{"id":104,"date":"2024-08-21T12:00:51","date_gmt":"2024-08-21T12:00:51","guid":{"rendered":"https:\/\/routledgelearning.com\/researchmethods\/?post_type=content&p=104"},"modified":"2024-08-22T10:38:46","modified_gmt":"2024-08-22T10:38:46","slug":"chapter-13-statistics-organising-the-data","status":"publish","type":"content","link":"https:\/\/routledgelearning.com\/researchmethods\/student-resources\/chapter-13-statistics-organising-the-data\/","title":{"rendered":"Chapter 13 – Statistics \u2013 organising the data"},"content":{"rendered":"\n
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\n\tHome\n<\/span><\/div>\n\n

Chapter 13 – Statistics \u2013 organising the data<\/h1>\n\n\n

This chapter introduces you to the kinds of procedures that are used to describe and to summarise quantities of data.<\/p>\n<\/div>\n<\/div>\n\n\n\n

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Exercises<\/h2>\n\n\n\n

Exercise 13.1<\/h3>\n\n\n\n

Identifying categorical and measured variables<\/strong><\/p>\n\n\n\n

Decide in each case below the type of variable for which data have been recorded: Categorical or Measured. Questions 1, 5, 9, 10 and 11 have further explanations that can be found by clicking on the reveal button.<\/p>\n\n\n\n

1. Number of words recalled from a learned 20 item list<\/p>\n\n\n\n

Show answer<\/summary>\n

Measured<\/p>\n<\/details>\n\n\n\n

2. Scores on an extroversion scale<\/p>\n\n\n\n

Show answer<\/summary>\n

Measured<\/p>\n<\/details>\n\n\n\n

3. Numbers of people who are extroverted or introverted<\/p>\n\n\n\n

Show answer<\/summary>\n

Categorical<\/p>\n\n\n\n

Further explanation: The numbers of people counted are on an interval scale but for each participant we have only a category; never confuse the frequencies with the measurement method used for each person\/case. Here, each person is either extroverted or introverted.<\/p>\n<\/details>\n\n\n\n

4. Whether people stopped at a red traffic light or not<\/p>\n\n\n\n

Show answer<\/summary>\n

Categorical<\/p>\n<\/details>\n\n\n\n

5. Grams of caffeine administered to participants<\/p>\n\n\n\n

Show answer<\/summary>\n

Measured<\/p>\n\n\n\n

Further explanation: Grams are units on a clearly measured scale. However, we could be conducting an experiment where we give 0 grams 50 grams or 200 grams to participants, in which case we would be using three categories; it is always possible to use an interval scale but create categories like these. If, for instance, we recorded in each case only whether participants solved a problem or not we would <\/strong>have a 3 X 2 cross tabs table for a \u03c7<\/em>2<\/sup> analysis \u2013 see Chapter 18.<\/strong><\/p>\n<\/details>\n\n\n\n

6. Number of errors made in completing a maze<\/p>\n\n\n\n

Show answer<\/summary>\n

Measured<\/p>\n<\/details>\n\n\n\n

7. Whether people were recorded as employed, self-employed, unemployed or retired<\/p>\n\n\n\n

Show answer<\/summary>\n

Categorical<\/p>\n<\/details>\n\n\n\n

8. Number of cigarettes smoked per day<\/p>\n\n\n\n

Show answer<\/summary>\n

Measured<\/p>\n<\/details>\n\n\n\n

9. Whether people smoked none, 1\u201315, 15\u201330, or more than 30 cigarettes per day<\/p>\n\n\n\n

Show answer<\/summary>\n

Categorical<\/p>\n<\/details>\n\n\n\n

10. Number of aggressive responses recorded by an observer of one child<\/p>\n\n\n\n

Show answer<\/summary>\n

Measured<\/p>\n<\/details>\n\n\n\n

11. Whether a child was recorded as strong aggressive or moderate aggressive or non-aggressive<\/p>\n\n\n\n

Show answer<\/summary>\n

Categorical<\/p>\n\n\n\n

Further explanation: <\/strong>Here an originally measured variable (number of aggressive responses) has been reduced to three possible categories.<\/strong><\/p>\n<\/details>\n\n\n\n

Exercise 13.2<\/h3>\n\n\n\n

Finding descriptive statistics<\/strong><\/p>\n\n\n\n

For those able to use IBM SPSS or any other spreadsheet software that will find descriptive statistics the file psychology test scores.sav (SPSS) or psychology test scores.xls (Excel) contains data on 132 cases that you can work with. For those working by hand this is rather a lot of data so I have provided a smaller data set below for you.<\/p>\n\n\n\n

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Psychology test scores<\/strong> (EXCEL)<\/a><\/div>\n<\/div>\n\n\n\n

Working on SPSS or equivalent with the psychology test score data find the:<\/p>\n\n\n\n

Mean<\/strong><\/p>\n\n\n\n

37.02<\/p>\n\n\n\n

Median<\/strong><\/p>\n\n\n\n

38<\/p>\n\n\n\n

Mode<\/strong><\/p>\n\n\n\n

39<\/p>\n\n\n\n

Range<\/strong><\/p>\n\n\n\n

38<\/p>\n\n\n\n

Note 1<\/strong> has been added to the SPSS answer for the range (37) for the reasons given in Chapter 13 of the book. We assume the range runs from the lower end of the lower interval to the upper end of the upper interval.<\/p>\n\n\n\n

Semi-interquartile range<\/strong><\/p>\n\n\n\n

3.5<\/p>\n\n\n\n

Note<\/strong> <\/strong>In SPSS use Analyze\/Descriptives\/Explore to find the interquartile range and then halve this value.<\/p>\n\n\n\n

Standard deviation<\/strong><\/p>\n\n\n\n

6.83<\/p>\n\n\n\n

For those working by hand here is a simpler data set:<\/p>\n\n\n\n

13        15        16        16        18        18        19        21        22        22        22        23        23        24        24        25        25        26        27        27            35        38        39<\/strong><\/p>\n\n\n\n

Try to calculate the same statistics (and read the notes above about calculations):<\/p>\n\n\n\n

Mean<\/strong><\/p>\n\n\n\n

23.65<\/p>\n\n\n\n

Median<\/strong><\/p>\n\n\n\n

23<\/p>\n\n\n\n

Mode<\/strong><\/p>\n\n\n\n

22<\/p>\n\n\n\n

Range<\/strong><\/p>\n\n\n\n

27<\/p>\n\n\n\n

Note 1<\/strong> has been added to the SPSS answer for the range (26) for the reasons given in Chapter 13 of the book. We assume the range runs from the lower end of the lower interval to the upper end of the upper interval.<\/p>\n\n\n\n

Semi-interquartile range<\/strong><\/p>\n\n\n\n

3.5<\/p>\n\n\n\n

Note<\/strong> Excel gives slightly different answers for quartiles and percentiles and hence the semi-interquartile range value will be different \u2013 2.75<\/p>\n\n\n\n

Standard deviation<\/strong><\/p>\n\n\n\n

6.58<\/p>\n\n\n\n

Exercise 13.3<\/h3>\n\n\n\n

Below are some statements contained in student practical reports. Each contains a statistical flaw. If you were marking the paper what might you write to the student? When you have done this you can look at what could be written. There is no automatic scoring for this exercise so just see how many you got right and how close you were.<\/p>\n\n\n\n

It is reported that the median for anxiety scores was 13 and the standard deviation was 3.4<\/p>\n\n\n\n

Show answer<\/summary>\n

The measure of central tendency and the measure of dispersion should match and should both be appropriate for the level of measurement, either mean and sd or median and semi-interquartile range.<\/p>\n<\/details>\n\n\n\n

The mean, median and mode of self-esteem scores are given.<\/p>\n\n\n\n

Show answer<\/summary>\n

It is bad form to report all three measures\u00a0 of central tendency. One is enough and appropriate.<\/p>\n<\/details>\n\n\n\n

It is stated that \u201dThe mean IQ score was higher than the mean extroversion sore\u201d.<\/p>\n\n\n\n

Show answer<\/summary>\n

IQ and extroversion are measures on different scales so such a comparison is meaningless. This is like comparing cheese and coal.<\/p>\n<\/details>\n\n\n\n

The report says that the average score for memory recall was 15.<\/p>\n\n\n\n

Show answer<\/summary>\n

Which average?<\/p>\n<\/details>\n\n\n\n

The mean number of words recalled is given as 13.7451.<\/p>\n\n\n\n

Show answer<\/summary>\n

This is spurious accuracy. The mean should only be one place more in decimals than the original values it is the mean off. If they were whole numbers (you can\u2019t recall 4.5 words!) then only one place of decimals is required for the mean.<\/p>\n<\/details>\n\n\n\n

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Weblinks<\/h2>\n\n\n\n

Statistics \u2013 Organising the data Weblinks<\/h3>\n\n\n\n

David Lane\u2019s Hyperstat \u2013 Online statistics handbook:<\/p>\n\n\n\n

https:\/\/www.davidmlane.com\/hyperstat<\/a><\/p>\n\n\n\n

Statistics support:<\/p>\n\n\n\n

Best Statistics Help and Practice | StudyPug<\/a><\/p>\n\n\n\n

\u2018The little handbook of statistical practice\u2019 – A general source for most analyses in forthcoming chapters:<\/p>\n\n\n\n

http:\/\/www.jerrydallal.com\/LHSP\/LHSP.htm<\/a><\/p>\n<\/div>\n\n\n\n

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On this page<\/h2>\n\n\n