Comparison of means calculator
Computational notes
This procedure calculates the difference between the observed means in two independent samples. A significance value (P-value) and 95% Confidence Interval (CI) of the difference is reported. The P-value is the probability of obtaining the observed difference between the samples if the null hypothesis were true. The null hypothesis is the hypothesis that the difference is 0.
The program first calculates the pooled standard deviation s:
where s_{1} and s_{2} are the standard deviations of the two samples with sample sizes n_{1} and n_{2}.
The standard error se of the difference between the two means is calculated as:
The significance level, or P-value, is calculated using the t-test, with the value t calculated as:
The P-value is the area of the t distribution with n_{1} + n_{2} − 2 degrees of freedom, that falls outside ± t (see Values of the t distribution table).
Literature
- Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.