P Value Calculator for Z-Score

Z-Score: 4.5
p value: 0.0000
This result is statistically significant

Tool Overview: P Value Calculator for Z-Score

This p value calculator allows you to convert your Z-statistic into a p value and evaluate it for a given significance level. Simply enter your Z score (we have a Z score calculator if you need to solve for the Z-statistic) and hit calculate. It will generate the p-value for that Z-statistic. This standard score indicates the probability of that value occuring within a variable that follows the standard normal distribution.

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.

How To Conduct Hypothesis Testing

Let's take a moment to explore statistical hypothesis testing. A hypothesis test is rigorous way to translating the observed result of a test into a statistical inference about the process or population you took the sample from. We reduce the question to two possibilities, each of which is mutually exclusive (and ideally, collectively exhaustive - the two options covers all reasonable possibilities). For example, we may run a political poll. This data can be used to predict if the incumbent candidate will stay in office (null hypothesis) or the challenger will win (alternate hypothesis).

We will then run an experiment (or take a sample). The data from this effort is used to assess the likelihood that your sample came from the null population. We identify a sampling distribution for your test statistic which describes what should naturally occur (modeling your default case as a random variable fitting specific parameters.

Here is an example of a statistical hypothesis test. Let us assume that when a manufacturing machine is operating properly, you should waste not more than 3% of the raw materials as scrap. Every shift, we start with the hypothesis that the machine is working correctly. The alternative hypothesis is that something has changed. We will look at where our sample falls on a normal curve. The p-value (probability value) associated with that spot tells us if we have a statistically significant result. We will approach this as cumulative distribution function.

We can refine this test with our assumptions. In addition to the test statistic, we will set an alpha level value, which is the risk of falsely rejecting the null hypothesis. 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).

Statistical hypothesis testing plays many key roles in applied science. The observed value of an experiment can have great influence. 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.

This tool effectively replaces the use of a Z-score table. We have another version that works for calculating the p value from a t statistic if you are working with small sample sizes and need to use Student's t-distribution.

For other resources, check out this overview or this tutorial video.

About this Website

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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