Question

Can someone interpret these results especially the test statistic, degree(s) of freedom, p-value, effect size, confidence interval, F statistic and R squared

Note: I have been sending in questions with the same data and no one has been answering.

Gender	Stat Experience	Mean	SD	Min	Max	n
Male (0)	No Stats Exp (0)	58.98	9.74	40.00	76.91	30
Male (0)	Some Stats Exp (1)	65.43	10.87	47.53	82.04	16
Female (1)	No Stats Exp (0)	63.76	10.89	42.46	83.37	35
Female (1)	Some Stats Exp (1)	78.78	11.52	57.69	100.00	19

Model Summary (General Linear Model)

R Squared	R Squared (adj)	F	p.value	df	df residual
0.3	0.28	13.84	0	3	96

Coefficient Summary Table

term	estimate	95% CI Lower	95% CI Upper	std.error	t	p.value
(Intercept)	58.98	55.11	62.85	1.95	30.26	0.000
stat_experienceSome Stats Exp	6.45	-0.11	13.01	3.30	1.95	0.054
genderFemale	4.78	-0.50	10.05	2.66	1.80	0.075
stat_experienceSome Stats Exp:genderFemale	8.57	-0.34	17.49	4.49	1.91	0.059

Answer 1

Model summary(general linear model):

Null Hypothesis (H0):The intercept only model and your model are equal.

Alternative Hypothesis (H1): The intercept only model is reduced significantly compared to your model.

Test statistic, F =13.84 whose p-value at df(numerator) =3 and at df(denominator) =96 is p-value =0.0000. Since p-value < 0.05 significance level, the null hypothesis(H0) is rejected.

Since p-value is very less, there is a strong evidence in favour of the alternative hypothesis. Thus, your model provides a better fit than the intercept only model.

R squared =0.3 =30%. It means 30% of the variation in the dependent variable is explained by the change in the independent variable. This does not consider whether the variable is significant or not.

Adjusted R squared =0.28 =28%. It means 28% of the variation in the dependent variable is explained by the change in the independent variable. This considers only those variables that are significant.

Coefficient Summary Table:

If the confidence interval contains 0, then the variable is not significant. It it does not contain 0, then the variable is significant.

If p-value < 0.05 significance level, the variable is significant. Otherwise, it is not significant.

So, the variables stat_experienceSome Stats Exp, gender Female, stat_experienceSome Stats Exp:gender Female are not significant. Intercept is significant.

Effect is measured by Cohen's d.

d =|M1 - M2|/Sd(pooled)

Where Sd(pooled) =pooled std.deviation =sqrt[(s1² + s2²)/2]; M1 and M2 are means of two groups that are being compared.

If d =0.2, the effect size is considered small.

If d =0.5, the effect size is considered medium.

If d =0.8, the effect size is considered large.