# One-sample t-test

**BRIEF DESCRIPTION**

The One-Sample t-test is for continuous scaled data and it compares an observed sample mean with a predetermined value. For example, is our customer satisfaction sample mean significantly different from a pre-set figure such as an industry benchmark or an action standard. It also helps us to answer a question such as “Are we 95% confident that the mean score is between 7.5 and 8.5”. The t-test is a parametric procedure.

**SIMILAR STATISTICAL PROCEDURES**

**One-sample z-test****Non-parametric counterparts**of the one-sample t-test include the Wilcoxon signed rank test and the Binomial test**The Runs test**

**CHARACTERISTICS OF THE VARIABLES**

**Dependent variable**: continuous scaled data**Independent variable**: not applicable

**ASSUMPTIONS**

- Continuous scaled data
- Population is normally distributed although it suffices if the sample data does not significantly deviate from a normal distribution
- Cases of the samples should be independent.
- Random sampling from a defined population
- No outliers

**WHERE TO FIND IN SPSS?**

ANALYZE / COMPARE MEANS/ ONE-SAMPLE T-TEST

**HOW TO REPORT THE FINDINGS?**

If the t-test is significant (e.g. p‘<‘.05) then it indicates that our sample mean differs significantly from our predetermined value (e.g. benchmark or action standard)

**Reporting example**: “A comparison was made between the job satisfaction results for the organisation (mean=2.80, sd=1.3) and the benchmark for the industry (mean =4.25). A one sample t-test revealed a statistically significant difference, t (95) = -3.20, p‘<‘.05″. The actual p-value can be reported in lieu of the ‘<‘.05 (e.g. p=.041). NOTE: If p‘>‘.05 you don’t report the value (e.g. p‘>‘.05 or p=.129) but only indicate it as NS (non-significant). At the end you may want to indicate the effect size (Cohen’s d) e.g. d=.45. Cohen’s d measures difference of means in standard deviation units.**Explanation of above example**: The t refers to our One-sample t-test procedure, the 95 in brackets is the degrees of freedom (df), the -3.20 is the actual t-test value, and the p<.05 indicates an actual p-value which is less (e.g. .023) than our chosen confidence level of .05.

**FURTHER COMMENTS.**

Be careful with any significance tests if you have a large sample, at which time it becomes critical to calculate the effect size (Cohen’s d).

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