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Z-Scores

Sometimes we want to do more than summarize a bunch of scores. Sometimes we want to talk about particular scores within the bunch. We may want to tell other people about whether or not a score is above or below average. We may want to tell other people how far away a particular score is from average. We might also want to compare scores from different bunches of data. We will want to know which score is better. Z-scores can help with all of this.

They Tell Us Important Things

Z-Scores tell us whether a particular score is equal to the mean, below the mean or above the mean of a bunch of scores. They can also tell us how far a particular score is away from the mean. Is a particular score close to the mean or far away?

If a Z-Score….

ü      Has a value of 0, it is equal to the group mean.

ü      Is positive, it is above the group mean.

ü      Is negative, it is below the group mean.

ü      Is equal to +1, it is 1 Standard Deviation above the mean.

ü      Is equal to +2, it is 2 Standard Deviations above the mean.

ü      Is equal to -1, it is 1 Standard Deviation below the mean.

ü      Is equal to -2, it is 2 Standard Deviations below the mean.

Z-Scores Can Help Us Understand…

How typical a particular score is within bunch of scores. If data are normally distributed, approximately 95% of the data should have Z-score between -2 and +2. Z-scores that do not fall within this range may be less typical of the data in a bunch of scores.

Z-Scores Can Help Us Compare…

Individual scores from different bunches of data. We can use Z-scores to standardize scores from different groups of data. Then we can compare raw scores from different bunches of data.