1. Inferential Statistics
Chi square
Sign test
Significance values and appropriate symbols (= ≤ < > ≥)
Inferential Statistics

2. Starter Test of a difference Nominal data (i.e. frequencies not %)
Can you recall the three reasons for each of the tests you learned last lesson?
Sign test
Chi-square
Tests for a difference between two sets of data
Related data (matched pairs or repeated measures)
Nominal data
Test of a difference
Nominal data (i.e. frequencies not %)
Data is independent

3. Learning Objective:
To further develop your understanding of the process of statistical testing, and look at techniques to remember the 5 tests.
Success Criteria
Recall reasons for choosing Chi-Square and Sign.
Conduct the final inferential statistical test (Spearman’s rho).
Create a key terms glossary.
Challenge Recall 3 reasons for conducting the 5 tests and look up critical values in a table.

4. Spearman’s rho

5. Spearman’s rho
This tests for a correlation (or a relationship) between two co-variables.
The data can be ordinal or interval.
A result of 0 means no correlation
A result of +1.0 is a perfect positive correlation
A result of -1.0 is a perfect negative correlation
Think of some data that are positively correlated:
Working memory and IQ
Attendance and exam results
Think of some data that are negatively correlated:
Age and mobility
Reaction time and time spent playing computer games

6. Spearman’s rho
Step 1. Write a null hypothesis and an alternative hypothesis.
Step 2. Record the data, rank each co-variable, and calculate the difference.
Step 3. Find the observed value of rho (correlation coefficient).
Step 4. Find the critical value of rho.
Step 5. State the conclusion.

7. Spearman’s rho
Step 1.
Alternative hypothesis = there will be a positive correlation between the attractiveness of married couples.
Null hypothesis = there will be no correlation between the attractiveness of married couples.

8. Spearman’s rho Step 2. Record the data 1 2 3 4 5 6 7 8 9 10 6 4 3 7 1
Calculate the ranks by ordering the data from 1 to 10 (i.e. the lowest rank is 1). If there are two or more with the same number then you calculate the mean of the ranks.
Now calculate the difference of the ranks (Rank F – Rank M)
This is the ‘matching hypothesis’ study.
Attractiveness was rated out of 10.
Now finally square the differences
Step 2. Record the data 1 2 3 4 5 6 7 8 9 10 6 4 3 7 1 8 10 5 6 3 10 2 8 6
4.5
2.5
7.5 1 9 10 5
7.5
2.5 10 1 9 1
-0.5
-2.5
-1.5 -1
1.5 2 1
0.25
6.25
2.25 4 18

9. Spearman’s rho
Step 3. Find the observed value of rho (correlation coefficient).
rho = 1 – (6 x 18)  10(100-1)
rho = 1 – (108  990)
rho = 1 – 0.11
rho = 0.89

10. Is the result significant?
Spearman’s rho
Step 4. Find the critical value of rho.
You need to know the value of N
Whether the hypothesis is directional or non-directional
Step 5. State the conclusion
The observed value (0.89) is greater than the critical value (0.564) we can reject the null null hypothesis (at p≤0.05) and conclude that there is a positive correlation between the attractiveness of married couples.
Is the result significant?

11. Final Task
Create a key terms glossary with the last two lesson’s words:
Inferential statistics test
Probability
Significance
Chance
Degrees of freedom
Type 1 error
Type 2 error
Spearman’s rho
Chi-Square
Sign test
Mann-Whitney U
Wilcoxon matched pairs signed ranks test

12. Quick Recap When would you use a Spearman’s rho test?
Test of a correlation
To test a relationship between 2 co-variables
At least ordinal data

13. Revision Task Let’s first recap the 5 tests.
Then complete the practice questions in your booklet.

14. Final task: is it significant?
Rho = +0.88
Is it significant?
one-tailed
p0.05
What is the value of N?
Participant
Study time (mins)
Test score (%) 1
100 60 2 25 47 3 95 70 4 53 5 10 41 6 75 51 7 80 61 8 45 44 9 55 85
Critical value = ??
Is this significant?
O is greater than C
So, yes it is significant
and you reject the null

15. Homework Remember what you were told at the start of last lesson:
You will never be asked to carry out a statistical test.
You could be asked to look up observed values in a table of critical values.
You can be asked to define key terms.
You could be asked if a value is significant or not.
Create flashcards on the 5 tests.