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Chapter 7 - Analysing the Data Part IV - Analysis of Variance Chapter 1 - Behavioural Science and research Chapter 2 - Research Design Chapter 3 - Collecting the Data Chapter 4 - Analysing the Data Part I - Descriptive Statistics Chapter 5 - Analysing the Data Part II - Inferential Statistics Chapter 6 - Analysing the Data Part III - Common Statistical Tests Frequency distributions Central tendancy Variability The normal distribution Transformations Standard scores - Z scores Correlation and regression Linear regression Readings and links


Chapter 4: Analysing the Data
Part II : Descriptive Statistics


The Normal Distribution

One of the more important distributions in statistics is the "normal" distribution. The normal distribution is depicted in Figure 4.7 below. Notice a few things about its features.

First, it is a symmetrical distribution, meaning that the left half of the normal distribution is a mirror image of the right half.

Second, most of the scores in a normal distribution tend to occur near the center, while more extreme scores on either side of the center become increasingly rare. As the distance from the center increases, the frequency of scores decreases.

Third, the mean, median, and mode of the normal distribution are the same.

Figure. 4.7 Histogram of Computer-Generated Normal Data

Some people claim that the many variables are distributed normally, including such things are heights, IQ scores, performance on psychological tests, and other things that psychologists often study. While there is some truth to the claim that many distributions are similar to the normal distribution, I believe the ubiquity of the normal curve as a description of a distributionŐs shape has been somewhat exaggerated. There is evidence that when you look carefully enough, many of the things that appear normally distributed in fact are not. Still, many of the constructs that we study, when measured, do approximate a normal distribution, so it is worth understanding its properties. As well, a prominent assumption or requirement for statistical tests is normality in the parent population from which the scores came. We can only check normality in the parent population by checking normality in the sample of scores we have. For most purposes, an approximately normal curve is fine. That is, one that does not deviate significantly from our symmetry.




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