Question

Describe how to obtain a p-value for a chi-squared test for independence.

Describe how the two sample means test is different from the paired means test, both conceptually and in terms of the calculation of the standard error.

What visualizations are useful for checking each of the conditions required for performing ANOVA?

Answer 1

Que 1. Describe how to obtain a p-value for a chi-squared test for independence

Ans:

Let Oi→observed count.

Ei→expected count.

Df=(r-1)*(s-1)

Then test statistics

Observed ( X^2)=

Then P value=prob(chisquar ≥observed(X^2))

Que2)

Describe how the two sample means test is different from the paired means test, both conceptually and in terms of the calculation of the standard error.

Ans:

When both samples are independent then we use two sample means test.

Standard errors=(√(S1^2/n1+S2^2/n2)

Test statistics(t) =(X1bar - X2 bar)/√(s1^2/n1+ s2^2/n2).

When the both sample are not independent (i.e same individual are selected in both sample.) Before abd after term are included.

We use paired means test.

Xd=X1-X2

Xd_bar=mean of difference(X1 -X2 )

Standard deviations of Xd( X1-X2)=Sd

Standard errors=Sd/√n

Test statistics(t)=(Xd_bar )/(Sd/√n).

Que3)

What visualizations are useful for checking each of the conditions required for performing ANOVA.

Ans:

Assumption of ANOVA.

1. Sample is distributed normally in each group.

2. The population variance is constant.

3.all sample are independent from each other.

4..the observations are independent.

Thanks!