# How to find p value from z score?

In statistical analysis, the p-value is a measure of the probability that the results of a study could have occurred by chance. It is used to determine the statistical significance of the results and to decide whether or not to accept or reject a hypothesis.

The z-score calculates how far a number deviates from a distribution’s mean by how many standard deviations. It is calculated by subtracting the mean of the distribution from the value in question, and dividing the result by the standard deviation of the distribution.

There could be instances where you want to find the p-value from a z-score, such as when you are performing a hypothesis test and need to determine the statistical significance of the results. In this case, you can use the z-score to calculate the p-value.

## How to calculate p value from z score?

To find the p-value from a z-score, you will need to use a z-table or a statistical software package.

### Step 1: Determine the z-score

The first step in finding the p-value from a z-score is calculating the z-score itself. This is done by subtracting the mean of the distribution from the value in question, and then dividing the result by the standard deviation.

For example, suppose you are interested in the height of adult males in a certain population. The mean height is 68 inches, and the standard deviation is 2.5 inches. If you measure the height of an individual male and find that he is 72 inches tall, you would calculate his z-score as follows:

Z-score = (72 inches – 68 inches) / 2.5 inches = 4 / 2.5 = 1.6

### Step 2: Look up the p-value in a z-table or statistical software

Once you have calculated the z-score, the next step is to look up the corresponding p-value in a z-table or statistical software package.

A z-table is a table of values that gives the area under the standard normal curve for a given z-score. To use a z-table, you will need to determine whether your z-score is positive or negative and then check the table to see what value corresponds.

If your z-score is positive, you will need to look up the value on the right-hand side of the table, It is equivalent to the region beneath the curve to the right of the mean. If your z-score is negative, you will need to look up the value in the left-hand side of the table, It is the region under the mean’s left-hand curve.

For example, using the z-score calculated in the previous step (1.6), you would look up the value in the right-hand side of the table since the z-score is positive. The corresponding p-value would be the area under the curve to the right of the mean, approximately 0.9332.

Alternatively, you can use a statistical software package such as R or SPSS to calculate the p-value from a z-score. These software packages have built-in functions allowing you to input the z-score and calculate the corresponding p-value automatically.

### Step 3: Interpret the p-value

Once you have calculated the p-value, the final step is to interpret the results. A p-value of less than 0.05 is generally considered statistically significant, indicating that it is improbable that the observed result was the result of pure chance.

However, it is important to note that a p-value of 0.05 does not necessarily mean that the null hypothesis is true. It simply means that the observed result is not statistically significant, and further research is needed to confirm or refute the hypothesis. For example, consider a z-score of 2.5. If we look in the standard normal distribution table, we find that the corresponding probability is 0.9938. This means that the p-value for a z-score of 2.5 is 0.9938.

## Conclusion: How to find p value from z score?

In conclusion, finding the p value from a z score can be useful for statistical analysis and hypothesis testing. By using the z score formula and a z score table, you can determine the probability that a given value falls within a certain range or distribution. This can help you to understand the likelihood of certain outcomes and make informed decisions based on statistical evidence. It is important to remember that the p value represents the probability of obtaining a result that is at least as extreme as the one observed, given that the null hypothesis is true. Consequently, the more evidence there is against the null hypothesis, the smaller the p-value and the more likely it is that the observed result is due to something other than chance. Overall, finding the p value from a z score can be a helpful way to analyze and interpret statistical data and provide valuable insights into the relationships and patterns within your data.