1 GE5 Tutorial 3 rules of engagement no computer or no power → no lessonno computer or no power → no lesson no SPSS → no lessonno SPSS → no lesson no homework done → no lessonno homework done → no lesson

2 Describing variables numerically (chapter 3 Howitt & Cramer) –Measures of central tendency –Measures of variability Creating a websurvey (LimeSurvey) Introduction to export data from LimeSurvey –Still some topics to cover Import to SPSS Previous seminar

3 1.Quiz (chapter 3, Howitt & Cramer + SD from Ch. 5) 2.Discussion homework 3.Presentation 1.Shapes of distribution of scores (Chapter 4 Howitt & Cramer) 2.z-scores (Chapter 5 Howitt & Cramer) 4.SPSS workshop 5.Discussion homework next week Content seminar

4 1. Quiz

5 2. Discussion homework

6 Shapes of distribution of scores Normal curve Distorted curves –Skewness –Kurtosis Other frequency curves –Bimodal –Multimodal –Cumulative frequency scores –Percentiles

7 - In a histogram, the width of the bars make the graph look different - Of course this only works when you have enough data points - When you have 1000s of data points, you'll get a curve

8 The normal curve Symmetrical, bell shaped

The normal curve 9 It was 'invented' by Gauss, a German scientist in the early 1800's He used it to describe the variability you can find when measuring natural (living) objects For example: – The length of all sunflowers in a field – The time it takes an egg to hatch

10 Skewness “The extent to which our frequency curve is lopsided rather than symmetrical” Negative skew –More scores to left of the mode than right –Mean and median smaller than the mode Positive skew –More scores to right of the mode than left –Mean and median bigger than the mode

11 Positive and negative skew

12 Kurtosis “The degree of steepness or shallowness of a distribution” Steep curve: –Called leptokurtic –Positive value of kurtosis Normal curve: –Called mesokurtic –Zero value of kurtosis Flat curve: –Called platykurtic –Negative value of kurtosis

13 Which curve has a larger kurtosis value?

14 Bimodal & multimodal Unimodal: one peak Bimodal: twin peaks Multimodal: multiple peaks The peaks do not have to all be of the same size.

15 Cumulative frequency curves The accumulation of frequencies

16 Percentiles “The score which a given percentage of scores equals or is less than” “Quick method of expressing a score relative to those of others”

17 Chapter 5 Howitt & Cramer

18 Standard deviation & z-scores Introduction Standard deviation Estimated standard deviation Z-score Use of z-scores Significance table

19 Introduction Need of standard units of measurement –E.g. Meter, Celsius, Gram, etc. –Helps us communicate easily, precisely, effectively Variables have many different types of units –Physical: meters, kg, etc. –Abstract: I.Q. Statisticians need also a standard unit for the measurement of variability

20 Standard deviation “the ‘average’ amount by which scores differ from the mean” Calculated as the average squared deviation i.e. square root of variance It is not a unit-free measurement Formula:p.49 Gives greater numerical emphasis to scores which depart by larger amounts from the mean Size of sd: indicator of variability in the scores –The bigger the sd the more the spread

21 Standard deviation Calculated as the average squared deviation i.e. square root of variance

22 Estimated sd

23 Z-Score A researcher measures parents’ involvement on their children’s tennis activities in a survey. He uses the following questions to obtain the answer to his question. Questions: 1.How much money do you spend per week on your child’s tennis coaching? 2.How much money do you spend per year on your child’s tennis equipment? 3.How much money do you spend per year on your child’s tennis clothing? 4.How many miles per week on average do you spend travelling to tennis events? 5.How many hours per week on average do you spend watching your child play tennis? 6.How many LTA tournaments does your child participate in per year?

24 Z-Score A researcher measures parents’ involvement on their children’s tennis activities in a survey. He uses the following questions to obtain the answer to his question. Questions: 1.How much money do you spend per week on your child’s tennis coaching? 2.How much money do you spend per year on your child’s tennis equipment? 3.How much money do you spend per year on your child’s tennis clothing? 4.How many miles per week on average do you spend travelling to tennis events? 5.How many hours per week on average do you spend watching your child play tennis? 6.How many LTA tournaments does your child participate in per year? Radically different units of measurement Solution: calculate z-scores for each, and add them to create a measure of parental involvement

25 Z-score: number of standard deviations No need of unit of measurement A z-score tells us how many units of standard deviation there are between mean and this score Imagine we measured 'time spend playing Warcraft per week'. Mean is 4 hours, with sd=7 John's plays for 25h a week His z score is (25-4) / 7 = 3 Big advantage: equally applicable to all types of variables Sometimes referred to as standard score

26 Use of z-scores Very useful since z-scores can be compared or even combined E.g.: parents’ involvement on their children’s tennis activities Questions: 1.How much money do you spend per week on your child’s tennis coaching? 2.How much money do you spend per year on your child’s tennis equipment? 3.How much money do you spend per year on your child’s tennis clothing? 4.How many miles per week on average do you spend travelling to tennis events? 5.How many hours per week on average do you spend watching your child play tennis? 6.How many LTA tournaments does your child participate in per year? Radically different units of measurement Solution: calculate z-scores for each, and add them to create a measure of parental involvement

27 Significance table Lists the percentage number of scores higher than a score with a given z-score Table assumes the distribution of scores is normal (bell shaped) Table 5.1 p.55 REMEMBER 68% of the data is within +/- 1 SD 95% of the data is within +/- 2 SD

28 5. SPSS workshop

Exercise 1 Export from LimeSurvey -> Import to SPSS

Step 1: Export data from limeSurvey Start Limesurvey Open Button  Responses and Statistics Button (export results to SPSS) Download syntax file and data file

Step 2: Import data in SPSS Open the SPSS syntax file downloaded from LimeSurvey (SPSS will start) Adapt line 4: fill in (after FILE = ) the name of the data file (including extension and complete path to the file!) and put the name between quotation marks Choose 'Run/All' (or select all and push the green arrow)

Exercise 2: Producing graphs Open BIG smartie survey 2014 Review guidelines for graphs on section 2.2 (p13- p22) of the book Produce measures of central tendency and dispersion and a histogram for the variable q_0014 (What is your age?) (By using menu item: Analyze) Find out skewness and kurtosis

Exercise 3 Creating Z-scores  Open BIG smartie survey 2014  Click analyse  Click descriptives  Select numbber of red smarties  Click save Z-scores  Click OK

Exercise 3 Recode variable q_0014 to eliminate outliers Re-produce graph (By using menu item: Graphs) Re-find skewness and kurtosis

35 6. Homework