One-Sample t-test

One-sample t-test is a parametric test of whether the mean of a continuous variable differs from a specified reference value, dividing the difference by the estimated standard error to form a t statistic.

일표본 t검정은 연속형 변수의 평균이 지정한 기준값과 다른지를, 그 차이를 추정 표준오차로 나눈 t 통계량으로 판단하는 모수 검정이다.

How do I test whether my sample mean differs from a known value or benchmark?

표본 평균이 기준값이나 알려진 값과 다른지 어떻게 검정하나요?

The one-sample t-test compares the mean of one continuous variable with a fixed value, such as a scale midpoint, a published norm or a target, and reports a t statistic with n − 1 degrees of freedom. It assumes approximately normal data, which matters mainly in small samples, and is usually reported with a confidence interval and Cohen's d.

When to use One-Sample t-test

• Comparing a sample mean with a population norm, target or scale midpoint
• One continuous variable measured in a single sample
• Approximately normal data, or a sample large enough for the central limit theorem to apply

When to use something else

• Small, clearly non-normal samples or ordinal scores: use the one-sample Wilcoxon signed-rank test
• Testing a proportion rather than a mean: use the one-proportion z-test

Assumptions and requirements

• Independent observations
• Continuous variable
• Approximately normal distribution, especially in small samples

What the analysis reports

• t statistic, degrees of freedom and two-sided p-value
• Sample mean and the test value (0 unless set)
• 95% confidence interval for the mean
• Cohen's d
• Normality check with histogram and Q-Q plot

How to report it

A one-sample t-test showed that the mean [variable] (M = [value], 95% CI [[value], [value]]) differed significantly from [test value], t([df]) = [value], p = [value], d = [value].

Related methods

• Paired Samples t test
• Wilcoxon Signed Rank Test
• One-Proportion z-test

Run One-Sample t-test on Quorant