Revision of topics for CMED 305 Final Exam

The exam duration: 2 hours Marks :25 All MCQ’s. (50 questions) You should choose the correct answer. No major calculations, but simple maths IQ is required. No need to memorize the formulas. Bring your own calculator. Cell phones are not allowed to use as a calculator.

Research Methodology( 10 Questions): Biostatistics Topics: ( 40 questions) 1. Sampling Techniques (4) 2. Sample size (2) 3. Type of data & graphical presentation(4) 4. Summary and Variability measures (6) 5. Normal distribution (3) 6. Statistical significance using p-values (5) 7. Statistical significance using confidence intervals (5) 8. Statistical tests for quantitative variables (6) 9. Statistical tests for qualitative variables (4) 10. Spss software (1)

Sampling Methods Probability Sampling Simple random sampling Stratified random sampling Systematic random sampling Cluster (area) random sampling Multistage random sampling Non-Probability Sampling Deliberate (quota) sampling Convenience sampling Purposive sampling Snowball sampling Consecutive sampling

Estimation of Sample Size by Three ways: By using (1) Formulae (manual calculations) (2) Sample size tables or Nomogram (3) Softwares

Scales of Measurement Nominal – qualitative classification of equal value: gender, race, color, city Ordinal - qualitative classification which can be rank ordered: socioeconomic status of families Interval - Numerical or quantitative data: can be rank ordered and sizes compared : temperature Ratio - Quantitative interval data along with ratio: time, age.

TYPES OF DATA QUALITATIVE DATA (Categorical data) DISCRETE QUANTITATIVE CONTINOUS QUANTITATIVE

DIAGRAMS/GRAPHS Categorical data --- Bar diagram (one or two groups) --- Pie diagram Continuous data --- Histogram --- Frequency polygon (curve) --- Stem-and –leaf plot --- Box-and-whisker plot --- Scatter diagram

Summary Measures 9 Arithmetic Mean Median Mode Describing Data Numerically Variance Standard Deviation Range Interquartile Range Geometric Mean Skewness Central TendencyVariationShapeQuartiles Harmonic Mean

WHICH MEASURE TO USE ? DISTRIBUTION OF DATA IS SYMMETRIC ---- USE MEAN & S.D., DISTRIBUTION OF DATA IS SKEWED ---- USE MEDIAN &QUARTILES(IQR)

Distributions Bell-Shaped (also known as symmetric” or “normal”) Skewed: positively (skewed to the right) – it tails off toward larger values negatively (skewed to the left) – it tails off toward smaller values 11

VARIANCE: Deviations of each observation from the mean, then averaging the sum of squares of these deviations. STANDARD DEVIATION: “ ROOT- MEANS-SQUARE-DEVIATIONS”

Standard error of the mean Standard error of the mean (sem): Comments: n = sample size even for large s, if n is large, we can get good precision for sem always smaller than standard deviation (s)

Standard error of mean is calculated by:

Normal Distribution Many biologic variables follow this pattern Hemoglobin, Cholesterol, Serum Electrolytes, Blood pressures, age, weight, height One can use this information to define what is normal and what is extreme In clinical medicine 95% or 2 Standard deviations around the mean is normal Clinically, 5% of “normal” individuals are labeled as extreme/abnormal We just accept this and move on.

Characteristics of Normal Distribution  Symmetrical about mean,   Mean, median, and mode are equal  Total area under the curve above the x-axis is one square unit  1 standard deviation on both sides of the mean includes approximately 68% of the total area  2 standard deviations includes approximately 95%  3 standard deviations includes approximately 99%

Sample z = x - x s Population z = x - µ  Measures of Position z score

Z Unusual Values Unusual Values Ordinary Values Interpreting Z Scores

Null hypothesis ‘No difference ‘ or ‘No association’ Alternative hypothesis Logical alternative to the null hypothesis ‘There is a difference’ or ‘Association’Hypothesis simple, specific, in advance

TYPE I & TYPE II ERRORS Every decisions making process will commit two types of errors. “We may conclude that the difference is significant when in fact there is not real difference in the population, and so reject the null hypothesis when it is true. This is error is known as type-I error, whose magnitude is denoted by the Greek letter ‘α ’. On the other hand, we may conclude that the difference is not significant, when in fact there is real difference between the populations, that is the null hypothesis is not rejected when actually it is false. This error is called type-II error, whose magnitude is denoted by ‘ β ’.

Diagnostic Test situation Disease (Gold Standard) Present Correct Negative Total Positive Test False Negative a+b a+b+c+d Total Correct a+cb+d c+d False Positive Result Absent a b cd

P S Investigation S Sampling P value Confidence intervals!!! Inference Results

Definition of p-value Stating the Conclusions of our Results When the p-value is small, we reject the null hypothesis or, equivalently, we accept the alternative hypothesis. “Small” is defined as a p-value  , where  acceptable false (+) rate (usually 0.05). When the p-value is not small, we conclude that we cannot reject the null hypothesis or, equivalently, there is not enough evidence to reject the null hypothesis. “Not small” is defined as a p-value > , where  = acceptable false (+) rate (usually 0.05).

Rejection Nonrejection region Rejection region region Z  /2 = 1.96 Reject H 0 if Z Z  /2 25 Testing significance at 0.05 level

Estimation Two forms of estimation Point estimation = single value, e.g., x-bar is unbiased estimator of μ Interval estimation = range of values  confidence interval (CI). A confidence interval consists of:

Mean, , is unknown PopulationRandom Sample I am 95% confident that  is between 40 & 60. Mean X = 50 Estimation Process Sample

Different Interpretations of the 95% confidence interval “ We are 95% sure that the TRUE parameter value is in the 95% confidence interval” “If we repeated the experiment many many times, 95% of the time the TRUE parameter value would be in the interval”

Most commonly used CI: CI 90% corresponds to p 0.10 CI 95% corresponds to p 0.05 CI 99% corresponds to p 0.01 Note: p value  only for analytical studies CI  for descriptive and analytical studies

CHARACTERISTICS OF CI’S --The (im) precision of the estimate is indicated by the width of the confidence interval. --The wider the interval the less precision THE WIDTH OF C.I. DEPENDS ON: ---- SAMPLE SIZE ---- VAIRABILITY ---- DEGREE OF CONFIDENCE

Comparison of p values and confidence interval p values (hypothesis testing) gives you the probability that the result is merely caused by chance or not by chance, it does not give the magnitude and direction of the difference Confidence interval (estimation) indicates estimate of value in the population given one result in the sample, it gives the magnitude and direction of the difference

Statistical Tests Z-test: Study variable: Qualitative Outcome variable: Quantitative or Qualitative Comparison: Sample mean with population mean Sample proportion with population proportion Two sample means & Two sample proportions Sample size: each group is > 30 Student’s t-test: Study variable: Qualitative Outcome variable: Quantitative Comparison: sample mean with population mean; two means (independent samples); paired samples. Sample size: each group <30 ( can be used even for large sample size)

Student’s t-test 1.Test for single mean 2. Test for difference in means Test for paired observation 3. Test for paired observation

Student ‘s t-test will be used: --- When Sample size is small, for mean values and for the following situations: (1) to compare the single sample mean with the population mean (2) to compare the sample means of two independent samples (3) to compare the sample means of paired samples

Karl Pearson Correlation Coefficient --- To quantify the linear relationship between two quantitative variables.

Statistical tests for qualitative (categorical) data

Statistical test (cont.) Chi-square test: Study variable: Qualitative Outcome variable: Qualitative Comparison: two or more proportions Sample size: > 20 Expected frequency: > 5 Fisher’s exact test: Study variable: Qualitative Outcome variable: Qualitative Comparison: two proportions Sample size:< 20 Macnemar’s test: (for paired samples) Study variable: Qualitative Outcome variable: Qualitative Comparison: two proportions Sample size: Any

When both the study variables and outcome variables are categorical (Qualitative): Apply (i) Chi square test ( two or more proportions; large sample size) (ii) Fisher’s exact test ( only two proportions; Small samples) (iii) Mac nemar’s test ( for paired samples; only two proportions; any sample size)

Degrees of Freedom (df )

Wishing all of you Best of Luck !