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

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?

significance tests Assess the odds that we could have gotten

such a difference (between the experimental and the control group) at random

We want to prove that the difference would only occur 5% of the time by luck

If we can, then the difference is significant – our experiment worked.

Data set 1 Experimental group 3 10 10 10 2 35 Mean=7; SD=4.1

Control group 5 7 6 5 7 30 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 10 6 7 9 8 7 10 8 Mean = 8 6 SD = 1.5 9 80

Control group 7 6 5 10 2 4 8 6 Mean = 6 5 SD = 2.2 7 60

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.