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Background to Statistics fornon-statisticians Dr. Craig Jackson Senior Lecturer in Health Psychology Faculty of Health BCU

Types of Data / Variables ContinuousDiscrete BPChildren Height Age last birthday Weight colds in last year Age OrdinalNominal Grade of conditionSex Positions 1 st 2 nd 3 rd Hair colour “Better- Same-Worse”Blood group Height groupsEye colour Age groups

Conversion & Re-classification Easier to summarise Ordinal / Nominal data Cut-off Points(who decides this?) Allows Continuous variables to be changed into Nominal variables BP> 90mmHg=Hypertensive BP=< 90mmHg=Normotensive Easier clinical decisions Categorisation reduces quality of data Statistical tests may be more “sensational” Good for summariesBad for “accuracy”

Types of statistics / analyses DESCRIPTIVE STATISTICSDescribing a phenomena FrequenciesHow many… Basic measurementsMeters, seconds, cm 3, IQ INFERENTIAL STATISTICSInferences about phenomena Hypothesis TestingProving or disproving theories Confidence IntervalsIf sample relates to the larger population CorrelationAssociations between phenomena Significance testinge.g diet and health

Multiple Measurement or…. why statisticians and love don’t mix 25 cells 22 cells 24 cells 21 cells Total = 92 cells Mean = 23 cells SD= 1.8 cells

NAgeIQ Total Mean20100 SD00 NAgeIQ Total Mean SD± 4.2 ± 19.2 NAgeIQ Total Mean SD± 8.5 ± 30.2 Small samples spoil research

Central Tendency Mode MedianMean MedianMean Patient comfort rating Frequency

Dispersion RangeSpread of data MeanArithmetic average MedianLocation ModeFrequency SDSpread of data about the mean Range mmHg Mean82mmHgMedian82mmHgMode82mmHg SD± 10mmHg

Dispersion An individual score therefore possess a standard deviation (away from the mean), which can be positive or negative Depending on which side of the mean the score is If add the positive and negative deviations together, it equals zero (the positives and negatives cancel out) central value (mean) central value (mean) negative deviation positive deviation

5’6” 5’7” 5’8” 5’9” 5’10” 5’11” 6’ 6’1” 6’2” 6’3” 6’4” 5’6” 5’7” 5’8” 5’9” 5’10” 5’11” 6’ 6’1” 6’2” 6’3” 6’4” Range 1st5th25th50th75th95th99thDispersionRange The interval between the highest and lowest measures Limited value as it involves the two most extreme (likely faulty) measures Percentile The value below / above which a particular percentage of values fall (median is the 50th percentile) e.g 5th percentile - 5% of values fall below it, 95% of values fall above it. A series of percentiles (1st, 5th, 25th, 50th, 75th, 95, 99th) gives a good general idea of the scatter and shape of the data

Standard Deviation To get around this, we square each of the observations Makes all the values positive (a minus times a minus….) Then sum all those squared observations to calculate the mean This gives the variance - where every observation is squared Need to take the square root of the variance, to get the standard deviation SD =  Σ x 2 – (Σ x) 2 / N (N – 1) (N – 1)

Non Normal Distribution Some distributions fail to be symmetrical If the tail on the left is longer than the right, the distribution is negatively skewed (to the left) If the tail on the right is longer than the left, the distribution is positively skewed (to the right) Grouped Data Normal Distribution SD is useful because of the shape of many distributions of data. Symmetrical, bell-shaped / normal / Gaussian distribution

central value (mean) 3 SD 2 SD 1 SD 0 SD 1 SD 2 SD 3 SD Normal Distributions Standard Normal Distribution has a mean of 0 and a standard deviation of 1 The total area under the curve amounts to 100% / unity of the observations Proportions of observations within any given range can be obtained from the distribution by using statistical tables of the standard normal distribution 95% of measurements / observations lie within 1.96 SD’s either side of the mean

balls dropped through a succession of metal pins….. …..a normal distribution of balls do not have a normal distribution here. Why? Quincunx machine 1877

The distribution derived from the quincunx is not perfect It was only made from 18 balls Normal & Non-normal distributions

5’6” 5’7” 5’8” 5’9” 5’10” 5’11” 6’ 6’1” 6’2” 6’3” 6’4” 5’6” 5’7” 5’8” 5’9” 5’10” 5’11” 6’ 6’1” 6’2” 6’3” 6’4”Height % of population Distributions Sir Francis Galton ( ) Alumni of Birmingham University 9 books and > 200 papers Fingerprints, correlation of calculus, twins, neuropsychology, blood transfusions, travel in undeveloped countries, criminality and meteorology) Deeply concerned with improving standards of measurement

Normal & Non-normal distributions Galton’s quincunx machine ran with hundreds of balls a more “perfect” shaped normal distribution. Obvious implications for the size of samples of populations used The more lead shot runs through the quincunx machine, the smoother the distribution in the long run.....

ExposedControlsT P n=197n=178 Age (yrs)(  9.4)(  7.3) I.Q (  10.8)(  8.7) Speed (ms) (  13.4)(  12.4) (ms) (  13.4)(  12.4) Presentation of data Table of means

ExposedControls Healthy Unwell Chi square (test of association) shows: Chi square = 7.2P = 0.02 Presentation of data Category tables

y-axis x-axis (abscissa) y-axislabel(ordinate) scale Data display area groups Legend key Title of graph Bar Charts A set of measurements can be presented either as a table or as a figure Graphs are not always as accurate as tables, but portray trends more easily

User rating Votes Movie goers’ ratings for both movies Vacation Empire Bar Charts Some Real Data A combination of distributions is acceptable to facilitate comparisons

With a scatter diagram, each individual observation becomes a point on the scatter plot, based on two co-ordinates, measured on the abscissa and the ordinate Two perpendicular lines are drawn through the medians - dividing the plot into quadrants Each quadrant should outlie 25% of all observations Correlation and Association ordinate abscisaa

Correlation is a numerical expression between 1 and -1 (extending through all points in between). Properly called the Correlation Coefficient. A decimal measure of association (not necessarily causation) between variables Correlation of 1 Maximal - any value of one variable precisely determines the other. Perfect +ve Correlation of -1 Any value of one variable precisely determines the other, but in an opposite direction to a correlation of 1. As one value increases, the other decreases. Perfect -ve Correlation of 0 - No relationship between the variables. Totally independent of each other. “Nothing” Correlation of Only a slight relationship between the variables i.e half of the variables can be predicted by the other, the other half can’t. Medium +ve Correlations between 0 and 0.3 are weak Correlations between 0.4 and 0.7 are moderate Correlations between 0.8 and 1 are strong Correlation and Association

Correlation is a numerical expression between 1 and -1 (extending through all points in between). Properly called the Correlation Coefficient. A decimal measure of association (not necessarily causation) between variables Correlation and Association

POPULATIONS Can be mundane or extraordinary SAMPLE Must be representative INTERNALY VALIDITY OF SAMPLE Sometimes validity is more important than generalizability SELECTION PROCEDURES RandomOpportunisticConscriptiveQuota Sampling Keywords

THEORETICAL Developing, exploring, and testing ideas EMPIRICAL Based on observations and measurements of reality NOMOTHETIC Rules pertaining to the general case (nomos - Greek) PROBABILISTIC Based on probabilities CAUSAL How causes (treatments) effect the outcomes Sampling Keywords

Clinical Research Types of clinical research Experimental vs. Observational Longitudinal vs. Cross-sectional Prospective vs. Retrospective Longitudinal Prospective Experimental Randomised Controlled Trial Observational Longitudinal Cross-sectional Survey RetrospectiveProspective Case control studies Cohort studies

patients Treatment group Control group Outcome measured patients Outcome measured #1 Treatment Outcome measured #2 Experimental Designs Between subjects studies Within Subjects studies

prospectively measure risk factors cohort end point measured aetiologyprevalencedevelopment odds ratios retrospectively measure risk factors start point measured cases aetiology odds ratios prevalencedevelopment Observational studies Cohort (prospective) Case-Control (retrospective)

Case-Control Study – Smoking & Cancer “Cases” have Lung Cancer “Controls” could be other hospital patients (other disease) or “normals” Matched Cases & Controls for age & gender Option of 2 Controls per Case Smoking years of Lung Cancer cases and controls (matched for age and sex) CasesControls n=456n=456 FP Smoking years (± 1.5)(± 2.1)

Cohort Study: Methods Volunteers in 2 groups e.g. exposed vs non-exposed All complete health survey every 12 months End point at 5 years: groups compared for Health Status Comparison of general health between users and non-users of mobile phones illhealthy mobile phone user non-phone user

Randomized Controlled Trials in GP & Primary Care 90% consultations take place in GP surgery 50 years old Potential problems 2 Key areas:Recruitment Bias Randomisation Bias Over-focus on failings of RCTs

RCT Deficiencies Trials too small Trials too short Poor quality Poorly presented Address wrong question Methodological inadequacies Inadequate measures of quality of life (changing) Cost-data poorly presented Ethical neglect Patients given limited understanding Poor trial management PoliticsMarketeering Why still the dominant model?

Quantitative Data Summary What data is needed to answer the larger-scale research question What data is needed to answer the larger-scale research question Combination of quantitative and qualitative ? Combination of quantitative and qualitative ? Cleaning, re-scoring, re-scaling, or re-formatting Cleaning, re-scoring, re-scaling, or re-formatting Measurement of both IV’s and DV’s is complex but can be simplified Measurement of both IV’s and DV’s is complex but can be simplified Binary measurement makes analysis easier but less meaningful Binary measurement makes analysis easier but less meaningful Binary data needs clear parameters e.g exposed vs controls Binary data needs clear parameters e.g exposed vs controls Collecting good quality data at source is vital Collecting good quality data at source is vital

Quantitative Data Summary Continuous & Discrete data can also be converted into Binary data Continuous & Discrete data can also be converted into Binary data Normal distribution of participants / data points desirable Normal distribution of participants / data points desirable Means - age, height, weight, BMI, IQ, attitudes Means - age, height, weight, BMI, IQ, attitudes Frequencies / Classifications - job type, sick vs. healthy, dead vs alive Frequencies / Classifications - job type, sick vs. healthy, dead vs alive Means must be followed by Standard Deviation (SD or ±) Means must be followed by Standard Deviation (SD or ±) Presentation of data must enhance understanding or be redundant Presentation of data must enhance understanding or be redundant

Further Reading Abbott, P. and Sapsford. Research methods for nurses and the caring professions. Open University Press, Buckingham Altman DG. Designing Research. In: Altman DG (ed.) Practical Statistics For Medical Research. Chapman and Hall, London 1991; Bland M. The design of experiments. In: Bland M. (ed.) An introduction to medical statistics. Oxford Medical Publications, Oxford 1995; Bowling, A. Measuring Health. Open University Press, Milton Keynes 1994 Daly LE, Bourke GJ. Epidemiological and clinical research methods. In: Daly LE, Bourke GJ. (eds.) Interpretation and uses of medical statistics. Blackwell Science Ltd, Oxford 2000;

Further Reading Gao Smith F, Smith J. (eds.) Key Topics in Clinical Research. BIOS scientific Publications, Oxford Jackson CA. Planning Health and Safety Research Projects. Croner Health and Safety at Work Special Report 2002; 62: Jackson CA. Analyzing Statistical Data in Occupational Health Research. Management of Health Risks Special Report, 81 Croner Publications, Surrey, June 2003 Kumar, R. Research Methodology: a step by step guide for beginners. Sage, London Polit, D. & Hungler, B. Nursing research: Principles and methods (7th ed.). Philadelphia: Lippincott, Williams & Wilkins 2003.