Z-score and p-value
If you are curious about the concepts of Z-score and p-value and ask yourself: "is p-value and z-score the same?" this article is here to help you. We will show you:
- The definition of the z-score and p-value;
- The difference between p-value and z-score; and
- The relevance of p-value and z-score in statistics and real life.
Before exploring the similarities and differences between p-value and z-score, let's first break down each concept individually.
Z-score
The Z-score is a statistical tool that measures the distance of a particular value from the mean of the whole data group. In other words, it shows how far below or above this value is placed in regard to the mean.
This distance is expressed in another statistical measure — standard deviation (SD). So if you have your Z-score, you will know how many standard deviations your value is below or above the mean. Different Z-score values convey a different meaning:
- Zero — the individual value is equal to the mean;
- Positive value — the value is above the mean; and
- Negative value — the particular value lies below the mean.
Not only interpreting, but also calculating the Z-score is quite straightforward:
You can always use the Z-score calculator for reliable calculations.
p-value
The p-value, or probability value, is a measure of statistical significance and credibility for studies. It indicates how likely your results are if the null hypothesis were true (the null hypothesis generally states that there is no real effect or difference, and that any observed effect is due to random chance). In other words, it shows whether your findings are statistically significant or could have happened by chance.
The smaller the p-value, the stronger the evidence against the null hypothesis and the greater the support for the alternative hypothesis. The p-value represents the probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true. Thus, generally:
- p ≤ 0.05 (small p-value) — suggests strong evidence against the null hypothesis; the observed results would be unlikely if the null were true; and
- p > 0.05 (bigger p-value) — suggests weak evidence against the null hypothesis; the results could reasonably be explained by chance.
For more calculations, check our p-value calculator.
By now, you can see how p-value and the Z-score are not the same, but if you want to have a better look at the difference between p-value and Z-score, you can find a comparison table below:
Z-score | p-value |
|---|---|
Distance measure in SD (–∞ to +∞) | Probability measure (0 to 1) |
Descriptive (sample distribution) | Inferential (probability and hypothesis testing) |
Identifies outliers, standardizes values | Assess degree of statistical significance, probability of true effect |
We already have a good idea about the z-score and p-value, so now let's go one step further — why does it matter?
When it comes to the Z-score, it is commonly used in various areas, such as:
- Business — Z-scores help assess risk, comparing a particular financial outcome to the norm;
- Trading — comparing returns with the average stock performance, improving strategies;
- Medicine — assessing whether a patient's test results fall within the normal range; and
- Education — how a student performed relative to their peers on an exam.
The p-value also has a diverse application in the real world:
- Scientific studies — determining whether research findings are meaningful or random;
- Business & marketing — to see whether one campaign, ad, or strategy significantly outperforms another; and
- Product development — measure whether changes in features or design lead to a significant increase in user engagement.
No, p-value and Z-score are not the same, though both are commonly used statistical tools.
The Z-score measures a value's distance from the mean in standard deviations. The p-value, on the other hand, tells us the probability of obtaining results at least as extreme as the observed ones, under the assumption that the null hypothesis is true.
A Z-score shows how many standard deviations a data point is from the mean, while a p-value is the probability of observing a Z-score at least as extreme as the one calculated, assuming the null hypothesis is true. The p-value can be derived from the Z-score, as with a higher Z-score, the p-value is smaller. This is because such results are less likely under the null hypothesis and fall in the tails of the normal distribution.
A Z-score is a descriptive measure that shows how far a value is from the mean in standard deviations and is often used to standardize data or identify outliers. A p-value, on the other hand, is an inferential measure that expresses the probability of observing such results if the null hypothesis is true, in order to assess statistical significance.
Since the Z-score measures the distance of a value from the mean, a high Z-score represents a data point situated far above the mean. Because the unit of measure is standard deviations, a higher positive value (e.g., +2, +3, or higher) indicates that this value is much greater than the average compared to most of the data. While there is no universal definition, a Z-score of +3 is generally considered unusually high in a normal distribution. By contrast, a low (negative) Z-score means the value is far below the average.
This article was written by Julia Kopczyńska and reviewed by Steven Wooding.