Summer Conference 2010

Collaborative & Individual Investigations

Presenting dataUsing statistics to analyse data- how far do you go?

Geoff Slater

Need to keep in mind…….

• A lot of our students do not have a maths/science background

• They should not be disadvantaged• SO….statistical analysis should be kept to a

basic level of understanding– to what is stated in the curriculum statement

Presentation

RESULTSTo what extent are the data appropriately

organised and presented by the student?– For numerical data

– Tables, graphs, histograms etc are presented and labelled appropriately

– Use graphs-statistics appropriate to the question in the proposal

– Raw data not is required

– For Qualitative Data– Provide a summary of themes, their frequencies,

relevant quotes and excerpts (illustrative comments from focus group data)- can be in tabular form.

Presentation- numerical data

COMPARISON OF SCORES

– compare mean scores, or– compare median scores or– use both- will depend on data

• eg- there may be some extreme scores (outliers)

– Could use other statistics (but usually not necessary)• eg- standard deviation, box plots (quartiles etc…), normal distributions

(data is usually not normally distributed anyway)

Note- important not to penalise those students who do not

have a good statistical background.

Presentation- numerical data

Example- Comparing scores– Data from the “Assertiveness Research Program”

eg-“ Does pre-exposure to an assertive situation influence ones’ assertiveness? ”

– Spreadsheet

Control Group Treatment Group

Mean Cognition Scores

35.6 35.5

12.5

17.5

22.5

27.5

32.5

37.5

42.5

47.5

Mean Cognition ScoresM

ean

Sco

res

title

Label vertical axisAppropriate scale -according to scores

Label horizontal axis

Indicate scores

or

Depending on the detail shown on graph, there may be no necessity to show a table of results

Don’t graph scores with different scaling on the same graph

Presentation- numerical data

Relationships between 2 scores

– Use a scatter plot– Can

• comment on degree and direction of scatter and/or• use line of best fit (no need for equation) and/or• use R2 or r values

– If using R2 or r values, then need to understand their relevance (otherwise no point in using)

Presentation- numerical data

What are r and R2 values?

r - The correlation coefficient– Measures the strength and direction of a linear relationship– Is– < 0.5 generally described as weak– > 0.8 generally described as strong

R2 - The coefficient of determination– a measure of how well the regression line represents the data– represents the %age of the data that is closest to the line of

best fit

– If r = 0.4385, then r 2 = 0.1923, which means that 19% of the total variation in y can be explained by the linear relationship between x and y (as described by the regression equation) The other 81% of the total variation in y remains unexplained.

2R

10

102

R

r

15 20 25 30 35 40 4510

15

20

25

30

35

40

45

50

R² = 0.192317634774063

Scatter plot of Cognition - Behaviour Scores for students from a large family

Behaviour Scores

Cogn

ition

Scor

es

Presentation- numerical data

Example- Relationships– Data from the “Assertiveness Research Program”

eg-“ Does family size influence the relationship between ones’ assertive cognitions and behaviour? ”

– Spreadsheet title

Label vertical axisAppropriate scale -according to scores

Label horizontal axis

No necessity to show a table of scores being plotted