What is a one sample t-test?

A one-sample t-test is a statistical hypothesis test used to determine whether the mean of a sample is statistically different from a hypothesized value. It's a common test used in various fields when you only have data from a single group.

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

Here are some common applications of a one-sample t-test:

• Comparing a sample mean to a known population mean: For instance, a bakery might use a one-sample t-test to see if the average weight of their bagels is significantly different from the advertised 100 grams.
• Comparing a sample mean to a theoretical value: A researcher might use a one-sample t-test to see if human reaction times on average differ from a hypothesized value of 0.2 seconds.

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

• Assumptions: The one-sample t-test assumes normality of the data (data follows a bell-shaped curve). If your data is highly skewed, you might need to consider non-parametric alternatives.
• Sample size: For reliable results, the sample size should be sufficient (generally recommended to be at least 30).
• Normality testing: Before performing the t-test, it's advisable to conduct normality tests like the Shapiro-Wilk test to check if the assumption of normality is met.

Statistical Programs for One-Sample t-Test

There are many statistical software programs that can perform a one-sample t-test. Here are a few popular options:

• R: t.test(data, mu = hypothesized_value) (where data is your sample and mu is the hypothesized mean)
• Python (SciPy library): scipy.stats.ttest_1samp(data, mu) (similar to R code)
• SAS: PROC TTEST
• SPSS: Analyze > Compare Means > One-Sample T Test
• Excel (Data Analysis ToolPak required): =TTEST(data, hypothesized_value, 2) (2 indicates a two-tailed test)

These are just a few examples, and most major statistical software packages will have a one-sample t-test function.