INFERENTIAL STATISTICS 1.Level of data 2.Tests 3.Levels of significance 4.Type 1 & Type 2 Error

WHAT YOU NEED TO KNOW FOR THE EXAM…. You will not have to conduct these tests in an exam(cue… sigh of relief) However you will have to; Know the purpose of using Inferential Statistics. Know what test you would use and why. Whether or not the results are significant?

WHY ARE THEY USED? 1)Statistical tests are used by Psychologists (and maths boffins) to prove or disprove a Hypothesis. 2) Statistical tests are used to determine whether data shows significance (if there is a relation or effect in the experiment). 3) Statistical tests see if the NULL Hypothesis is true(that results are due to chance/random). So the test is there to find out if the result was found by chance. 4) Which test you use depends on the data you have!

NOMINAL DATA Nominal Data is data which cannot be assigned a numerical value of any true mathematical significance

EXAMPLE Suppose you want to study happiness and sadness on a Monday morning. You decide to use a questionnaire to collect this data. This could be a very simple questionnaire with one question: ‘Please circle the word which best describes your mood on this Monday morning.’ Answers: ‘Happy’, ‘Sad’ – This would collect nominal data. The results of this study might be: Happy – 12 Sad – 38 We could display these results in a number of ways including bar charts and pie charts. Depending on what method and design you have used you will have to use different inferential statistics to analyse the data.

ORDINAL DATA Ordinal data is data which is numerical and can be put into an order, but nothing else can be inferred from the numbers, we can only use the numbers to establish an order

EXAMPLE If the exam question stipulates that you should collect ordinal data, then the easiest way of doing that is to use a self-report questionnaire with rating scales. Remember that you can use questionnaires within experiments, if the question also stipulates that you have to use an experiment. You can also use structured observations because they collect ordinal data E.G. ‘On a scale of 1-10 please rate your motivation to complete this fitness regime (1 being not at all and 10 being completely motivated).’ Answer: ‘1 – 10′

INTERVAL/RATIO DATA

INTERVAL/RATIO Interval data is measured on a scale in which each interval is exactly the same size. Interval data has data points which are evenly spaced. The simplest example of interval data is temperature because the difference between data points is always the same. For example 1˚C and 2˚C have the same distance between them as 60˚C and 61˚C. Ratio data is only different as it starts at zero (e.g. Time) Reaction time cannot really be zero so this would be interval data

IDENTIFY THE CORRECT LEVEL OF MEASUREMENT  See if males and females are good or bad drivers  Rank people on a scale running from prejudiced to non prejudiced  Measure people’s reaction time  Pairs – work together to answer questions on the correct level of measurement

You need to be able to identify: A)Whether you are testing for difference between groups or scores or for a relationship between variables B) Whether your experimental design is independent groups or repeated measures/matched pairs C) Whether your data are nominal or ordinal IDENTIFYING THE CORRECT TEST – POSSIBLE EXAM QS.

INFERENTIAL STATISTICS Non-Parametric statistical tests: 1.Mann Whitney U: Test significance of the difference between two conditions when an independent design has been used and the level of data is at least ordinal. 2.Wilcoxon matched participant signed rank: Test significance of the difference between two conditions when an repeated measures design has been used and the level of data is at least ordinal. 3.Chi-Squared: test of significance of association used when nominal data has been collected. 4.Spearmans Rho Test: when data is at least ordinal and a correlational method is used.

When Testing for a Difference/Association When Testing for a Correlation Data TypeIndependent Measures Repeated Measures Design/Matched Pairs Matched Pairs Nominal (categorical) Chi-squared ( x ²) Association Nominal Sign Test S Difference Nominal Repeated Measures ___ Ordinal or Interval Mann Whitney U test U Difference Ordinal Wilcoxon Test T Difference Ordinal/Interval Spearman’s Rank Rho Correlation Ordinal/Interval

1. WHICH TEST WOULD YOU USE? Participant number New Mathematics Help Scheme Participant number No Scheme implemented IV = Whether or not given Maths help Scheme DV = Maths test score

2. WHICH TEST WOULD YOU USE? ParticipantStudy time (mins)Test score (%)

3. WHICH TEST WOULD YOU USE? Participant number Neutral WordsEmotionally threatening words IV = Whether word presented is neutral or emotionally threatening DV = Recall of words

4. WHICH TEST WOULD YOU USE? Art StudentsScience Students Row Total Extroverted Introverted Column Total3025Total: 55 IV = Whether Art Students or Science Students (Natural Experiment) DV = Extroversion- Introversion score

P is an estimate of the probability that the result has occurred by statistical accident. What does p ≤ 0.05 level of significance mean? (2) Experiment This means that this is a 95% p robability that the change in the DV is as a result of the IV and a less than 5% probability that this is due to random chance. The findings are therefore statistically significant. Thus we can reject the null hypothesis and accept the experimental hypothesis. Non-Experimental This means that this is a 95% probability that the change in the DV is as a result of the IV and a less than 5% probability that this is due to random chance. The findings are therefore statistically significant. Thus we can reject the null hypothesis and accept the alternative hypothesis. Correlation This means that this is a 95% probability that the relationship between the two variables is significant and a less than 5% probability that this is due to random chance. The findings are therefore statistically significant. Thus we can reject the null hypothesis and accept the alternative hypothesis. P < 0.05

LEVELS OF SIGNIFICANCE Is there a difference between the groups that is REAL or is it due to CHANCE? LevelProbabilitySignificanceWhen used 1%(p<0.01)HighlyStringent - Where we would want to take few chances 5%(p<0.05)SignificantAcceptable for psychological research 10%(p<0.10)MarginallyMay indicate need for better methodology Less than

SIGNIFICANCE Spearman Observed value of Rho Wilcox Observed Value T Mann-Whitney Observed Value or U Chi ² Observed Value of x ² Sign Test Observed Value of S The Observed Value refers to the statistical calculation The Critical Value is found on the critical tables

V. WHETHER OR NOT THE RESULTS ARE SIGNIFICANT? Spearman’s rho Chi square Mann Whitney U Wilcoxon T Sign Test rho≥C x²≥C U ≤ C T ≤ C S ≤ C Critical Value – found in tables Observed value

If the results are significant, the null hypothesis can be rejected and the alternate hypothesis can be accepted. If they are not significant then the null hypothesis is accepted and alternative hypothesis is rejected

TYPE 1 & 2 ERRORS There is a possibility that errors may have been made: Type 1 ErrorDeciding to reject the null when actually the results was due to chance or some other factor. Type 2 ErrorDeciding to retain the null when actually the result was caused by the IV. Too LowP = <0.10Type 1 Error more likely Too HighP = <0.001Type 2 Error more likely

PROBABILITY What does p ≤ 0.05 level of significance mean? (2) Experiment This means that this is a 95% probability that the change in the DV is as a result of the IV and a less than 5% probability that this is due to random chance. The findings are therefore statistically significant. Thus we can reject the null hypothesis and accept the experimental/alternative hypothesis. Correlation This means that this is a 95% probability that the relationship between the two variables is significant and a less than 5% probability that this is due to random chance. The findings are therefore statistically significant. Thus we can reject the null hypothesis and accept the alternative hypothesis.

INFERENTIAL STATISTICS (QS) June 2012: What does p ≤ 0.05 level of significance mean? (2) This means that this is a 95% probability that the change in the DV is as a result of the IV and a less than 5% probability that this is due to random chance. The findings are therefore statistically significant. Thus we can reject the null hypothesis and accept the experimental/alternative hypothesis. If you obtained this level of significance in your practical project, explain what this would mean in relation to your null hypothesis. (4) June 2011: You must use a repeated measures design experiment and plan to collect quantitative data. State an appropriate statistical test to analyse the data you would collect. Give reasons for your choice. (3)

INFERENTIAL STATISTICS (QS) June 2010: You must use a correlation design and plan to collect at least ordinal data. State an appropriate statistical test (non-parametric) to analyse the data you would collect. Give reasons for your choice. (3) June 2013: How could you obtain nominal level data from your practical project? (3) June 2014: You must use an independent measure design and plan to collect data which measures observable behaviour. State and appropriate inferential statistical test to analyse the data that would be collected in your practical project. Give reasons for your choice. (3

INFERENTIAL STATISTICS (QS) Specimen Papers: You must use a repeated measures design experiment and plan to collect at least ordinal level data. State an appropriate statistical test to analyse the data you would collect. Give reasons for your choice. (3) If having carried out your investigation and an inferential statistical test, your experimental hypothesis was found to be significant for p≤0.05, what would p≤0.05 mean? (3) Identify and describe the rational for choosing an appropriate inferential statistical test that could be used to calculate the significance of any correlation in your practical project. (3) If your practical project comes up with the findings or what does p ≤ 0.05 level of significance mean? (2)