# Z score table calculator

Use this P to Z calculator to easily convert P-values to Z-scores standard scores and see if a result is statistically significant.

## Z Score Calculator

Supports one-tailed and two-tailed p-values. Detailed information about what a Z-score is. If you have a p-value statistic for a given set of data and want to convert it to its corresponding Z score this P to Z calculator will help you accomplish that. Simply enter the P-value and choose whether it was computed for a one-tailed or two-tailed significance test to calculate the corresponding Z score using the inverse normal cumulative PDF probability density function of the normal distribution.

If you have made a directional inference, saying something about the sign or direction of the effect, then your p-value should have been calculated as one-tailed, corresponding to a one-sided composite null hypothesis.

### Z-Score Guide

If the direction of the effect did not matter in the initial p-value calculation, select two-tailed, which corresponds to a point null hypothesis. Since the normal distribution is symmetrical, it does not matter if you are computing a left-tailed or right-tailed p-value: just select one-tailed and you will get the correct result for the direction in which the observed effect is. If you want the Z score for the other tail of the distribution, just reverse its sign, e. The Z-score is a statistic showing how many standard deviations away from the normal, usually the mean, a given observation is.

It is often called just a standard score, z-value, normal score, and standardized variable. The standard score is calculated by estimating the variance and standard deviation, then deriving the standard error of the mean, after which a standard score is calculated using the formula  :. The interpretation of a Z-score has problems similar to that of p-values and confidence intervals, on which you can read more in our respective pages. One of the applications of standard scores is in constructing prediction intervals.

A prediction interval [L,U] is an interval such that a future observation X will lie in the interval with a given probability, i. Below are some commonly encountered p-values and their corresponding standard scores, assuming a one-tailed hypothesis. Forster Eds.

## z-Score Calculator: Standard Normal Distribution

Handbook of the Philosophy of Science. The Netherlands: Elsevier. If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.

Calculators Converters Randomizers Articles Search. Type of P-value. Calculate Z-score. Share calculator:. Embed this tool! Using the p-value to z-score calculator If you have a p-value statistic for a given set of data and want to convert it to its corresponding Z score this P to Z calculator will help you accomplish that.Please provide any one value to convert between z-score and probability.

This is the equivalent of referencing a z-table. Related Standard Deviation Calculator. The z-score, also referred to as standard score, z-value, and normal score, among other things, is a dimensionless quantity that is used to indicate the signed, fractional, number of standard deviations by which an event is above the mean value being measured. Values above the mean have positive z-scores, while values below the mean have negative z-scores.

The z-score can be calculated by subtracting the population mean from the raw score, or data point in question a test score, height, age, etc. The z-score has numerous applications and can be used to perform a z-test, calculate prediction intervals, process control applications, comparison of scores on different scales, and more. A z-table, also known as a standard normal table or unit normal table, is a table that consists of standardized values that are used to determine the probability that a given statistic is below, above, or between the standard normal distribution.

The table below is a right-tail z-table. Although there are a number of types of z-tables, the right-tail z-table is commonly what is meant when a z-table is referenced. Financial Fitness and Health Math Other.The probability of a result x in an experiment consisting of a large number of equally probable independent trials n is approximated by the normal probability density function :. Since the mean value and standard deviation depend upon the number of trials in the experiment, comparison between experiments with differing numbers of trials is facilitated by standardising the result: transforming it to a distribution with mean value zero and standard deviation of 1.

A normally distributed experimental result x is thus standardised by subtracting the mean and dividing by the standard deviation of the experiment:. The probability can be calculated from the cumulative standard normal distribution :.

Which gives the probability P that an experimental result with a z value less than or equal to that observed is due to chance. Subtracting P from one:. Unfortunately, there is no closed form solution for Pso it must be evaluated numerically. This page allows you to calculate the probability of chance occurrence of a given zor to calculate z given a probability Q. All calculations are performed with six decimal places of accuracy; the maximum z accepted is 6.

Note that the probability calculated from the z is an approximation which is valid only for large values of nand is therefore only meaningful when calculated for experiments with a large number of individual trials. In order to use this page, your browser must support JavaScript. The text field below indicates whether JavaScript is available; if not, consider switching to a browser which implements it.

Calculate probability Q from z One of the most common probability calculations is determining, given the measured z value from an experiment or set of experiments, the probability of the result being due to chance. Enter the z value in the box below, press the Return key or the Calculate button, and the probability will appear in the Q box.

The chance probability, Qis: or about one in Calculate z from probability Q To determine the z score indicating a probability Q of non-chance occurrence for an experiment, enter Q in the box below and press the Return key or the Calculate button.Definition: Z-score, sometimes called standard score, is a measurement of how many standard deviations a point is away from the mean of its data set.

To be more specific it is a measurement of the number of standard deviations a data point is above or below the mean population. This statistical measurement is used to compare data points from different data sets to find correlations.

Z score can be zero, positive or negative. If the score is zero, it indicates that the score is identical to the mean. In other words, it point is average. Positive values represent how far above the mean a point is on the distribution curve. Negative values represent how far below the mean a point is on the distribution curve. This concept was adapted to the business and finance world by Dr. Edward Altman who used it predict the likelihood that a company would go bankrupt.

His calculation called the Altman Z-score, sums several weighted financial ratios and compares it to a graded scale. The lower the score, the more likely the company is to declare bankruptcy. The Z-score formula is calculated by subtracting the total score from mean and then dividing it by standard deviation. The Altman Z-score equation is calculated by weighting various financial ratios and comparing their sum to a graded scale. The equation looks like this:. As you can see, the Altman score weights different profitability and liquidity metrics to arrive at the overall score. This overall score is then compared to the following grading scale. A student named Emily asked the teacher if by scoring 70 she has performed well or not.

Considering the standard deviation of 15, it is very likely that there is a significant variation among the scores. To answer the question how well Emily performed in the coursework compared to other students in the class we can use the Z score. For finding out the number of students in the class that scored higher or lower than Emily, we will look at the normal distribution table. In this case the Z-value comes to 0. It means that the probability of a score being higher than 0. Coming back to the question, we can clearly see that Emily performed better than Use this free calculator to generate a Z score. Enter a value, population mean and the standard deviation for the population. Before we dig in and explain to you how you can use our z score calculator, we believe that it is always best to start at the beginning. And with this w mean to start by explaining to you some things you need to know about the z score.

Simply put, a z score is the number of standard deviations from the mean a data point is. The truth is that you can see that this is a much more simple definition of z score than the one that you probably heard in your classroom.

However, if you want to put the z score definition in more technical terms, then we can say that the z score is a measure of how many standard deviations above or below the population mean a raw score is.

One of the things that you should keep in mind is that sometimes, the z score is also referred to as a standard score.

Besides, it is worth to point out that you can place the z score on a normal distribution curve. Discover how to find a confidence interval.

Notice that w are referring to the results from surveys and tests that can have thousands of possible units or results.

When you are using z scores, it is important that you have something to compare them against or they may be meaningless. Understanding the F Test. When you are trying to do a z score calculation, you can do it by hand but you can also use our simple and free z score calculator that is located at the top of this page. If you take a quick look at our z value calculator, you can easily see that there are three different variables. So, if you check our z value calculator, you can see that you will need to fill out three different blanks: the population mean, the population standard deviation, and the value.

As soon as you fill out all these values, you just need to click on the Calculate button to get your z score. Imagine that you just had a test and you scored So, you want to calculate your z score to know where you are standing compared to the rest of the classroom.

So, you will need to add to the calculator the population mean which, in this case is 70, the standard deviation which in this case is 6, and the value for which you want to calculate the z score which in this case is As you can see, it is very easy to use our z score calculator when you want to calculate the z score.Different data sets will have different means and standard deviations, so values from one set cannot always be compared directly with those from another.

The z-score standardizes normally distributed data sets, allowing for a proper comparison and a consistent definition of percentiles across data sets.

Z-scores can be found in a table, but using a TI Plus calculator is easier and more accurate. There are two methods of finding the z-score of a data set: you can use the TI Plus to find the mean and standard deviation and then use the z-score equation, or you can use the TI Plus invNorm function with a percentile as the argument. The screen will change to show the current lists and an entry line at the bottom of the screen. If less than three lists exist in the calculator memory, the screen will show empty columns.

Move the cursor to an empty list using the arrow keys if the list currently selected is not empty. Calculate the mean and standard deviation of the data set. Press STAT and then the right arrow key, which will bring up the menu for statistics calculations.

Make sure the list name shown is the same list in which you entered your data. If it is not, use the arrow keys to move to the list name and type in the correct list. Leave FreqList blank. The screen will change again to show several statistics parameters, including the mean and standard deviation.

Record these two parameters to use in the z-score equation. Calculate the z-score by subtracting the mean from any data point in your list and then dividing that answer by the standard deviation. Enter the desired percentile as a decimal next to the word area. For example, to find the z-score associated with the 95th percentile, type 0.

Press Enter again, and the TI Plus will calculate the z-score associated with the chosen percentile. Joshua Bush has been writing from Charlottesville, Va. He has authored several articles in peer-reviewed science journals in the field of tissue engineering. Bush holds a Ph.The Normal Distribution Calculator makes it easy to compute cumulative probability, given a normal random variable; and vice versa.

### P-value to Z-score Calculator

To learn more about the normal distribution, go to Stat Trek's tutorial on the normal distribution. Note : The normal distribution table, found in the appendix of most statistics texts, is based on the standard normal distributionwhich has a mean of 0 and a standard deviation of 1.

To produce outputs from a standard normal distribution with this calculator, set the mean equal to 0 and the standard deviation equal to 1. Instructions: To find the answer to a frequently-asked question, simply click on the question.

If you don't see the answer you need, try the Statistics Glossary or check out Stat Trek's tutorial on the normal distribution. The normal distribution is important because it describes the statistical behavior of many real-world events.

The shape of the normal distribution is completely described by the mean and the standard deviation. Thus, given the mean and standard deviation, you can use the properties of the normal distribution to quickly compute the cumulative probability for any value. This process is illustrated in the Sample Problems below. There are an infinite number of normal distributions. Although every normal distribution has a bell-shaped curve, some normal distributions have a curve that is tall and narrow; while others have a curve that is short and wide.

The exact shape of a normal distribution is determined by its mean and its standard deviation. The standard normal distribution is the normal distribution that has a mean of zero and a standard deviation of one. The normal random variable of a standard normal distribution is called a standard score or a z-score. The normal random variable X from any normal distribution can be transformed into a z score from a standard normal distribution via the following equation:.

Because any normal random variable can be "transformed" into a z score, the standard normal distribution provides a useful frame of reference. In fact, it is the normal distribution that generally appears in the appendix of statistics textbooks. In this equation, the random variable X is called a normal random variable.

Normal Distribution Table - Z-table Introduction

A unique cumulative probability can be associated with every normal random variable. Given the normal random variable, the standard deviation of the normal distribution, and the mean of the normal distribution, we can compute the cumulative probability i.