Week 4 Understanding CI PDF

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🧶Week 4 : Understanding CI4 Hypothesis testing vs EstimationBoth are to find out unknown larger populationHypothesis testing : Answers Yes/NoEstimation : Answers exactly how muchWhat is a sample? A set of individuals selected from a populationWhat is validity? How closely your result reflects the tr...

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Week 4 : Understanding CI 4.1 Hypothesis testing vs Estimation Both are to find out unknown larger population Hypothesis testing : Answers Yes/No Estimation : Answers exactly how much What is a sample? A set of individuals selected from a population

What is validity? How closely your result reflects the truth.

Sensitivity & Specificity are measures of Accuracy/Validity e.g. using a CALIBRATED thermometer to measure a patients temperature you record the following accurate measurements: 98.5, 98.4, 98.6, 98.7, 98.6 What is reliability / reproducibility? Obtaining similar results with repeated measurement/samples

*Reliability is about the consistency of a measure, and validity is about the accuracy of a measure. Why do we need validity and reliability in statistics? we need to know how closely the sample statistics represents the true population parameter, and how reproducible that specific population statistic is. The more accurate and precise the statistic, the more representative the sample is to the population What are confidence intervals? expressing the usefulness of research data. Cuz we are generalising the population from just a sample, there may be uncertainty a/w estimation process - Confidence intervals (given as a range around an estimate) provides information about the degree of uncertainty surrounding data from a sample 4.2 Sampling problems - several diff means Standard error of the mean Measure of how much the diff sample means differ How much is the mean from this sample in your study likely to vary when evaluating other samples? Smaller standard error indicates that samples are all similar and represent true population mean

𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐸𝑟𝑟𝑜𝑟= (𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛/ √𝑆𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒)

4.3 Confidence Intervals We need confidence intervals to give an estimated range of values which is likely to include the mean.

CIs are an estimate of the accuracy and precision of the mean Typically the 95% Confidence Interval is reported -- 1.96 × SE on either side of the mean = 95% Confidence Interval For 95% CI, if the population is sampled repeatedly and a CI computed each time, 95% of the time the population mean would fall within the computed CI 4.4 How do you calculate CI?

To Estimate 95% CI Mean ± 1.96 × Standard Error of the Mean

Mean 1.96 × (𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛/√(𝑆𝑎𝑚𝑝𝑙𝑒 𝑠𝑖z𝑒))

For other levels of CI, the factor to multiply SEM will change: 90% CI = Mean ± 1.65 x SEM (narrower) 99% CI = Mean ± 2.58 x SEM (wider) *95% of the sample falls within 2 standard deviations of the mean. And that’s the same as 1.96 rounded up – 95% of sample means from a population fall with 2 or 1.96 standard errors of the mean.

4.5 What then is the difference between standard error and standard deviation? Standard deviation is estimate of variability of the elements in a given set of data. Standard Error is used to make inferences from sample or several samples to whole population - Standard Error answers the question of what outcomes to expect if you repeat the experiment using a different sample from the larger population The standard deviation SD measures the amount of variability, or dispersion, from the individual data values to the mean, while the standard error of the mean SEM measures how far the sample mean (average) of the data is likely to be from the true population mean 4.6 How do you increase the precision of the data? WIDTH of the CI is a measure of the Precision of the study To increase PRECISION (more narrow CI, increase the SAMPLE SIZE Imprecise data is more prone to Type II error FN 4.7 Confidence Intervals in Testing Confidence Intervals may apply to ratios Odds Ratio, Relative Risk) or to differences between 2 groups (mean values, proportions) For Ratios, CI significant if it does not include 1 For Differences, CI significant if it does not include 0 If CI is significant, then usually p < 0.05 4.8 CI Vs P values P values - tells u if its sig. or not and if null hypothesis is true CI - Additional info on precision of the point estimate(probability of result), wide range is worse than a narrow range , allows u to compare diff studies 4.9 Sample Size Why is sample size impt? Power = Ability to reject the Null Hypothesis when it is false Bigger samples usually result in more narrow confidence intervals because the standard error of their mean is smaller. 5.0 Factors that affect sample size

What is the 𝜶 level? (the maximum p value accepted) What is the 𝜷 level? (the power desired) What is the expected effect size (the difference between the groups)? What is the variance in the population?

5.1 Interpreting Confidence Intervals

Significance : If the CI includes 0 and crosses/includes 1, it is not significant as well If CI doesn't include 0 or 1 - we can say it is stats. sig. Clinical meaningfulness : Look at how wide the CI range is

Not sig cuz includes 0. CI too wide, P value not sig

The Mean birthweight was measured in a sample of 15 non-smokers 3.59Kg) and 14 heavy smokers 3.20Kg). The difference in the mean weight was 390g 95%CI 60g to 721g). Is this difference statistically significant? Is this difference clinically meaningful? Results are stat. sig cuz CI doesn’t include 0. no it is not clinically meaningful. Sample size too small, CI is too wide – so not clinically meaningful...