BASIC STATISTICS AND THEIR INTERPRETATION AND USE IN EPIDEMIOLOGY 050822.pdf
- 1. BASIC STATISTICS, THEIR INTERPRETATION AND USE IN EPIDEMIOLOGY By Olufela, Oridota (FMCPH)
- 2. Learning Objectives • Introduction to basic statistics. • Skewed data and its implication and normal distribution. • Concepts in inferential statistics. • Parametric and non-parametric test.
- 3. Introduction ▪ Statistics is a fundamental tool for investigation in medical science. ▪ A health care professional should understand when statistical calculations are valid and how they should be interpreted.
- 4. Scale of Measurement •Categorical or qualitative data •Numerical or quantitative data
- 5. Categorical or qualitative data • Nominal • Ordinal
- 6. Quantitative • Discrete • Measured or numerical continuous • Interval and ratio scales
- 7. Nominal - Categorical • These are data that one can name and put into categories. They are not measured but simply counted. • Examples includes gender, dichotomous disease status (disease, unaffected).
- 8. Ordinal Categorical • The data are arranged both in categories and in order, ordinal data provide more information than categories alone. • Example includes educational level and tumour stages.
- 9. Discrete data •All values are clearly separate from each other. Although numbers are used, they can only have a certain range of values. •For example, age last birthday, number of operations performed in one year.
- 10. Measured or numerical continuous • Each value can have any number of values in between, depending on the accuracy of measurement. • There can be decimals • Example: Height can be 1.67m
- 11. Interval and ratio scales • One can distinguish between interval and ratio scales. In an interval scale, such as body temperature , a difference between two measurements has meaning, but their ratio does not. • It does not have absolute zero
- 12. Interval and ratio scales Consider measuring temperature (in degrees centigrade) then we cannot say that a temperature of 20°C is twice as hot as a temperature of 10°C. e.g. temperature , date of birth.
- 13. Interval and ratio scales • In a ratio scale, however, such as body weight, a 10% increase implies the same weight increase whether expressed in kilograms or pounds. • Both interval between the measurement and their ratio can be calculated. • Ratio scale has an absolute zero ( true zero point) e.g. weight, height.
- 14. Measures of central tendency • Mean • Mode • Median
- 15. Example Set of observation 2,4,2,10,5,7,12 Mean =42/6 =7 Mode = 2 Median =5
- 16. Skewness • Measure of symmetry, or more precisely, the lack of symmetry. • A distribution, or data set, is symmetric if it looks the same to the left and right of the center point.
- 17. Positively skewed Extreme values to the right. Mean>median>mode e.g. 2,5,4,7,8,5,6,11,10,12,70,68.
- 18. Negatively skewed • Mean<Median<mode • e.g. 45,50,57,35,40,42,3,5.
- 19. Positive and negative skew
- 20. Measures of dispersion • Range • Variance • Standard deviation • Coefficient of variation =(SD/mean) *100 • Quartiles (including the interquartile range): It shows the spread of the data
- 21. NORMAL DISTRIBUTION • It is an important tool in analysis of epidemiological data. • Biological variables follow the normal distribution pattern e.g. Height, weight, blood pressure. • It plays a major role in statistical inference. • If any data set is normally distributed, we can predict the proportion of values that lie within a certain range
- 22. Characteristics of a normal distribution • It is bell shaped. • It is symmetrical about the mean. • Mean=median=mode • The mean ±1 standard deviation covers 68% of the area under the curve • The mean ±2 standard deviation covers 95% of the area under the curve • The mean ±3 standard deviation covers 99% of the area under the curve
- 24. Example If the mean weight of a group of market women is 50 kg and the standard deviation is 5kg Then • 68% will have weight 50kg ± 1SD = 45-55kg • 95% will have weight 50Kg ± 2SD = 40-60kg • 99% will have weight 50kg ± 3SD = 35-65kg
- 25. FREQUENCIES AND PROPORTIONS • Frequency: the number of units with a certain characteristic • Proportion: ratio of frequency to the total number of units, the numerator is part of the denominator. • Rate: proportion over a specified time
- 26. RATES, RATIOS & PROPORTIONS • Rates are numbers such that the count in the numerator is part of the denominator and with a time dimension (per year, per hour etc) • Proportions are simply fractions or percentages • Ratios are numbers such that the numerator and denominator usually refer to different events or counts from different populations
- 27. Inferential Statistics • Inferential statistics deals with extrapolation. • From what we observe from the sample, we draw conclusion to the population. • Enable generalization about a population based on the attributes of a sample
- 28. KEY APPROACHES • (A) SETTING UP A CONFIDENCE INTERVAL • (B) HYPOTHESIS TESTING
- 29. Hypothesis • Statistical hypotheses are stated in such a way that they may be tested. • Statistical hypotheses have both the null hypothesis and the alternative hypothesis designated Ho and HA (or H1) • It is the null hypothesis that the researcher tests.
- 30. Null Hypothesis (Ho), • Null Hypothesis (Ho), is the hypothesis that the samples or population being compared in an experiment, study or test are similar. Any difference discerned is due to chance and not to any other measurable factor. Examples: • H0: μ1 = μ2 • H0: π1 = π 2
- 31. Alternative Hypothesis • Alternative Hypothesis (HA), is the hypothesis that the samples or population being compared in an experiment, study or test are not similar. Any difference discerned is not due to chance but to any other measurable factor. Examples: • HA: μ1 ≠ μ2 • HA: π1 ≠ π 2
- 32. P value • Probability that an effect as extreme as observed in a study could have occurred by chance alone, given that H0 is true • It tells us the probability of rejecting H0 when in fact H0 is correct.
- 33. P Value •The lower the P value, the less likely that our rejection of H0 is erroneous. •By convention, most analysts will not claim that they have found statistical significance if there is more than 5% chance of being wrong. •Statistical significance is found when p is equal to or less than 0.05 (p=<0.05)
- 34. CONFIDENCE INTERVAL • Assist in addressing the questions of clinical importance and magnitude of an observed effect • Specifies a range of values on either side of the sample statistic within which the population parameter can be expected to fall with a chosen level of confidence.
- 35. Type I (false-positive) error • Type I (false-positive) error: The error committed when we reject a true null hypothesis is called type I (false- positive) error. • It occurs when we conclude from an experiment that a difference between treatments exists when in truth it does not. • The probability of committing a type I error is called α (alpha). • Another name for α is the level of statistical significance.
- 36. Type II (false-negative) error: • Type II (false-negative) error: The error committed when we fail to reject a false null hypothesis is called type II (false-negative) error. • It occurs when we conclude from an experiment that no difference between treatments exists when in truth it does. • The probability of making a type II error is called β (beta).
- 37. The power of the study • The power of a study is its ability to detect a true difference in outcome between the intervention and control . • The power of the study = 1- β • Ideally, α and β should be set at zero, eliminating the possibility of false-positive and false-negative results. • In practice they are made as small as possible.
- 38. Standard error • The standard error is the indicator of variability, and much of the complexity of the hypothesis test involves estimating the standard error correctly • It is a measure of the dispersion of sample means around population mean. • Equals standard deviation divided by the square root of the sample size
- 39. When do we use the mean Parametric tests ▪t-tests ( Independent t-test and paired t-test) ▪ANOVA
- 40. Median May require non-parametric tests ▪ Mann-Whitney, ▪ Kruskal-Wallis ▪ Wilcoxon signed rank
- 41. Non Parametric methods • Use the median • For non-normally distributed data • Not affected by extreme observations and more robust • Not efficient at detecting real differences
- 42. Parametric Tests Non-parametric Tests Single sample t-test Wilcoxon-signed rank test Paired sample t-test Paired Wilcoxon-signed rank 2 independent samples t-test Mann-Whitney test(Note: sometimes called Wilcoxon Rank Sums test!) One-way Analysis of Variance Kruskal-Wallis Pearson’s correlation Spearman Rank Repeated Measures Friedman
- 43. How are the populations (samples) related? ▪ INDEPENDENT ▪ PAIRED (RELATED)
- 44. INDEPENDENT ▪Chi-square test, Fisher’s Exact test ▪Mann-Whitney ▪Kruskal-Wallis ▪Independent t-test ▪ANOVA
- 45. PAIRED (RELATED) •McNemar’s test •Sign test •Wilcoxon-signed rank •Friedman’s test •paired t-test •Repeated measures ANOVA (RM ANOVA).
- 46. • Thank you for listening