## Z Scores

 Getting Started General Instructions | Introduction to Your Study | Experimental Design | Stating a Hypothesis Descriptive Statistics Histograms | Central Tendency | Standard Deviation | Confidence Intervals Comparing Two Samples Samples and Populations | Choosing a T-Test | Paired T-Test | P-Values and T-Tables Important Concepts The Normal Distribution | Z Scores | Probability Distributions Levels You are currently on Z Scores at level 2. Level 1 | Level 2 | Level 3 Next Topic The Normal Distribution | Probability Distributions

### Explanation

Calculating and Using z Scores

The method of calculating a z score is very simple: subtract the sample mean from the value and divide what you get by the sample standard deviation.

It should be obvious to the reader that the resulting number (z) has the following properties:

• z is positive when the value is greater than the mean
• z is negative when the value is less than the mean
• z is the number of standard deviations between the value and the mean.
• z is zero when the value equals the mean
• z has no theoretic upper or lower bound apart from that caused naturally by the range that values can take.
In normally distributed data, 99.99% of the distribution falls below the point where z = 4, so z will rarely be greater than 4 or less than -4.

### Exploration

The formula for calculating a z score is given below.

It reads: z equals x minus the sample mean, all over the sample standard deviation, where x is the value for which a z score is required.

Hover over any part of the formula for an explanation of what it means.

### Application

Now we turn to your own data. We will look at items correctly recalled in the 100 msecs sample. The mean of items correctly recalled in the 100 msecs sample is 13.9 and the standard deviation is 1.92.

Use the calculator to calculate z scores for the following values from your data. Give your answers to 2 decimal places.

 To calculate the z score for the value 15,first calculate 15 - 13.9: Now divide the number you entered aboveby the standard deviation (shown above)The value you get is the z score for 15 Calculate the z score for 10 Calculate the z score for 12 Calculate the z score for 14 Calculate the z score for 18
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