1

GE5 Tutorial 3

rules of engagement• no computer or no power → no lesson• no SPSS → no lesson• no 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 homework3. Presentation

1. Shapes of distribution of scores (Chapter 4 Howitt & Cramer)

2. z-scores (Chapter 5 Howitt & Cramer)

4. SPSS workshop5. 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

9The normal curve

• 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

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.55REMEMBER

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