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

 

CHARACTERISTICS OF THE VARIABLES

  • Dependent variable: continuous scaled data
  • Independent variable: not applicable
 
ASSUMPTIONS
  1. Continuous scaled data
  2. Population is normally distributed although it suffices if the sample data does not significantly deviate from a normal distribution
  3. Cases of the samples should be independent.
  4. Random sampling from a defined population
  5. 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)
  1. 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. 
  2. 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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