The results let you know if those differences could have occurred by chance, or rather, whether the difference is statistically significant.Ī t-test uses the test statistic, sometimes called a t-value or t-score, the t-distribution values, and the degrees of freedom to calculate the statistical significance of the difference. Where Z is the Z-value for the chosen confidence level, X̄ is the sample mean, σ is the standard deviation, and n is the sample size.A t-test calculates how significant the difference between the means of two groups are. Only the equation for a known standard deviation is shown. For the purposes of this calculator, it is assumed that the population standard deviation is known or the sample size is larger enough therefore the population standard deviation and sample standard deviation is similar. Depending on which standard deviation is known, the equation used to calculate the confidence interval differs. For a sample size greater than 30, the population standard deviation and the sample standard deviation will be similar. If the population standard deviation cannot be used, then the sample standard deviation, s, can be used when the sample size is greater than 30. It does not calculate confidence intervals for data with an unknown mean and unknown standard deviation.Ĭalculating a confidence interval involves determining the sample mean, X̄, and the population standard deviation, σ, if possible. This calculator computes confidence intervals for normally distributed data with an unknown mean, but known standard deviation.

For example, the following are all equivalent confidence intervals:

It can also be written as simply the range of values. The range can be written as an actual value or a percentage. The selected confidence interval will either contain or will not contain the true value, but we cannot say anything about the probability of a specific confidence interval containing the true value of the parameter.Ĭonfidence intervals are typically written as (some value) ± (a range). If 1 of these 100 confidence intervals is selected, we cannot say that there is a 95% chance it contains the true value of the parameter – this is a common misconception. Specifically, the confidence level indicates the proportion of confidence intervals, that when constructed given the chosen confidence level over an infinite number of independent trials, will contain the true value of the parameter.įor example, if 100 confidence intervals are computed at a 95% confidence level, it is expected that 95 of these 100 confidence intervals will contain the true value of the given parameter it does not say anything about individual confidence intervals. This confidence level, such as a 95% confidence level, indicates the reliability of the estimation procedure it is not the degree of certainty that the computed confidence interval contains the true value of the parameter being studied. If the parameter is the population mean, the confidence interval is an estimate of possible values of the population mean.Ī confidence interval is determined through use of observed (sample) data and is calculated at a selected confidence level (chosen prior to the computation of the confidence interval). A confidence interval is a statistical measure used to indicate the range of estimates within which an unknown statistical parameter is likely to fall.

Degrees of freedom calculator