How to calculate Sample Size
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Sample size and how to calculate it - Why sample size is important - Alpha and beta errors - Main outcome and Effect size - Practical examples using Means-Proportions-Correlation- Confidence Interval
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How to calculate Sample Size
- 1. Mohamed MamdouhAbdAlBary Ass. Lecturer of Internal Medicine (Nephrolo
- 2. Poor quality research “Errors” Too small : not powerful to demonstrate difference Too large : Waste of resources
- 3. The variable Level of significance Statistical power One-sided or two-sided Effect size
- 4. Type Continuous Variable (Mean & SD) Categorical variable (proportion) Variance (σ2) Data from previous studies Pilot study Estimate or guess
- 7. REALITY Decision H₀ True H₀ False Reject H₀ Error : Type I (α) Correct (1-β) Not Reject H₀ Correct (1-α) Error: Type II (β) Prove difference No difference False +ve Difference is real Fail to prove it False -ve The Power
- 10. Testing relation in one directions Smoking and lung cancer Testing relation in both directions “A” is either better or worse than “B”
- 13. Note: Calculated sample size is the minimal number required
- 18. Variables Qualitative Nominal no natural order e.g. gender, race Ordinal ordered categories e.g. stages of cancer Quantitative Continuous Measured units & fraction is possible e.g. bl. pr., age, weight, height, hemoglobin Discrete Counted units & fraction is not possible E.g. no. of deaths, no. of patients
- 23. Binominal Enumeration = exact power Usually the same results But for small sample and extreme values choose binominal. Enter null proportion (P0) and if use: Alternative proportion (P1) >> Proportions Alternative difference (P1-P0) >> Differences Alternative ratio (P1/P0) >> Ratios alternative odds ratio >> Odds Ratios
- 24. The higher the difference the lower the sample size needed
- 25. Two proportion
- 26. Group Allocation : Equal (N1 = N2). Enter N1, solve for N2 and vice versa. Enter R = N2/N1, solve for N1 and N2. Enter percentage in Group 1, solve for N1 and N2. P1 = Treatment Group P2 = Control Group.
- 27. One Mean
- 47. The confidence interval method to be used is the Yates chi-square simple asymptotic method with continuity correction.
Editor's Notes
- If the study has more than one important outcome variables: Separate sample size calculations should be done for each important variable & select the largest calculated size
- كل مرة بترفض فيها ال h0 فيه احتمالية للخطأ
- Reject H₀ when it is true. (type 1 error). = Accept H₁ = False positive. .. Alpha = probability of type 1 reject a true null hypothesis Reject H₀ when it is false. (Correct) Not Reject H₀ when it is true. (Correct) Not reject H₀ when it is false. (type II error) = Reject H₁ = False negative. Beta = probability of fail to reject a false null hypothesis.
- Things do not always work out as expected, you may be surprised by your results. (2) Use two-sided tests unless there is a very good reason for doing otherwise . (3) If you use one sided tests , direction of the test must be specified in advance. (4) Never use one sided tests to make a non-significant difference significant 4. One tail 2 tail :: نشتغل بنية إثبات إ،ه أعلى في جهة واحدة لو جايز يطلع العكس يبقى اتجاهين One tail :: عدد أقل
- The variable of interest is not their actual weight, but how much their weight changed. In this design, the data are analyzed using a one-sample t-test on the differences between the paired observations. The null hypothesis is that the average difference is zero. The alternative hypothesis is that the average difference is some nonzero value.
- hazard ratio (HR) is the ratio of the hazard rates corresponding to the conditions described by two levels of an explanatory variable. For example, in a drug study, the treated population may die at twice the rate per unit time as the control population. The hazard ratio would be 2, indicating higher hazard of death from the treatment. Or in another study, men receiving the same treatment may suffer a certain complication ten times more frequently per unit time than women, giving a hazard ratio of 10.
- Z-test is a statistical test where normal distribution is applied and is basically used for dealing with problems relating to large samples when n ≥ 30. For example suppose a person wants to test if both tea & coffee are equally popular in a particular town. Then he can take a sample of size say 500 from the town out of which suppose 280 are tea drinkers. To test the hypothesis, he can use Z-test.