2300 FT Lecture3 Slides

2300 FT Lecture3 Slides - Lecture 3 Descriptive Statistics...

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Hannah Wong School of Health Policy and Management Faculty of Health Lecture 3: Descriptive Statistics – Describing Data With Numerical Measures 1
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Lecture outline Measures of central tendency: Mean, Median, Mode Measures of deviation: Range, IQR, Variance and Standard Deviation Measures of deviation from normality: Modality, Skewness and Kurtosis Measures of stability: Standard Error 2
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Descriptive statistics Two different types of statistical techniques that researchers can utilize: Descriptive statistics – used to simply describe research data Help us to get to know our data Help others to know about our data Help to identify problems with data Inferential statistics – used to help generalize findings from one study to the wider population 3
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Example Stroke Heart attack 39 27 27 27 26 1 29 23 26 25 27 26 9 23 27 35 14 23 33 25 28 40 22 32 21 9 29 32 26 13 23 22 23 13 29 25 18 21 30 30 Assume we are interested in discovering whether there are differences between stroke patients and heart attack patients in their ability to come to terms with their illness. We have given a group of patients with each illness a questionnaire that measures how well they are coping after they have left hospital (the higher the value, the better able they are at coping with their illness). Let’s describe the typical score in the sample (measures of central tendency) variability or dispersion of scores in the sample Coping scores 4
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Measures of central tendency Central tendency refers to where the scores tend to ‘cluster’ or ‘converge’ on a variable. It is where the ‘centre’ is, where ‘most’ or ‘typical’ scores are. Mean “if all cases had the same score, that score would be…” Median “the score that has half of the cases above it and half below” Mode “the most frequently occurring score on the variable” 5
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The mean is the most commonly reported measure of central tendency. It is calculated by: Adding up the scores in the sample Then dividing by the number of such scores E.g. for these scores: 3, 7, 9, 6 Adding these gives us 25 Divide by the number of scores (which is 4) this gives us 6.25 Thus the mean is 6.25 Measures of central tendency – the mean 3 + 7 + 9 + 6 4 = = 6.25 6
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Measures of central tendency – the mean Stroke Heart attack 39 27 27 27 26 1 29 23 26 25 27 26 9 23 27 35 14 23 33 25 28 40 22 32 21 9 29 32 26 13 23 532 23 13 29 25 18 21 30 30 Mean coping score: Stroke: 21.25 Heart attack: 27.65 The mean can be rather misleading in terms of how it represents the whole dataset. Suppose we had the same data as the heart attack patients but the score of 22 is changed to 532. Now we have a new mean of 53.15. The mean is influenced by extreme scores! Coping scores Saying the typical score is 53.15 is rather misleading as the vast majority of scores are between 25 and 35. Thus the mean does a poor job of describing our dataset.
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