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StatisticsStatistics Dr. Ahmed Abd Elmaksoud Lecturer of Anesthesiology & ICU Faculty of medicine Ain Shams University When guessing is informed decision

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Objectives Define statistics and understand its terminology Discuss the importance and need of statistics in medical field Distinguish types of data and variables Describe types of statistics & statistical tests

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What is statistics? Statistics is the science of collecting, describing, and analyzing data in order to get a good decision.

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Collecting data Describing data Analyzing data Good Decision

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Why do we need statistics? Variability (atropine) Causes: - Uncontrollable (too many) factors Immeasurable factors Unknown factors

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Why do we need statistics? Variability (atropine) Effect of variability Large amount of data describing the same thing (many values for one variable) No certainty “Deterministic vs probabilistic” Sampling

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Functions of statistics (new hypothetical β-blocker drug) Describe (Descriptive statistics) Inference (Inferential statistics)

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Variables & Data A variable is something whose value can vary. For example, age, gender and blood type are variables. Data are the values you get when you measure a variable

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Mrs Brown Mr Patel Ms Manda Age 322420 Gender FemaleMaleFemale Blood type OOA The Variables…… ………and the Data

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Types of variables 1.Qualitative variables (data) a)Categorical variable The values (data) of a categorical variable are categories Gender: (dichotomous –binary) Male Female Type of ICU admission Medical Surgical Physical injuries Poisoning Others

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Types of variables 1.Qualitative variables (data) b)Ordinal variable Categorical variable whose values are ordered Degree of illness Mild Moderate Severe Physical status ASA I ASA II ASA III ASA IV ASA V Glasgow’s coma scale

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Types of variables 2.Quantitative (Numerical) variables a)Discrete variable Episodes of myocardial ischemia b)Continuous (interval – ratio) variable Cardiac index Creatinine clearance

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Types of variables Changing data scales

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Sample and Population A sample is a group (subset) taken from a population. Population is the group of ALL individuals (entities) sharing specific characteristics

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Sample and Population All human beings Day case surgical patients undergoing general anesthesia Low-risk CABG surgery patients ICU patients with septic shock Women undergoing CS under spinal anesthesia Human Skeletal muscle fibers Cardiac muscles of rates

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Descriptive statistics Descriptive statistics is a series of procedures designed to illuminate the data, so that its principal characteristics and main features are revealed. This may mean sorting the data by size; perhaps putting it into a table, may be presenting it in an appropriate chart, or summarizing it numerically; and so on.

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Descriptive statistics Qualitative variables Frequency Relative frequency

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Descriptive statistics Qualitative variables Frequency Relative frequency Cumulative frequency

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Descriptive statistics Qualitative variables Frequency Relative frequency Cumulative frequency Cross tabulation

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Descriptive statistics Qualitative variables Frequency Relative frequency Cumulative frequency Cross tabulation (what about numerical variables?, grouping)

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Descriptive statistics Qualitative variables In terms of describing data, an appropriate chart is almost always a good idea. What ‘appropriate’ means depends primarily on the type of data, as well as on what particular features of it you want to explore. Finally, a chart can often be used to illustrate or explain a complex situation for which a form of words or a table might be clumsy, lengthy or otherwise inadequate.

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Descriptive statistics Qualitative variables Charts Pie chart

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Advantage:- 1.Summarize (Area-relative frequency) 2.show magnitude (relative frequency) Disadvantage:- 1.one variable only 2.loose clarity if more than 4-5 categories. 3.no cross tabulation “separate pies”

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Descriptive statistics Qualitative variables Charts Pie Chart Bar Chart Simple

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Alternative Width spacing

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Descriptive statistics Qualitative variables Charts Pie Chart Bar Chart Simple Clustered bar chart

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Descriptive statistics Qualitative variables Charts Pie Chart Bar Chart Simple Clustered bar chart Stacked bar chart

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Descriptive statistics Qualitative variables Charts Pie Chart Bar Chart Simple Clustered bar chart Stacked bar chart Histogram

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one variable – no gapping

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Descriptive statistics Qualitative variables Charts Pie Chart Bar Chart Simple Clustered bar chart Stacked bar chart Histogram Frequency polygon Cumulative frequency polygon (Ogive)

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Descriptive statistics Numerical variables Measures of Central tendency (summary measures of location) Mean (Average) 1 – 1 – 3 – 5 - 10 Advantages – Disadvantages – Ratio

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Descriptive statistics Numerical variables Measures of Central tendency (summary measures of location) Median 1 – 1 – 3 – 5 - 10 1-3-5-9 Odd vs Even

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Descriptive statistics Numerical variables Measures of Central tendency (summary measures of location) Mode 1 – 1 – 3 – 5 - 10

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Descriptive statistics Numerical variables Measures of Central tendency (summary measures of location) Midrange 1 – 1 – 3 – 5 - 10

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Descriptive statistics Numerical variables Measures of Central tendency (summary measures of location) 1 – 1 – 3 – 5 - 10 Mean = 4 Median = 3 Mode = 1 Mid range = 4.5

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Descriptive statistics Numerical variables Measures of Central tendency (summary measures of location) Measures of degree of dispersion (summary measures of spread) Range 1 – 1 – 3 – 5 - 10

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Descriptive statistics Numerical variables Measures of Central tendency (summary measures of location) Measures of degree of dispersion (summary measures of spread) Percentiles – quartiles 1 – 1 – 3 – 5 - 10 1-2-5-6-8-9-11-13-17-20-22 1 st quartile 3 rd quartile 70 th quartile 90 th percentile

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Descriptive statistics Numerical variables Measures of Central tendency (summary measures of location) Measures of degree of dispersion (summary measures of spread) Inter-quartile range (Q3 – Q1) 1 – 1 – 3 – 5 - 10 1 st quartile 3 rd quartile

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Descriptive statistics Numerical variables Measures of Central tendency (summary measures of location) Measures of degree of dispersion (summary measures of spread) Variance – standard deviation 1 – 1 – 3 – 5 - 10

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Descriptive statistics Numerical variables Measures of Central tendency (summary measures of location) Measures of degree of dispersion (summary measures of spread) Variance – standard deviation 1 – 1 – 3 – 5 - 10

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Descriptive statistics Numerical variables Measures of Central tendency (summary measures of location) Measures of degree of dispersion (summary measures of spread) 1 – 1 – 3 – 5 - 10 Range Inter-quartile range Variance Standard deviation = 9 = 4 = 3.35 = 11.2

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Descriptive statistics Numerical variables

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Inferential statistics (Informed guess) Making inference about population parameters from sample statistics

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Inferential statistics (Informed guess) Making inference about population parameters from sample statistics Standard Error (SD of the statistic) Confidence interval (95% CI)

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Inferential statistics (Informed guess) Hypothesis testing Almost all clinical research begins with a question. For example, is stress a risk factor for breast cancer? To answer questions like this you have to transform the research question into a testable hypothesis called the null hypothesis, conventionally labeled H 0. This usually takes the following form: H 0 : Stress is NOT a risk factor for breast cancer H 0 : The drug has NO effect on mean heart rate

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Inferential statistics (Informed guess) Hypothesis testing Null hypotheses reflect the conservative position of no difference, no risk, no effect, etc., To test this null hypothesis, researchers will take samples and measure outcomes, and decide whether the data from the sample provides strong enough evidence to be able to reject the null hypothesis or not. If evidence against the null hypothesis is strong enough for us to be able to reject it, then we are implicitly accepting that some specified alternative hypothesis, usually labelled H 1, is probably true.

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Inferential statistics (Informed guess) Hypothesis testing Example Is the new hypothetical β-blocker is more efficient than another conventional β- blocker (e.g. Inderal) in decreasing heart rate or not.

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Inferential statistics (Informed guess) Hypothesis testing Example Let the mean heart rate of all people having Inderal is 1 Let the mean heart rate of all people having the other new drug is 2

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Inferential statistics (Informed guess) Type I & Type II Errors The H o is: Truefalse The decision about H o Accept Good decisionType II error reject Type I errorGood decision

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Inferential statistics (Informed guess) : Probability of conducting type I error : Probability of conducting type II error p –value: the probability of getting the outcome observed (or one more extreme), assuming the null hypothesis to be true. Sample size & power of the study

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Inferential statistics (Informed guess) How does it work? Probability distributions

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Inferential statistics (Informed guess) How does it work? Parametric vs non-parametric tests

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Inferential statistics (Informed guess) Some example of testing of hypothesis? Comparisons One sample Two independent samples Two dependent samples More than two samples (independent-dependent) Comparing two or more factors Association

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Inferential statistics (Informed guess) Some example of testing of hypothesis? Comparisons One sample Two independent samples Two dependent samples More than two samples (independent-dependent) Association Prediction

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Inferential statistics (Informed guess) Some example of testing of hypothesis? Comparisons One sample Two independent samples Two dependent samples More than two samples (independent-dependent) Association Prediction Diagnostic test (dichotomous – continuous)

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Diagnostic tests The disease (outcome) is: PresentAbsent The test is: Positive TPFP Negative FNTN

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Inferential statistics (Informed guess) Some example of testing of hypothesis? Comparisons One sample Two independent samples Two dependent samples More than two samples (independent-dependent) Association Prediction Diagnostic test (dichotomous – continuous) Survival analysis (censored data)

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Final words If valid data are analyzed improperly, then the results become invalid and the conclusions may well be inappropriate. At best, the net effect is to waste time, effort, and money for the project. At worst, therapeutic decisions may well be based upon invalid conclusions and patients’ wellbeing may be jeopardized.

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Thank you

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