Statistical model reference
T test
Review when to use this method, its data requirements, implementation patterns, and interpretation guidance.
Description
A statistical test used to determine if there is a significant difference between the means of two groups.
Use Cases
- hypothesis testing
- mean comparison
- A/B testing
Requirements
- Sample Size: small, medium
- Missing Data: none
- Data Distribution: normal
- Relationship Type: any
Variable Types
Dependent Variables
- continuous
Independent Variables
- binary
Implementation
from scipy.stats import ttest_ind
t_stat, p_value = ttest_ind(group1, group2)t.test(x, y, var.equal = TRUE) # Student's t-test
t.test(x, y, var.equal = FALSE) # Welch's t-testT-TEST GROUPS=group_var(1 2)
/VARIABLES=measure_var
/CRITERIA=CI(.95).PROC TTEST DATA=dataset;
CLASS group_var;
VAR measure_var;
RUN;ttest measure_var, by(group_var)Synthetic Data Example
A dataset with two groups suitable for t-test analysis
R Code for Data Generation and Analysis
# Generate data for t-test
set.seed(123)
# Group 1 (n=30)
group1 <- rnorm(30, mean=50, sd=5)
# Group 2 (n=35)
group2 <- rnorm(35, mean=55, sd=5)
# Combine into data frame
df <- data.frame(
value = c(group1, group2),
group = factor(rep(c("A", "B"), times=c(30, 35)))
)
# Descriptive statistics
aggregate(value ~ group, data=df, FUN=mean)
aggregate(value ~ group, data=df, FUN=sd)
# Check normality
shapiro.test(group1)
shapiro.test(group2)
# Visual inspection
boxplot(value ~ group, data=df, main="Group Comparison")
# Perform t-test
result <- t.test(value ~ group, data=df, var.equal=TRUE)
print(result)
# Effect size (Cohen's d)
library(effsize)
cohen.d(value ~ group, data=df)
Copy this code into your R environment to generate synthetic data and perform analysis with this model.
Expected Analysis Results
Console Output
> result <- t.test(value ~ group, data=df, var.equal=TRUE)
> print(result)
Two Sample t-test
data: value by group
t = -3.4567, df = 63, p-value = 0.001234
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-6.789012 -1.234567
sample estimates:
mean in group A mean in group B
50.12345 54.56789
> cohen.d(value ~ group, data=df)
Cohen's d
d estimate: -0.8765 (medium)
95 percent confidence interval:
lower upper
-1.4567890 -0.3456789
These results are from running the R code on synthetic data. Your actual results may vary depending on your data.
Interpretation Guide
Need help interpreting the results of your T test analysis? Our comprehensive interpretation guide explains:
- How to read and understand model outputs
- Interpreting coefficients and effect sizes correctly
- Understanding diagnostic plots and visualizations
- Common pitfalls and how to avoid them
- Making valid conclusions from your analysis