T-Score: 4.5

p value: 0.0002

This result is statistically significant

p value: 0.0002

This result is statistically significant

The P value in statistics is part of hypothesis testing. A statistician will define the problem in terms of two mutually exclusive statements: the null hypothesis (the default state being correct) and the alternative hypothesis (the sample data is unlikely to occur by accident and is statistically significant). The p value the probability of the observed results of the test occuring if we accept that the null hypothesis is true.

P-values tell us whether our data is the result of random events or represents a true change in the process. The specifics of the latter depend on how you set up the problem. It could be things such as are temperatures above normal, is a factory process out of control, or does a pattern of transactions indicate likely fraud.

This p value calculator allows you to convert your t statistic into a p value and evaluate it for a given significance level. Simply enter your t statistic (we have a t score calculator if you need to solve for the t score) and hit calculate. It will generate the p-value for that t score.

This calculator is designed to help you run a statistical hypothesis test. This is rigorous method of translating the observed result of an experiment into a statistical inference. We express this inference as two mutually exclusive (and collectively exhaustive) hypotheses. The null hypothesis represents the "default state" of your process, the results of which are modeled as a random variable. The alternate hypothesis is the viewpoint that the observed result is sufficiently different from the expected values of the sampling distribution that it came from a different sampling distribution.

For example, let us assume the average sandwich in the cafeteria is five inches wide, give or take an inch (the excess being a uniformly distributed random variable). Our null hypothesis might be: nothing changed. If we take a sample of sandwiches and see a bunch of foot long measurements, that is clearly outside the range of the expected distribution. We must reject the hypothesis that nothing changed and look for root causes (like a new bread supplier). For many common tests, we will compare this difference to a normal curve to assess if this is a statistically significant result.

In practice, you will identify a test statistic. You can also specify the alpha level value for the test, which is the risk of falsely rejecting the null hypothesis. This is expressed as a probability value. We refer to this as the level of significance for the test. Depending on your test, other items may be needed to refine your comparisons: measures of the underlying population variation (standard deviation, standard error), sample standard deviation, or average value (mean). This helps give perspective to the observed value of your statistic.

Statistical hypothesis testing plays many key roles in applied science. Drug trials are a hypothesis test that the new drug works as expected. Political surveys test if the sample proportion in the survey is enough to conclude you will win on election day. Colleges may use standard score tests to assess if a student is ready for college admissions.

It important to keep the key assumptions and common sense in mind when doing statistical hypothesis testing. Remember that you can only predict what is represented in your sample. I also keep an eye on effect size (different between null and alternate hypothesis), especially if there is a risk my sample isn't representative. That 1 foot wave on a quiet lake isn't predictive of what happens in a winter storm.

If you're just using this as a tool to check your homework, that should be sufficient. However, if you enter a given significance level and specify if you want to look at this as a one-tailed or two-tailed probability, the p value calculator will also render an opinion on the statistical significance of that result. This is generated using Student's t distribution, adjusted for degrees of freedom (basically, your sample size).

This tool effectively replaces the use of a t score table. We have another version that works for calculating the p value from a z score if you are working with large sample sizes and want to use the standard normal distribution.

This t score calculator is part of a larger collection of tools we've assembled as a free replacement to paid statistical packages. The other tools on this site include a descriptive statistics tool, confidence interval generators (standard normal, proportions), linear regression tools, and other tools for probability and statistics. Many calculators allow you to save and recycle your data in similar calculations, saving you time and frustration. Bookmark us and come back when you need a good source of free statistics tools. This specific page replaces the need for a critical value calculator with sample size.

Other Tools: P Value From Z Score, P Value From T Score, Confidence Interval (proportion), t critical value calculator, z critical value calculator

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