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 astandard normal distribution(SND).The standard normal distribution represents all possible Z-scores in a visual format. The total area under this curve is 1, or 100% when expressed as a percentage. Each Z-score corresponds to a specific area under this curve. A Z-table is kind of like a cheat sheet that statisticians and mathematicians use to quickly figure out what percentage of scores are above or below a certain Z-score.There are two z-score tables which are: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.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.
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 astandard normal distribution(SND).
The standard normal distribution represents all possible Z-scores in a visual format. The total area under this curve is 1, or 100% when expressed as a percentage. Each Z-score corresponds to a specific area under this curve. A Z-table is kind of like a cheat sheet that statisticians and mathematicians use to quickly figure out what percentage of scores are above or below a certain Z-score.
There are two z-score tables which are:
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.
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).
The p-value is the probability of obtaining a result at least as extreme as the one observed, assuming thenull hypothesisis 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 givenZ-scoreon a standard normal distribution.
Here’s how you can read it:
Look at the Z-table. Theleft columnwill 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.
Next, look at thetop rowof 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.
Theintersection of the rowfrom 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.
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.
Using a z-score table to calculate the proportion (%) of the SND to the left of the z-score.
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.
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
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)
