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

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

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.

Spearman’s rho

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

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.

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.

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

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

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?

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

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

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

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

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.