The normal distribution and z-scores
Overview: The normal distribution plays a key role in many statistics and has a set of well-defined characteristics. In general, a normal distribution is one that is symmetric (i.e., not skewed) around the mean, bell-shaped, and with tails that are asymptotic in nature (i.e., the tails continue on to positive and negative infinity, while never actually reaching the X axis). Moreover, there is a fixed relationship between the area under the normal curve and the standard deviation. The normal distribution is actually a family of distributions, each with its own mean and standard deviation. Because there are an infinite number of distributions in this family, the ability to make comparisons between distributions requires the use of some type of "standard". The unit normal (also referred to as the standard normal) distribution is a special distribution that has a mean of 0 and standard deviation of 1. To foster comparisons using this distribution, we convert a normally distributed raw score distribution into z-scores. Using computed z-scores with the unit normal distribution allows us to easily find areas underneath ANY normal curve. Below are links to videos and Powerpoints covering the assessment of normality (versus non-normality), the unit normal distribution and z-scores, and how to use SPSS to compute z-scores and find areas underneath the normal curve using those scores.
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(new, August, 2019) Understanding and assessing normality (versus non-normality) using SPSS: video, Powerpoint, SPSS data
(new, August, 2019) Computing z-scores and using z-table to find areas under normal curve: video, Powerpoint, z-table
(new, August, 2019) Obtaining z-scores (and more) in SPSS: video, SPSS data
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Link to z-score table (creative commons by Emmanuel Rousseaux), pdf
Using SPSS to find z-scores and area under normal curve (Powerpoint), SPSS data file
Additional video presentation of unit normal distribution and z-scores