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
Using The One Sample t test Calculator
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.
Interpreting One Sample t test Results
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.