Mean Difference Test (T-Test) on Simulated Data

This educational script illustrates the process of statistical simulation. It begins by creating a synthetic population of 10,000 individuals with randomly generated sex and height attributes. It calculates the true population means, extracts a simple random sample of 50 individuals, then performs a Student's T-test to determine if the difference in average height between sexes is statistically significant in this sample.

Data Analysis

Type : INTERNAL_CREATION

The 'random_pop1' data is dynamically generated in the first Data Step using random number functions (UNIFORM, NORMAL).

1 Code Block

DATA STEP Data

Explanation :
Generation of a 'random_pop1' table with 10,000 observations. The 'male' variable is randomly assigned (~50%). The 'height' variable is generated according to a normal distribution with different mean and standard deviation parameters depending on sex.

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1	DATA random_pop1 (drop = i x);
2	DO i=1 to 10000;
3	x = uniform(123456);
4	IF x >.5 THEN male = 1;
5	ELSE male = 0;
6	IF male = 1 THEN height = round(71 + 4.32*normal(0), .01);
7	ELSE IF male = 0 THEN height = round(64.3 + 2.11*normal(0), .01);
8	OUTPUT;
9	END;
10	RUN;

2 Code Block

PROC MEANS

Explanation :
Calculation of descriptive statistics (mean, standard deviation, etc.) for the 'height' variable for each sex group ('male') across the entire generated population.

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1	PROC MEANS DATA = random_pop1;
2	class male;
3	var height;
4	title1 "Population Mean Height for Males and Females";
5	RUN;

3 Code Block

PROC SURVEYSELECT Data

Explanation :
Selection of a Simple Random Sample (SRS) of 50 observations from the 'random_pop1' population, stored in the 'random_subpop1' output table.

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1	PROC SURVEYSELECT DATA=random_pop1 noprint
2	seed = 2001
3	method = srs
4	sampsize = 50
5	out = random_subpop1;
6	RUN;

4 Code Block

PROC TTEST

Explanation :
Execution of a Student's T-test for independent samples on the subpopulation. It tests the null hypothesis that the mean heights are equal between males and females.

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1	PROC TTEST DATA = random_subpop1;
2	class male;
3	var height;
4	title1 "T-Test for Difference in Mean Height of Males and Females in Random Population 1";
5	RUN;

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