assumptions

Levene

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

Table 29: 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 30: 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 31: Levene's Test for Homogeneity of Variance (Brown-Forsythe Adaption)

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

Markdown Test Output

Lukas Burk

2020-06-01 UTC