Question

How to use Stata to perform descriptive statistics and show the manual computation of calculating the following test statistics. Also use tables to locate the critical values at the 5% level to test the appropriate hypotheses. using a hypothetical example

Please state these clearly for each test and your final decision and conclusion from test.
a. Pearson’s Chi-squared
b. Student’s independent t-test for two samples
c. F-calculated for One-way analysis of variance
d. Mann Whitney test Z-score
e. Confounding and effect modification investigation either M-H adjusted OR/RR or the weighted Chi-Square for the M-H test of homogeneity of ORs/RRs or if some prefer compute both

Answer 1

To perform descriptive statistics in Stata and manually compute test statistics, you can use the 'summ' command and the relevant formulas. Critical values can be found in statistical tables to make a decision regarding the null hypothesis.

Step-by-step explanation:

Descriptive Statistics in Stata:

To perform descriptive statistics in Stata, you can use the 'summ' command. For example, if you have a variable named 'x', you can type 'summ x' in the Stata command window. This will generate basic descriptive statistics such as mean, standard deviation, minimum, and maximum.

Manual Computation of Test Statistics:

To manually compute test statistics, you need to understand the formulas for each test. Below are the formulas for the test statistics you mentioned:

a. Pearson’s Chi-squared: χ2 = ∑ ((Oij - Eij)2) / Eij

b. Student’s independent t-test for two samples: t = (x1 - x2) / sqrt((s12/n1) + (s22/n2))

c. F-calculated for One-way analysis of variance: F = (MSB / MSW)

d. Mann Whitney test Z-score: Z = (R - (N(N+1))/2) / sqrt((N(N+1)(2N+1))/6)

e. Confounding and effect modification investigation: The calculations depend on the specific tests being conducted.

Critical Values and Decision:

To locate critical values at the 5% level, you will typically refer to statistical tables. The critical values will vary based on the degrees of freedom and the specific test being performed. Based on the test statistics and critical values, you can make a decision regarding the null hypothesis. If the test statistic falls in the critical region, you would reject the null hypothesis; otherwise, you would fail to reject it.