&#38; &#38;&#38;

! ! ! ! !

We have looked at the use of measures of average and variability in trying to understand quantitative data. Here is another example to consider, above. The chart on the left suggests a preference for ‘yes’ but ‘no’ responses are also quite high, with even more ‘undecided’. If this were the result of asking 48 learners, “have you improved your skills in maths as a result of this lesson?”, what might you conclude from the chart on the left? Would you be more confident if your results looked like the chart on the right – and if so how would you justify this in your ‘conclusion section’?

We&#38;have&#38;looked&#38;at&#38;the&#38;use&#38;of&#38;measures&#38;of&#38;average&#38;and&#38;variability&#38;in&#38;trying&#38;to&#38;understand&#38;quan,ta,ve&#38; data.&#38;&#38;Here&#38;is&#38;another&#38;example&#38;to&#38;consider,&#38;above.&#38;The&#38;chart&#38;on&#38;the&#38;le\&#38;suggests&#38;a&#38;preference&#38;for&#38; ‘yes’&#38;but&#38;‘no’&#38;responses&#38;are&#38;also&#38;quite&#38;high,&#38;with&#38;even&#38;more&#38;‘undecided’.&#38;&#38;If&#38;this&#38;were&#38;the&#38;result&#38;of&#38; asking&#38;48&#38;learners,&#38;“have&#38;you&#38;improved&#38;your&#38;skills&#38;in&#38;maths&#38;as&#38;a&#38;result&#38;of&#38;this&#38;lesson?”,&#38;what&#38;might&#38; you&#38;conclude&#38;from&#38;the&#38;chart&#38;on&#38;the&#38;le\?&#38;&#38;Would&#38;you&#38;be&#38;more&#38;confident&#38;if&#38;your&#38;results&#38;looked&#38;like&#38;the&#38; chart&#38;on&#38;the&#38;right&#38;–&#38;and&#38;if&#38;so&#38;how&#38;would&#38;you&#38;jus,fy&#38;this&#38;in&#38;your&#38;‘conclusion&#38;sec,on’?&#38;&#38;&#38;&#38;

Finally, and to help you in making wise judgements about the outcomes of your research, here are some other questions you should ask yourself when evaluating data and making judgements about it (drawing wisdom out of knowledge). These questions will ‘sharpen your critical senses’ whenever you need to evaluate statistical findings.

1. How large was the sample in the study? In the Version 2 chart, above, would you be more confident in the outcome of the research if the numbers in the vertical axis were in hundreds (e.g. 8=800 learners, not just 8)?

2. Might other things be causing the observed changes in the data? Might learners’ scores have increased because you did something different with them (they were less bored and more engaged) rather than specifically what you did that was different (e.g. trying a specific approach to improving learners’ English skills)?

3. What further research might be necessary to increase your confidence in the results or to clarify potential causal factors?

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