Kin 550 Statistics Review:
Use the organizational tree in the back of the stats book.
Nominal – numbers are mutually exclusive categories- football players by number
Ordinal- ranking ( but not based on time for instance)
Internal: ranking and intervals are equal
Ratio- 0 represents absence of attribute, distance between numbers is meaningful order, and intervals are equal
Mean sum of x / n
Median – middle score
Mode- most frequent score
Standard deviation- extent to which data deviate from the mean
Tests between two means
Not skewed in either direction- positively or negatively
If the distribution is not normal then you need to use non-parametric statistics such as:
Chi squared, Wilcoxin, mann- whitney U, Kruskal Wallace,
If the distribution is normal then you use parametric statistics.
Use T-tests to test between two means of different groups
paired T-tests to test between two conditions of the same group
If you are testing two or more groups you can use a t-test with a bonferonni adjustment makes it less likely ( more rigorous) that you will find a significant difference each test you perform.
Analysis of variance
but the more accepted method is to use an analysis of variance- This takes into account the fact that you are testing multiple groups.
This test only tells you that there is a difference between groups it doesn't tell you where the differences are.
Need to use post hoc tests to tell where the differences are. It tests between group means. You can only use this if there is a significant difference for "main effects" using the F- test.
Two way analysis of variance.
Two conditions with two or more groups. Smallest would be a 2 X 2 analysis of variance. Possible main effects would be.
1) a significant difference between either of the conditions pre and post
2) an interaction meaning differences that do not change the same way over time.
If there are significant differences then post hoc tests can be performed to see where the differences are. This is not such a problem with a 2 X 2 but with more groups than that it is difficult to see the differences.
Calculation of the
F statistic: MSb/ MSw = (between groups variance ) / ( within groups variance)
F obt > or equal to F crit then reject the null hypothesis
F obt < F crit then retain the null hypothesis
the greater the number of subjects the lower the F statistic needs to be to be significant
Sum of Squares =
Power – Higher the power the more sensitive the experiment
Power is a probability and varies between 1 and 0
The power is the probability of making a correct decision when Ho is false.
Null hypothesis: independent variable has no effect on dependent variable
Example: marijuana has no effect on reaction time.
Type 1 error: reject null hypothesis when null hypothesis is true
Find significant difference when there is no difference.
Poor design or want to see a difference when there is none.
Type 2 error: retain null hypothesis when null hypothesis is false
Don’t find a significant difference when there is one
(small sample size etc)
Predicting grade point average from IQ.
Grade point average is the dependent variable
IQ is the independent variable
Taken the course before
Quality of reading materials
Number of class periods attended etc.
Each factor can be weighted to determine how much it contributes to grade point average.
Not used to predict one variable from another but used to see if there is a relationship and what direction it is.
For instance… price of real estate as a function of distance from San Francisco or some other desireable location.
Real estate price as a function of quality of the school district.
Correlation of 1 as one variable increases so does the other
BW and sprint time.
Correlation of –1 as one variable increases the other decreases:
BW and sprint speed.