A two-sample t-test for independent samples, also known as an independent-samples t-test or Student's t-test, is a statistical hypothesis test used to compare the means of two independent groups. It determines if the observed difference between the means is likely due to random chance or reflects a true difference between the populations the samples were drawn from.

What do you use a two-sample t-test for?

Here are some common applications of a two-sample t-test for independent samples:

• Comparing the effectiveness of two treatments: Researchers might use a t-test to see if a new medication is significantly more effective than a standard treatment in reducing blood pressure.
• Analyzing customer preferences: A company might use a t-test to compare customer satisfaction ratings for two different product designs.
• Examining group differences: A study might use a t-test to see if there's a significant difference in average exam scores between students who participated in a tutoring program and those who didn't.

What to pay attention to while performing a two-sample t-test?

• Independence of samples: The groups must be independent, meaning there's no connection between the data points in each group (e.g., participants assigned randomly to different groups).
• Normality of data (sometimes): While not always a strict requirement, the data in each group ideally follows a normal distribution (bell-shaped curve) for more reliable results.
• Homogeneity of variance: This refers to the assumption that the variances (spread) of the data in both groups are similar. Some versions of the t-test are more robust to violations of this assumption.

Statistical Programs for two-sample t-test

Many statistical software programs can perform a two-sample t-test for independent samples. Here are a few popular options:

• R: t.test(data1, data2, var.equal = TRUE) (data1 and data2 are your independent samples, var.equal specifies assumption of equal variances)
• Python (SciPy library): scipy.stats.ttest_ind(data1, data2, equal_var = True) (similar to R code)
• SAS: PROC TTEST (specify independent samples in the code)
• SPSS: Analyze > Compare Means > Independent Samples T Test
• Excel (Data Analysis ToolPak required): =TTEST(data1, data2, 2) (2 indicates a two-tailed test)

These are just a few examples, and most major statistical software packages will have a function for this type of t-test.