204 Part III . Taking Chances for Fun and Profit Standard scores are so powerful and useful because they can be compared with one another without regard to their mean or stan- dard deviation values. Also, we can use our knowledge of the normal curve and assign a probability to the occurrence of a value that is 1 standard devia- tion from the mean. This is a very powerful idea, and we'll do it later in the chapter. Although there are other types of standard scores (such as t scores), the one that you will see most frequently in your study of statistics is called a z score. This is the result of dividing theamount that a raw score differs from the mean of the distribution by the standard deviation (see Formula 8.1). ( x - X) Z (8.1) where is the z score; X is the individual score; X is the mean of the distribution; and is the distribution's standard deviation. For example, in Formula 8.2, you can see how the z score is cal- culated if the mean is 100, the raw score is 110, and the standard deviation is 10: (110-100) 2 = = +1.0 (8.2) 10 It's just as easy to compute a raw score given a z score as the other way around. You already know the formula for a z score given the raw score, mean, and standard deviation. But if you know only the z score and the mean and standard deviation, then what's the corresponding raw score? Easy. Just use the formula X - (z x s) + X . You can easily convert raw scores to z scores and back again if necessary. For example, a z score of -0.5 in a distribution with a mean of 50 and an s of 5 would equal a raw score of X = (-0.5 x 5) + 50, or 47.5.Let's say I'm interested in studying the relationship between how much time 9 year-old children spend outdoors playing and their academic achievement. 1A) What would the NULL hypothesis be in this example?. 1B) Write a possible directional hypothesis for this example. 2) Name at least 2 qualities or characteristics of a NORMAL distribution. 3) Let's calculate some z-scores. You may do this by hand using the formula on pg. 204, or making an excel spreadsheet and using the =STANDARDIZE() function. These scores were taken from a data set with a M=25, SD=5 A) 35 Z= B) 25 Z = C) 20 Z = D) 23:5 Z= 4) In social research (SW, psychology, sociology, etc.), we accept a significance level of p<.05. what is significance level and why does it matter>