INFERENTIAL STATS- non/parametric tests Flashcards
Statistical tests are classified into two types
Parametric
Non-parametric
Criteria for using a parametic test
-Populations drawn from should be normally distributed.
-Variances of populations should be approximately equal.
-Should have at least interval or ratio data.
-Should be NO extreme scores.
Powerfulness of parametric tests
If there is a difference in populations or a relationship between two variables, these tests are likely to find more info from the data.
Reasons for using NON-PARAMETRIC tests
- When assumptions of parametric test cannot be fulfilled.
- When distributions are not normal.
Types of non-parametric tests
-Mann Whitney U test
-Chi Square
-Binomial sign test
-Wilcoxon signed ranks test
-Correlations Spearman’s Rho
Type of data when using non-parametric test
Do the findings use nominal, ordinal or interval data?
Experimental design when using non-parametric
Independent measures or repeated measures design.
Differences in conditions when using non-parametric
Are you exploring differences in performance, test scores, between two conditions in your experimental study?
What are you looking for when using a non-parametric test
A relationship (correlation) between two co-variables
Observed value
Number produced after various steps and calculations for a statistical test have been carried out.
Critical value
Value taken from a statistical test table, must be reached in order for results to be significant.
Significant
If observed value of U is SMALLER than critical value
Ordinal/ Interval data & Independent measures
Mann Whitney U test
Ordinal/ Interval & Repeated measures
Wilcoxon signed ranks test
Nominal & Independent measures
Chi square
(can also be used to test an association)
Nominal & Repeated measures
Binomial sign test
Exploring relationship between 2 co-variables correlations & ordinal/ interval data
Spearman’s Rho
Checklist for Mann Whitney U test
~ DV produces ORDINAL/INTERVAL type data.
~ Independent measures design.
~ Explores a difference between each condition (levels of IV).
Step 1 Mann Whitney
Place data in rank order from low to high (put both groups together).
Rank should only go up to number of ps in total.
If there are double values ( two same numbers ranked after each other)
Add two together and divide by how many had same score.
Step 2
Add up all ranks for first condition. (R1)
Step 3
Repeat same procedure and add ranks of condition 2. (R2)
Step 4
Use formula (will be provided in exam)
U (1) = R (1) - n1 (n1 + 1)
—————-
2
OR
U (2) = R (2) - n2 (n2 + 1)
—————-
2
How to choose which formula
Use smallest total value, whether that is total of rank 1 or total of rank 2.
Step 5
Using table of critical U values, Match number of ps (n) in each group (n1 and n2) together and look for critical value on the table.
Step 6
To determine if research is SIGNIFICANT…
Observed value of U has to be EQUAL OR LESS than critical value of U.
Observed value is less than critical=
Null hypothesis is rejected.
Highly significant difference is found between conditions.
Observed value more than critical=
Results NOT significant.
Accept null.
Checklist for Wilcoxon signed rank test
-DV produces ordinal/interval data
-Repeated measures design
-Exploring difference between each condition (levels of IV)
Step 1 Wilcoxon
Find difference between each set of scores.
Some of these differences may be positive and negative.
Step 2
Rank differences.
-Ignore positive and negative signs and 0 values. (just look at number)
-Order smallest difference score to lowest.
If similar scores, calculate average.
Step 3
Look at difference column, count how many positive figures and how many negative figures there are.
Step 4
Make calculations using the less frequent sign. (if less positive figures, use positive) Add scores in ranked order of the difference column which belong to the less frequent sign.(pos or neg)
Step 5
Calculate n value.
It is not same as calculating degrees of freedom.
do not count ps who omit no difference.
n=
number of differences
Step 6
Match n value to table of critical wilcoxon signed ranks values.
Found at 0.05 significance level for two-tailed hypothesis.
Step 7
When examining values it is apparent the observed Wilcoxon value is LARGER than critical value.
(observed > critical)
Observed value LARGER than critical wilcoxon value
Results NOT significant.
Null hypothesis is accepted as there is no difference in conditions scores/results.
If observed value LOWER than critical wilcoxon value
Suggested results of study were significant
Null is rejected.
Chi-Square
Aims to compare the frequencies with occurring frequencies.
When using ps, it is important not to count ps more than once.
Checklist for Chi-Square
-DV produces nominal type data
-Independent measures design
-Exploring difference between each condition (level of IV) (Or an association)
Step 1 Chi-square
Add totals for each column.
Step 2
Calculate expected frequencies for each cell.
Step 3
Calculate expected values for each cell.
Formula for expected frequencies=
Overall total
Step 4
Calculating Chi-square:
Use formula in each cell.
(Observed number is original data number given on table).
Formula for Chi-square (x²)
(observed - expected)²
∑ ——————————–
expected
(gives our observed value)
Step 5
Calculate degrees of freedom
Degrees of freedom formula
(number of rows -1) x (number of columns -1)
Step 6
Use table of critical values of Chi squared to find critical value.
Degrees of freedom are along the side, level of significance (0.05) is along the top of the table.
In order for study to be significant
Observed Chi squared value must be LARGER or EQUAL to critical value of Chi squared.
(Reject null) Significant association/ difference found between conditions.
If observed is LESS than critical
Suggests study was NOT significant, Accept null hypothesis.
