Many of the measures that are of interest in psychology are distributed in the following manner: 1) the majority of scores are near the mean 2) the more deviant a score is from the mean the less frequently it appears 3) when large numbers of observations are made the distribution has a smooth, symmetrical shape. IE(DS)

Normal Curve or Distribution Standard Deviations Note: this is a frequency Polygon Ordinate = Frequency Abscissa = Standard Deviations IE(DS)

Normal Curve or Distribution tails Standard Deviations Note: This curve is Asymptotic Tails never touch the abscissa (there are no ends) Represents idea that no extreme is ever impossible IE(DS)

Standard Normal Curve or Distribution Standard Deviations Since there are no ends, we use the Mean of the distribution as the reference point. Mean = 0s IE(DS)

Standard Deviation (SD) - average distance of the scores in the distribution from the mean. What does the word mean? Deviant = different - the larger the SD is for a distribution of data the more spread out the data. Standard = Measurement unit - a set amount used to compare other things to. IE(DS)

Standard Deviation is a measurement unit we use to assess how different one data score is from the mean of the distribution of observations Example: Height in men X = 5’9” SD = 2 John is 5’11” How many SDs is he from the mean? Pat is 5’9 Ron is 5’5”? IE(DS)

Kate’s height is +2 SDs from the mean. Bridget’s is - 3 SDs from the mean. Who is Taller? Cathy is +1.5 SDs from the mean. Is she taller or shorter then Kate? IE(DS)

1) A z score is the number of SDs from the mean a score falls If you know how many standard deviations you are from the mean you can estimate your percentile rank (i.e., what proportion of the people are taller, or shorter than you) in the population. 1) A z score is the number of SDs from the mean a score falls IE(DS)

= .38 Remember fractions from Grade 3? Cutting up a pie? We are going to be doing the same thing except the shape of our pie, is that of the normal curve. = .63 IE(DS)

Normal Curve or Distribution Standard Deviations We can determine the percentage of scores that fall between the mean and any place on the normal curve. IE(DS)

z score = (Score - mean)/ standard deviation Your Test Score = 84 Class Mean = 74 Standard Deviation = 5 z score = (Score - mean)/ standard deviation Measure of how many standard deviations your score is away from the mean. IE(DS)

If the Standard Deviation was 10 what would the z score be? For a normal distribution we can determine the percentage of scores below (or above) any score. IE(DS)

Z-scores allow us to compare our standings (percentile position) in two classes. Since the mean and standard deviations of the two classes are not the same, it is very possible that a person could have a higher class standing in a class in which they had a lower test score. In the following example, the mean for each exam is 50, but they differ on their standard deviations. In which class is a grade of 60 a better score relative to the rest of the class? Class A Mean = 50 s = 10 z =(60 – 50)/10 = +1.0 84th percentile Class B Mean = 50 s = 5 z = (60 – 50)/5 = +2.0 97th percentile IE(DS)

The diagram of the normal curve can be used when the z –score is a whole number (0, 1, 2, or 3). It cannot be used when the z score is any number other than 0, 1, 2 or 3. In that case you need to use a z Table. IE(DS)

Therefore, (.50 + .1915) or 60.15% of the scores are below From Table, the proportion of the distribution that falls between the mean and z = 0.5 is 0.1915. Therefore, (.50 + .1915) or 60.15% of the scores are below 70. IE(DS)

IE(DS)