How to Use the Z-Score Table (Standard Normal Table) (2024)

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Saul McLeod, PhD

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Saul McLeod, PhD

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Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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A Z-score table, also called the standard normal table, or z-score chart, is a mathematical table that allows us to know the percentage of values below (usually a decimal figure) to the left of a given Z-score on a standard normal distribution (SND).

How to Use the Z-Score Table (Standard Normal Table) (1)

There are two z-score tables which are:

  1. Positive Z-score Table: Used when the Z-score is positive and above the mean. A positive Z-score table allows you to find the percentage or probability of all values occurring below a given positive Z-score in a standard normal distribution.

  2. Negative Z-score Table: Used when the Z-score is negative and below the mean. A negative Z-score table allows you to find the percentage or probability of all values occurring below a given negative Z-score in a standard normal distribution.

Each type of table typically includes values for both the whole number and tenth place of the Z-score in the rows (e.g., -3.3, -3.2, …, 3.2, 3.3) and for the hundredth place in the columns (e.g., 0.00, 0.01, …, 0.09).

A Z-score table can be used to determine if a score is statistically significant by providing a way to find the p-value associated with a given Z-score.

The p-value is the probability of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is true.

How To Read Z-Score Table

Reading a Z-score table might initially seem tricky, but it becomes pretty straightforward once you understand the layout.

There are two kinds of Z-tables: for “less than” probabilities and for “more than” probabilities. The “less than” table is the most commonly used one.

A Z-score table shows the percentage of values (usually a decimal figure) to the left of a given Z-score on a standard normal distribution.

Here’s how you can read it:

  1. Look at the Z-table. The left column will contain the first part of the Z-score (e.g., the whole number and the first digit after the decimal point). Go down this column until you find your Z-score’s first part.

  2. Next, look at the top row of the Z-table. This row will contain the second part of the Z-score (the remaining decimal number). Go across this row until you find your Z-score’s second part.

  3. The intersection of the row from the first part and the column from the second part will give you the value associated with your Z-score. This value represents the proportion of the data set that lies below the value corresponding to your Z-score in a standard normal distribution.

For example, imagine our Z-score value is 1.09.

First, look at the left side column of the z-table to find the value corresponding to one decimal place of the z-score. In this case, it is 1.0.

Then, we look up the remaining number across the table (on the top), which is 0.09 in our example.

How to Use the Z-Score Table (Standard Normal Table) (2)

The corresponding area is 0.8621, which translates into 86.21% of the standard normal distribution being below (or to the left) of the z-score.

How to Use the Z-Score Table (Standard Normal Table) (3)

To find the p-value, subtract this from 1 (which gives you 0.1379), then multiply by 2 (which gives you p = 0.2758).

The results are not statistically significant because the p-value is greater than the predetermined significance level (p = 0.05), and the null hypothesis is accepted.

Right of a positive z-score

To find the area to the right of a positive z-score, begin by reading off the area in the standard normal distribution table.

Since the total area under the bell curve is 1 (as a decimal value equivalent to 100%), we subtract the area from the table from 1.

For example, the area to the left of z = 1.09 is given in the table as .8621. Thus the area to the right of z = 1.09 is 1 – .8621. = .1379.

Left of a negative z-score

If you have a negative z-score, use the same table but disregard the negative sign, then subtract the area from the table from 1.

Right of a negative z-score

If you have a negative z-score, use the same table but disregard the negative sign to find the area above your z-score.

Finding the area between two z-scores

To find the area between two negative z-scores, we must first find the area (proportion of the SND) to the left of the lowest z-score value and the area (proportion of the SND) to the right of the highest z-score value.

Next, we must add these proportional values and subtract them from 1 (the SND’s total area of the SND.

Further Information

Z-Score Table (for positive or negative scores)

Finding the proportion of a normal distribution that is above a value by calculating a z-score and using a z-table (Kahn Academy Video) Statistics for Psychology Book Download

How to Use the Z-Score Table (Standard Normal Table) (2024)

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