If the p-value is greater than alpha, there is insufficient evidence to reject the null hypothesis. If the p-value is less than or equal to alpha, typically 0.05, the results are considered statistically significant, leading to the rejection of the null hypothesis in favor of the alternative hypothesis. The calculated p-value is used in comparison with a predefined significance level (alpha) to make decisions about the null hypothesis.
It is clear to see that we must be very careful to know which inference procedure we are working with. The number of degrees of freedom for the denominator is the total number of data values, minus the number of groups, or n - c. To perform a two sample t-test, simply fill in the information below and then click the Calculate. The number of degrees of freedom for the numerator is one less than the number of groups, or c - 1. If this is not the case, you should instead use the Welch’s t-test calculator. This type of test assumes that the two samples have equal variances. A lower p-value suggests stronger evidence against the null hypothesis, indicating that the observed result is unlikely to have occurred by random chance alone. As discussed above, if has a standard normal distribution, has a Gamma distribution with parameters and and and are independent, then the random variable defined as has a standard Students t distribution with degrees of freedom. A two sample t-test is used to test whether or not the means of two populations are equal. The p-value represents the probability of obtaining results as extreme as, or more extreme than, the observed data, assuming the null hypothesis is true. When performing each t-test, you’ll have to calculate a test statistic and a corresponding degrees of freedom. It takes as input the observed test statistic, the null hypothesis, and the relevant parameters of the statistical test (such as degrees of freedom), and computes the p-value. For the statistic t, with degrees of freedom, A(t ) is the probability that t would be less than the observed value if the two means were the same (provided that the smaller mean is subtracted from the larger, so that t 0). A P-value calculator is used to determine the statistical significance of an observed result in hypothesis testing.