BHSc MSc PhD Student University of Oxford December 201 5 Twitter nikbobrovitz Stats Topics Descriptive measures Summary measures Measures of variability How do you know if a difference is significant ID: 920019
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Slide1
StatisticsNik Bobrovitz BHSc, MSc PhD Student University of Oxford December 2015
Twitter: @
nikbobrovitz
Slide2Stats TopicsDescriptive measuresSummary measuresMeasures of variability How do you know if a difference is significant? 95% confidence intervals P-values
Slide3Descriptive measuresDescriptive measures are used to summarize the data you observe Means, medians, proportions
Slide4MeanAverage Blood pressure, heart rate, number of drug
150
m
m hg
170
mm hg
130
m
m hg
BP (mm
hg)
145
148
155
163
Slide5MedianMiddle number (50th percentile) Useful when extreme values are presentQOL measures
150
m
m hg
170
mm hg
130
m
m hg
50%
Mean
Slide6ProportionCategories: gender Males15 participants: 3 males, 12 females
Slide7Describing the spread of dataPeople are naturally different: measures of variability describe the spread of the dataMean: standard deviationMedian: interquartile rangeProportions: no dispersion for descriptive proportions so no measures of variability
Slide8Standard deviation (mean)Measure of dispersion of data +/- the SD (includes 68% of observations)
150
m
m hg
170
mm hg
130
m
m hg
BP (mm
hg)
145
148
155
163
Mean =
153.5
+SD
-
SD
Slide9Interquartile range (median)Measure of the dispersion of data
150
m
m hg
170
mm hg
130
m
m hg
25%
75%
50%
Slide10How do you know if a difference is statistically significant?InterventionControlBlood pressureHeart rateQuality of lifeBaseline – post intervention
Baseline – post intervention
Difference
DifferenceSignificant difference?
Slide1195% confidence intervals that don’t cross the “null” value (0 for subtraction, 1 for ratios) P-values less than the “level of significance” (0.05)Statistically significant?
Slide12Statistically significant?InterventionControlBlood pressureBeforeAfter
150
m
m hg
170
mm hg
130
m
m hg
150
m
m hg
170
mm hg
130
m
m hg
150
m
m hg
170
mm hg
130
m
m hg
150
m
m hg
170
mm hg
130
m
m hg
Slide13Statistically significant?InterventionControlPoint estimates of the mean difference within each group
0
m
m hg
+20
mm hg
-20
m
m hg
0
m
m hg
+20
mm hg
-20
m
m hg
-7.5
-12.2
95% confidence interval
(-12.7 to -2.3)
(-17.4 to -7.0)
T-test: statistical test
for mean differences
Slide14Point estimates and confidence intervals Point estimate: Single value representing your estimate of the population value Confidence intervalsTwo values: range which contains the “true” population value100 samples, 95% of the time the value would be in that range Narrower the range, the better
Slide15Assessing differences with statisticsInterventionControl
0
m
m hg
+20
mm hg
-20
m
m hg
0
m
m hg
+20
mm hg
-20
m
m hg
-7.5
-12.2
(-12.7 to -2.3)
(-17.4 to -7.0)
Difference
between
groups
0
m
m hg
+20
mm hg
-20
m
m hg
-4.7 (-11.7 to 2.3)
T-test: statistical test
for mean differences
Slide16P - valuesP valuesProbability that a result is due to chance (random variability)When P-values less than the “level of significance” we accept them as being statistically significantP<0.05 = <5% probability it occurred by chance
Slide17Stats LessonsDescriptive measures are used to summarize the data you observe (mean, median, proportion)Measures of variability (SD, IQR) tell you about the spread of data Statistically significant?95% CI that don’t cross the null value (0 for subtraction, 1 for ratios)P-values less than the level of significance (<0.05)