T-Test

Assumptions to check:

Each sample has been randomly selected from the populations from which the samples are derived.
The distribution of data in the underlying population from each of the samples is derived is normal. Normal distribution (testable by e.g. Kolmogorov–Smirnov test, Shapiro–Wilk test, the Anderson-Darling test, Q-Q plot)
The variances of the underlying population represented by populations are equal. Equal variances (homoscedasticity) of the group samples (testable by e.g. F-test, Levene’s test, Bartlett’s test, Brown-Forsythe test)
Group independence (for independent/unpaired test) or full dependence (for dependent/paired test)

Report design in methods section

Is this a one or two group test?
For two groups: is it paired (dependent groups) or unpaired (independent groups) test?
One or two tails? Justify the use of one tail test, if applicable.
Name the statistical package or program used in the analysis

Report statistics in results section

The t-statistic, degrees of freedom and exact p-value.
Strongly recommended: report effect size (e.g Cohen’s) with confidence intervals.
Report on assumptions.

Examples

One sample:
- Methods section: The hypothesis was checked with one sample t-test with two tails. We used SPSS (RRID:SCR_002865) to perform the analysis.
- Results section: A one sample t-test showed a statistically significant difference between the cholesterol level of patients on the provided diet compared to the norm of 200 mg/dL (t(28)=2.16, p=0.039, CI=[185, 194]). The effect size, as measured as Cohen’s d=0.61, indicates a medium effect.

  
    
    Static
        Degrees of freedom df
        Significance p-value
        Confidence interval
        Effect size
  

    Factor
    t=2.16    
    df=28
    p=0.039
    CI=[185, 194]
        d=0.61
  

According to the Shapiro-Wilk and Levene tests, the normality (W=0.955, p=0.77) and homoscedasticity (F=2.428, p=0.122) assumptions were not violated.

Two independent samples:
- Methods section: Hypothesis was checked with an independent two-tailed t-test. We used GraphPad Prism (RRID:SCR_002798) to perform the analysis.
- Results section: Hypothesis was checked with the independent two-tailed t-test which indicated a statistically significant difference in measurements between the group getting placebo and the group getting the medicine(t(35)=2.52, p=0.022, 95% CI=[114, 183] with effect size measured with Cohen’s d=0.55 -medium effect)

  
    
    Static
        Degrees of freedom df
        Significance p-value
        Confidence interval
        Effect size
  

    Placebo/medicine
    t=2.52    
    df=35
    p=0.022
    [114,183]
95%

        0.55 (Cohen)
  

According to the Shapiro-Wilk and Levene tests, the normality (W=0.955, p=0.77) and homoscedasticity (F=2.428, p=0.122) assumptions were not violated.

Two dependent samples:

Methods section: To check significance of the difference for before and after treatment results we used two tailed t-test for dependent samples. To perform the analysis we used Microsoft Excel (RRID:SCR_016137).
Results section: We used two tails paired samples t-test, which indicated a significant difference between the groups before and after treatment (t=5.180, df=99, p=0.001, 95% CI=[0.17,1.83] with effect size measured with Cohen’s d=0.518 -medium effect)

  
    
    Static
        Degrees of freedom df
        Significance p-value
        Confidence interval
        Effect size
  

    Before/after
    t=5.180    
    df=99
    p=0.001
    [0.17,1.83]
95%

        0.518 (Cohen)
  

According to the Shapiro-Wilk test, the normality assumption was not violated (W=0.976, p=0.063).