the use of statistics in psychology

statistics Essential Occasionally misleading

Two types Descriptive – mathematical summaries of results Inferential – statements about large populations derived from small samples

Descriptive statistics Measures of the central score Mean – the average score, found by adding all the scores together and then dividing by the number of scores Vulnerable to skewing by very high scores

Measures of the central score ii Median – the middle score after the scores are arranged from highest to lowest Much less sensitive to skewing

Central score measures iii Mode – the most common score Usually of limited interest

The normal distribution A symmetrical distribution of scores clustered around the mean aka “the bell curve”

Measures of variation Enough about the “central score”, how the scores differ, or vary, within a distribution is just as important The Range – the difference between the highest and lowest score The Standard Deviation – a measurement of the amount of variation among scores in a normal distribution

examples Sample distribution – 1,2,3,3,21 Measures of Central Score Mean = 6 Median = 3 Mode = 3 Variation Range = 20 Standard Deviation = 7.5

Inferential statistics We found a difference between the experimental group and the control group. What does that tell us about the population we are interested in? Could the difference have resulted from chance?

Inferential statistics ii Procedures used to decide whether differences really exist between sets of numbers Does our experimental group significantly differ from the population from which it was drawn?

P or probability value Assesses the odds that we could have gotten such a difference (between the experimental and the control group) at random We want p<.05 and the smaller the p the better we feel. If p<.05, we can claim that the difference is significant – our experiment worked.

Data set 1 Experimental group Mean=7; SD=4.1 Control group Mean= 6; SD= 1

Inferential statistics Statements about large populations taken from small samples How can we be sure that our results really mean something? That they apply to the entire population and not just to the sample?

data set 2 Experimental group Mean = 8 6 SD = Control group Mean = 6 5 SD =

In other words… If the experimental group’s free throw shooting performance had not been affected by the relaxation technique, we would only see such a difference between the two groups in 1 out of 500 occasions. We can reasonably claim that the results supported our hypothesis.