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Randomisation S1 Beginners guide to randomisation Research supported by TLRI

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Randomisation S2 Experiments & the Randomisation Test: The difference between two medians Watch out for: The chance is acting alone explanation How we assess the plausibility of the chance alone explanation – (test for chance alone)

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Randomisation S3 Randomisation iNZightVIT What does chance alone look like?

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Randomisation S4 Did she brush her teeth? 1. She has brushed her teeth. 2.The toothbrush is dry. 3.The-toothbrush-is-dry would be highly unlikely if she had brushed her teeth. 4. Therefore, its a fairly safe bet she has not brushed her teeth. I have evidence that she has not brushed her teeth. 1.Formulate statement to test. 2.Data (information at hand). 3.Consider 1. and the data: If 1. is true, then what are the chances of getting data like that in 2.? 4.Review the statement in 1. in light of 3. together with the data in 2.

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Randomisation S5 Did she brush her teeth (2)? 1. She has brushed her teeth. 2.The toothbrush is wet. 3.The-toothbrush-is-wet would NOT be surprising if she had brushed her teeth. 4. Therefore, she could have brushed her teeth. I have no evidence that she has NOT brushed her teeth. 1.Formulate statement to test. 2.Data (information at hand). 3.Consider 1. and the data: If 1. is true, then what are the chances of getting data like that in 2.? 4.Review the statement in 1. in light of 3. together with the data in 2. Or she could have just run the brush under the tap.

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Randomisation S6 The Walking Babies Experiment Exercise Control Does a special exercise programme lower walking age? Phillip R. Zelazo, Nancy Ann Zelazo, & Sarah Kolb, Walking in the Newborn Science, Vol. 176 (1972), pp314-315 10 male infants (& parents) were randomly assigned to one of two treatment groups.

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Randomisation S7 The Walking Babies Experiment Treatment Age (months) Exercise99.59.751011 Control13.2511.51213.511.5 Does a special exercise programme lower walking age? Phillip R. Zelazo, Nancy Ann Zelazo, & Sarah Kolb, Walking in the Newborn Science, Vol. 176 (1972), pp314-315 10 male infants (& parents) were randomly assigned to one of two treatment groups. First walked without support:

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Randomisation S8 The Walking Babies Experiment Age (months) 91112101314 Does it appear that these data provide evidence that the treatment is effective? Yes.

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Randomisation S9 looking through a window with ripples in the glass What I see … is not quite the way it really is Looking at the world using data is like

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Randomisation S10 The Walking Babies Experiment Age (months) 91112101314 Is it possible that these babies walking ages have nothing to do with whether they undertook the exercises or not,...

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Randomisation S11 The Walking Babies Experiment Age (months) 91112101314... i.e., it doesnt matter which group they were randomly assigned to, they would still have the same walking age,...

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Randomisation S12 The Walking Babies Experiment Age (months) 91112101314... and so the observed difference pattern is purely and simply the result of the luck-of-the-draw as to which babies just happened by chance to be assigned to which group and nothing else? Yes. Under this scenario we say: Chance is acting alone.

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Randomisation S13 The Walking Babies Experiment Possible explanation: One possible explanation for the observed difference between these two groups: Chance is acting alone (the exercise has no effect)

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Randomisation S14 The Walking Babies Experiment Is the chance alone explanation simply not plausible? Would our observed difference be unlikely when chance is acting alone? How do we determine whether an observed difference is unlikely when chance is acting alone? Answer: See whats likely and whats unlikely when chance is acting alone. Possible explanation: One possible explanation for the observed difference between these two groups: (the exercise has no effect) Chance is acting alone

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Randomisation S15

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Randomisation S16 2.25

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Randomisation S17

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Randomisation S18

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Re-randomisation distribution of differences (under chance alone) Is chance alone likely to generate differences as big as our difference? Tail proportion: roughly __%

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Randomisation S20 The Walking Babies Experiment Possible explanation: One possible explanation for the observed difference between these two groups: Chance is acting alone (the exercise has no effect) Our tail proportion of roughly __% means: Roughly __ times out-of-a-1000 times we get a median difference of 2.25 months or more, when chance is acting alone. Under chance alone, it would be highly unlikely to get a difference equal to or bigger than our observed difference of 2.25 months.

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Randomisation S21 The Walking Babies Experiment Possible explanation: One possible explanation for the observed difference between these two groups: Chance is acting alone (the exercise has no effect) Our tail proportion of roughly __% means: Roughly __ times out-of-a-1000 times we get a median difference of 2.25 months or more, when chance is acting alone. Under chance alone, it would be highly unlikely to get a difference equal to or bigger than our observed difference of 2.25 months. An observed difference of 2.25 months or greater is highly unlikely when chance is acting alone... therefore, it probably isnt. Its a fairly safe bet chance is not acting alone.

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Randomisation S22 The Walking Babies Experiment We can rule out chance is acting alone as a plausible explanation for the difference between the two groups. We have evidence against chance is acting alone We have evidence that chance is not acting alone Possible explanation: One possible explanation for the observed difference between these two groups: Chance is acting alone (the exercise has no effect)

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Randomisation S23 The Walking Babies Experiment We can rule out chance is acting alone as a plausible explanation for the difference between the two groups. We have evidence against chance is acting alone We have evidence that chance is not acting alone Possible explanation: One possible explanation for the observed difference between these two groups: Chance is acting alone (the exercise has no effect) If chance is not acting alone, then what else is also acting to help produce the observed difference? Remember: Random assignment to 2 groups & each group receives different treatment.

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Randomisation S24 Conclusion: Because the male infants (& parents) were randomly assigned to the groups, we may claim that the exercise was effective in lowering the walking age. Because these subjects in this experiment were volunteers ( not randomly selected ), then we would need to consider carefully as to which wider group(s) this conclusion may apply. The Walking Babies Experiment

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Randomisation S25 Did she brush her teeth? 1. She has brushed her teeth. 2. The toothbrush is dry. 3. The-toothbrush-is-dry would be highly unlikely if she had brushed her teeth. 4. Therefore, its a fairly safe bet she has not brushed her teeth. I have evidence that she has not brushed her teeth. Steps 1.Statement to test. 2.Collect data (information). 3.Consider 1. and the data: If 1. is true, then what are the chances of getting data like that in 2.? 4.Review the statement in 1. in light of 3. together with the data in 2.

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Randomisation S26 Is the exercise programme effective? Steps 1.Statement to test. 2.Collect data. 3.Consider 1. and the data: If 1. is true, then what are the chances of getting data like that in 2. or more? 4.Review the statement in 1. in light of 3. together with the data in 2. 1. Chance is acting alone. (The exercise has no effect.) 2.Diff between medians = 2.25 mths. 3.A difference of 2.25 months or more is highly unlikely when chance is acting alone. (Tail prop = roughly __%) 4.Therefore, its a fairly safe bet chance is not acting alone. We have evidence against chance is acting alone.

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Randomisation S27 Steps 1.Statement to test. 2.Collect data. 3.Consider 1. and the data: If 1. is true, then what are the chances of getting data like that in 2. or more? 4.Review the statement in 1. in light of 3. together with the data in 2. 1. Chance is acting alone. (The exercise has no effect.) 2. diff medians= 2.25 mths. 3. A diff of 2.25 mths or more is highly unlikely when chance is acting alone. 4. Therefore, its a fairly safe bet chance is not acting alone. We have evidence against chance is acting alone. Is the exercise programme effective?

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Randomisation S28 Questions…

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Randomisation S29 Two types of Inference There are two types of inference 1.Sample-to-population eg x = 172cm so the population mean is about 172cm. 2.Experiment-to-causation eg The treatment was effective

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Randomisation S30 When the tail proportion is small (less than 10%).: the observed difference would be unlikely when chance is acting alone... therefore, its a fairly safe bet chance is not acting alone. we have evidence against chance-is-acting-alone we have evidence that chance is not acting alone Guidelines for assessing Chance alone

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Randomisation S31 When the tail proportion is large (10% or more ) then: the observed difference is not unusual when chance is acting alone, therefore chance could be acting alone we have NO evidence against chance is acting alone EITHER chance could be acting alone OR something else as well as chance COULD also be acting. -- we do NOT have ENOUGH INFORMATION to MAKE A CALL as to which one. Guidelines for assessing Chance alone

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