Free statistics calculators designed for data scientists. This One Sample t test Calculator:

- Compares Sample to Expected Mean
- Assesses if significant difference
- Save & Recycle Data Between Projects

For the details about designing your test, read the guidance below. To use the calculator, enter the data from your sample as a string of numbers, separated by commas. Adjust the calculator's settings (expected population mean, significance level, one or two tailed test) to match the test goals. Hit calculate. It will compute the t-statistic, p-value, and evaluate if we should accept or reject the proposed hypothesis.

For easy entry, you can copy and paste your data into the entry box from Excel. You can save your data for use with this calculator and other calculators on this site. Just hit the "save data" button. It will save the data in your browser (not on our server, it remains private). Saved data sets will appear on the list of saved datasets below the data entry panel. To retrieve it, click the "load data" button next to it.

- Statistics and Histogram Graph
- Save data sets in your browser
- Easily Share results via email

- Critical Value Calculator (New!)
- P From Z Score
- P From T Score
- Critical value of t
- Critical value of Z
- Binomial Distribution
- Bernoulli Distribution
- Chi Square Distribution
- F Distribution

- Poisson Distribution
- Hypergeometric Distribution
- Beta Distribution
- Gamma Distribution
- Geometric Distribution
- Negative Binomial
- Lognormal Distribution
- Pareto Distribution
- Weibull Distribution

This calculator is designed to evaluate a statement about the mean of a population using a sample drawn from that population. We refer to this statement as the null hypothesis, a claim we would accept in the absence of other evidence. This occurs by accepting the alternate hypothesis, which should be a mutually exclusive claim. For example, in quality control, we may test a batch of product to ensure it meets a particular standard about the strength of the product. Our null hypothesis would be that the strength rating is at least 150 lbs; our test will confirm this (accept the null hypothesis) or indicate we should accept the alternative hypothesis (strength under 150 lbs, reject).

One of the parameters in the calculator asks you to select if you want to run a one sided or two-sided test. A one sided test can be used to test if the sample mean is significantly below the expected mean for the population. The example above was a one-sample test. A two sided test looks for any significant deviation (up or down) relative to the null hypothesis. The two sided test is best when screening for differences, the one side test is useful if checking for a particular defect.

Mathematically, the t-statistic is a composite of several basic metrics from the descriptive statistics panel. We compare the sample mean with the expected value and compare the difference with the sample standard deviation, adjusted for sample size. The sample size is also used to calculate the degrees of freedom for the statistical distribution. The t-statistic is converted into a probability value based on Student's t-distribution, which is used to make the final assessment about the null hypothesis.

It is critical to remember some fundamental assumptions about the underlying population and sample process, particularly if you regularly sample. Increasing the sample size will inevitably make any result appear more significant, through increasing the degrees of freedom reflected in the statistic. This can be problematic if subtle factors in the underlying population change in the process (shift changes, time of day, operating conditions). It often makes sense to split your experiment into parts and seek to replicate results across different periods and operators to ensure your determination is accurate.