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 standard normal curve](jpg/standard-normal-curve.jpg)
There are two z-score tables which are:
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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.
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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:
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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.
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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.
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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 How do you find the Z score on a table?](jpg/z-score-table.jpg)
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.
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.