Making Social Work Count Lecture 7

• An ESRC Curriculum Innovation and Researcher Development Initiative

Using Numbers to Describe a Sample

How to tell a story with data

Learning outcomes

Identify and define levels of measurement and measures

of central tendency

Calculate frequency, percentage, range, measures of central tendency and be able to critique and justify their use for the exercise

problems

Describe situations in which different levels of

measurement and measures of central tendency are useful

and appropriate

Case # Variable1

Variable 2

Variable 3

Variable 4

Variable 5

Variable 6

Variable 7

Variable 8

1 1 2 25 16 2 3 89 300

2 1 2 34 17 2 0 76 350

3 1 2 33 14 2 1 77 325

4 2 3 35 15 1 0 80 300

5 1 1 46 16 2 0 81 325

6 2 2 24 13 2 2 82 350

7 2 2 22 14 2 3 84 400

8 2 1 21 15 1 1 75 300

9 1 3 24 14 1 0 76 325

10 1 2 23 12 2 1 73 300

11 1 2 32 13 2 2 86 400

12 2 2 23 14 2 0 80 350

Why gather information?

• To identify similarities • To identify differences• To establish patterns in

characteristics or behaviours• To predict patterns in

characteristics or behaviours in the future

• To describe a particular phenomenon

• To make sense of a particular phenomenon

Why gather information?

• What kind of information might we want to know about a group of:– Looked after children?– Carers?– Young offenders?– Adults with direct payments?

Collect information about individuals

The information is transformed into numbers and aggregated into a database

Case # Variable 1

Variable 2

Variable 3

1 1 25 1

2 1 22 1

3 1 23 1

4 2 24 3

5 2 25 1

6 1 21 2

7 2 20 5

8 1 22 1

9 1 24 1

The aggregate data is analysed to tell a story

Case #

Variable 1

Variable 2

Variable 3

1 1 25 1

2 1 22 1

3 1 23 1

4 2 24 3

5 2 25 1

6 1 21 2

7 2 20 5

8 1 22 1

9 1 24 1

Our data could tell us a story of:

• The educational outcomes of looked after children

• The average number of hours a carer spends caring a week

• The relationship between offending and educational attainment

• Adults’ satisfaction levels regarding using direct payments

How to tell a story with data: Chapter 1

In order to tell the story, we need to collect the information (data)

What are the different forms of collecting information (data)?

• The level of measurement used in collecting data determines the statistical techniques which can be used in analysis.

• Levels of measurement:– Nominal– Ordinal– Interval/Ratio

The story of the drinking glassesAn illustration of the different levels of measurement

Levels of measurement: Nominal

• Nominal – classifies variables into categories; the number of cases within each category is counted. – Yes/No– Sex– Religious affiliation– Type of glass

Levels of measurement: Ordinal

• Ordinal – ranks variables according to a particular characteristic or criteria. The order matters, but not the difference between values.– Degree classifications:

First, Upper second, Lower second, Third, Fail

– Order of preference: First, second, third, fourth, fifth

– Amount of pain on a scale of 1 to 10

– Tallest to shortest

Levels of measurement: Interval and ratio

• Interval – Equal units of measurement between variables. Can interpret the order and distance between variables– Temperature, expressed in

Fahrenheit or Celsius

• Ratio - Has a true zero in that when the variable equals 0, there is none of that variable– Length; time; age; weight– Liquid capacity as measured

my ml 650ml 400ml 325ml 300ml 200ml

The story of the drinking glasses

• There are 4 types of drinking glasses: – 2 mugs– 4 wine glasses– 4 champagne flutes– 3 water glasses.

• The glass height decreases:1. champagne flute 2. first wine glass3. wine glass4. water glass 5. mug

• Despite the champagne flute being the tallest, it holds the least amount of liquid at 200ml with the water glass holding the most at 650ml. The average amount of liquid all of the glasses can hold is 375 ml.

How to tell a story with data: Chapter 2

Once we have collected the information, we need to analyse the data

What are the different ways of analysing the data?

• Frequency • Proportion • Percentage• Measures of central tendency –An indication of

the middle point of distribution for a particular group or sample– Mean– Median– Mode

The story of the reablement service: An illustration of analysing different types of data

Form of analysis: Frequency

• Frequency –combining like variables with like and counting the number within each category (f)

• There are 311 service users (N) of the reablement service. We want to summarise the three main reasons why people access the service and the frequency of males and females

Reason f Physical disability 160 Temp. ill 144 Mental health 7

Total N = 311

Sex f Male 112 Female 199

Total N = 311

Form of analysis: Proportion

Proportion (P)• Counting the number of

variables in one category (f) and then dividing by the total number of variables (N).

• P = f/N• What is the P of males to

females in the reablement service?

Sex f

Male 112

Female 199 Total N = 311

Form of analysis: Proportion

Proportion (P)• Counting the number of

variables in one category (f) and then dividing by the total number of variables (N).

• P = f/N• What is the P of males to

females in the reablement service?

Sex f P Male 112 0.36 Female 199 0.64 Total N = 311

Form of analysis: Percentage

Percentage (%)• A percentage standardises for

size by multiplying the proportion (P) by 100 to indicate the frequency as per 100 cases.

• % = (100) f/N• What is the % of service users

that enter the service due to temporary illness?

• What is the % of males and females in the reablement service?

Reason f Physical disability

160 Temp. ill 144 Mental health 7

Total N = 311

Sex f

Male 112

Female 199 Total N = 311

Form of analysis: Percentage

Percentage (%)• A percentage standardises for

size by multiplying the proportion (P) by 100 to indicate the frequency as per 100 cases.

• % = (100) f/N• What is the % of service users

that enter the service due to temporary illness?

• What is the % of males and females in the reablement service?

Reason f % Physical disability 160

51.4% Temp. ill 144 46.3% Mental health 7 2.3%

Total N = 311 100%

Sex f % Male 112 36% Female 199 64%

Total N = 311 100%

Form of analysis: Mean

• Mean – summing all the scores in a dataset and dividing by the total number of scores. Provides an average score.

• What is the mean hours of care for service users when entering the reablement service?

• What is the mean hours of care when exiting the service?

Hours at Entry Hours at Exit

10 5

7 0

5 0

15 7

5 0

6 0

7 0

10 7

4 0

7 4

4 0

7 2

Form of analysis: Mean

• Mean – summing all the scores in a dataset and dividing by the total number of scores. Provides an average score.

• What is the mean hours of care for service users when entering the reablement service?

• What is the mean hours of care when exiting the service?

Hours at Entry Hours at Exit

10 5

7 0

5 0

15 7

5 0

6 0

7 0

10 7

4 0

7 4

4 0

7 2

7.25 2.08

Form of analysis: Median & Mode

• Median – The middlemost score in a list of scores

• Mode – The most frequent or common score in a list of scores

• What is the median and mode number of hours of care at entry and exit?

entry: 10 7 5 15 5 6 7 10 4 7 4 7

exit: 5 0 0 7 0 0 0 7 0 4 0

2

Form of analysis: Median

• Median – The middlemost score in a list of scores

• Mode – The most frequent or common score in a list of scores

• What is the median and mode number of hours of care at entry and exit?

entry: 4 4 5 5 6 7 7 7 7 10 10 15

exit: 0 0 0 0 0 0 0 2 4 5 7

7

Form of analysis: Mode

• Median – The middlemost score in a list of scores

• Mode – The most frequent or common score in a list of scores

• What is the median and mode number of hours of care at entry and exit?

entry: 4 4 5 5 6 7 7 7 7 10 10 15

exit: 0 0 0 0 0 0 0 2 4 5 7

7

Form of analysis: Range

• Range – The difference between the highest score and lowest score in a list of scores– What is the range of number of

hours of care at entry and exit?

entry: 4 4 5 5 6 7 7 7 7 10 10 15

exit: 0 0 0 0 0 0 0 2 4 5 7

7

Form of analysis: Range

• Range – The difference between the highest score and lowest score in a list of scores– What is the range of number of

hours of care at entry and exit?

entry: 4 4 5 5 6 7 7 7 7 10 10 15 exit: 0 0 0 0 0 0 0 2 4 5 7 7

How do we know which analysis to perform?• The level of measurement

used in collecting data determines the statistical techniques which can be used in analysis.

Level of measurement and type of data analysis Levels of measurement Types of data analysis

Nominal - Example of religious affiliation

FrequencyPercentageMode

Ordinal - Example of degree classification

FrequencyPercentageMedian and Mode

Interval - Example of level of satisfaction

Frequency, Percentage, mode and median (if the variables are discrete, such as thoughts, behaviours)Mean, Median, and Mode

Ratio - Example of assessment scores

Mean, Median, and ModeRange

The story of the reablement service (1)

Users

Male

36%

Fe-male64%

Reasons for entering the service

2%

51%

46%

mental health difficultiesPhysical disabil-ity temporary illness

The story of the reablement service (2)

• The mean number of hours of care at entry was 7.25, which declined to 2.08 at exit.

• The median number of hours of care at entry was 7, yet declined to 0 at exit.

• The mode number of hours of care at entry was 7, yet declined to 0 at exit.

Assessment Scores of Students

Student Number

Sex Age Satisfaction with module

Assessment mark

Classification

1 F 25 Very Satisfied 70 First

2 F 22 Very Satisfied 68 Upper second

3 M 20 Satisfied 62 Upper second

4 F 25 Very Satisfied 65 Lower second

5 F 42 Unsatisfied 54 Upper second

6 F 36 Very Satisfied 52 Upper second

7 M 22 Satisfied 48 Third

8 M 20 Very Satisfied 74 First

9 F 38 Unsatisfied 38 Fail

10 M 20 Very Satisfied 58 Lower second

Assessment Scores of Students: Levels of Measurement

• What level of measurement are each of the following variables and how would you suggest analysing them?– Sex– Age– Satisfaction with module– Assessment Score– Classification

How to tell a story with data: Chapter 3

Once we have collected the information and analysed the data, we need to present the findings (tell a story)

Assessment Scores of Students Student Number

Sex Age Satisfaction with module

Assessment mark

Classification

1 2 (F) 25 4 (Very Satisfied) 70 5 (First)

2 2 (F) 22 4 (Very Satisfied) 68 4 (Upper second)

3 1 (M) 20 3 (Satisfied) 62 4 (Upper second)

4 2 (F) 25 4 (Very Satisfied) 65 4 (Upper second)

5 2 (F) 42 2 (Unsatisfied) 54 3 (Lower second)

6 2 (F) 36 4 (Very Satisfied) 52 3 (Lower second)

7 1 (M) 22 3 (Satisfied) 48 2 (Third)

8 1 (M) 20 4 (Very Satisfied) 74 5 (First)

9 2 (F) 38 2 (Unsatisfied) 38 1 (Fail)

10 1 (M) 20 4 (Very Satisfied) 58 3 (Lower second)

Code: Sex (1 = M; 2 = F); Satisfaction (1 = very unsatisfied; 2 = unsatisfied; 3 = satisfied; 4 = very satisfied; Classification (1 = fail; 2 = third; 3 = lower second; 4 = upper second; 5 = first).

Example storytelling

• Analyse the data of the assessment scores of students

• Justify your choice of analysis

• Summarise your findings to tell a story about the students

Learning outcomes

Are you able to:• Identify and define levels of

measurement and measures of central tendency?

• Describe situations in which different levels of measurement and measures of central tendency are useful and appropriate?

• Calculate frequency, percentage, range, measures of central tendency and be able to critique and justify their use for the exercise problems?

Activity

Activity – Part A

The students should read the following research report: “Evaluation of the Southwark Reablement Service” available from http://www.york.ac.uk/media/spsw/documents/cmhsr/Southwark%20Reablement%20Service%20Evaluation%2021.6.13.pdf.

Ask the students to complete the following tasks:• Identify an example of a frequency, percentage, mean and range. • Calculate the percentage of the 81 clients who engaged with the Reablement

service that were male and the percentage that were female (page 4). • Create an argument for why the authors should have included the median and

mode when reporting the “mean age of the sample” (page 6). • Create an argument for why the authors included the sample size alongside the

percentages when reporting the “Payment by Results Clusters” (page 7). • Based on the analysis of the quantitative date, ask the students to “tell a story” of

the Reablement program in Southwark.

Activity – Part B

• Ask the students to download a copy of the RAND 36-Item Short Form Health

• Survey available from http://www.rand.org/health/surveys_tools/mos/mos_core_36item_survey_print.html. Ask the students to look at questions 1-20 and answer the following questions:

• What is the level of measurement for items 1-20 on the questionnaire?

• How would you propose analysing items 1-20 and why? In particular, consider percentage, frequency, mean, median, mode and range.

References

• RAND Health (2010). RAND 36-Item Short Form Health Survey. Developed as part of the Medical Outcomes Study. Available from http://www.rand.org/health/surveys_tools/mos/mos_core_36item.html.

• Reidy, H., Webber, M., Rayner, S., & Jones, M. (2013). Evaluation of the Southwark Reablement Service. Available from http://www.york.ac.uk/media/spsw/documents/cmhsr/Southwark%20Reablement%20Service%20Evaluation%2021.6.13.pdf.

• Rosenthal, J.A. (2012). Statistics and data interpretation for social work. New York, NY: Springer Publishing Company. – Lecturers should refer to Chapter 3 “Central Tendency” (pp. 29-38).

• Schneider, J., Brandon, T., Wooff, D., Carpenter, J., & Paxton, R. (2006). Assertive outreach: policy and reality. The Psychiatrist, 30, 89-94. (Lecturers could refer to this article as a good demonstration of the use of percentages. )

• Scourfield, J. (2010). Professional doctorate programmes in social work: the current state of provision in the UK. British Journal of Social Work, 40, 567-582. (Lecturers could use this article as an example of measures of central tendency. Table 4 (p. 574) can arguably be mis-leading with a reported mean of 6 students per programme, based on a couple of outliers. The mode and median were 3, which may in fact be more appropriate to report. )