Module 8 Help Session F18.pdf

# Module 8 Help Session F18.pdf - PHC 4069 Biostatistics in...

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PHC 4069 Biostatistics in Society Module 8 Testing hypotheses for proportions By: Hanze Zhang Presented By: Ying Ma

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Two types of statistics Statistics Descriptive Collecting, organizing Summarizing, presenting Inferential Hypotheses Relationships predictions Probability
Definition of hypothesis testing Hypothesis: a scientific guess. Usually about a given characteristic of a given population Ex: The proportion of Twitter users among USF students is higher than the average for all Americans (50% for example) P>0.50 Use inferential statistics to test this guess

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Procedure for Hypothesis testing Obtain a representative sample from the population we are trying to infer about. Define null and alternative hypotheses Example null hypothesis: P=0.50 Example alternative (research) hypothesis: P>0.50 Analyze the evidence from the sample Sample statistic: in this case p (sample proportion) Is there significant difference between the sample statistic and the hypothesized parameter to reject the null hypothesis? or are the observed differences due to random sampling variation? ^
Hypothesis testing Is there significant difference between the sample statistic and the hypothesized parameter to reject the null hypothesis? or are the observed differences due to random sampling variation? What’s the probability of seeing the observed sample proportion if the null hypothesis is true? If the probability is low enough, then we reject the null hypothesis

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Level of significance If the probability of observing the obtained data, given that the null hypothesis is true , is lower than the alpha level , then we reject the null hypothesis This is called a p-value Alpha is usually set at 0.05 (5%), 0.01 (1%)
Sample Size Requirement for the Central Limit Theorem When the sample size n and the population proportion, P, satisfy n*P ≥ 10 and n *(1 - P) ≥ 10, we can apply Central Limit Theorem on and use a normal distribution to approximate its distribution. p ˆ

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One-sample hypothesis testing for P Used to infer the proportion of a certain outcome among a specific population. Ex: The proportion of Twitter users among USF students
P = population proportion; proportion of USF students who use Twitter = sample proportion; estimate of the population proportion (aka “p - hat” or “small p”) P-value: probability of observing the obtained sample proportion (or sample mean if we were dealing with a continuous variable), given that the null hypothesis is true Another way to interpret the P-value: it is the probability that the observed difference between the value of the sample statistic and the null hypothesis value is due only to random sampling variation, if the Null hypothesis is really true (p. 136 of the textbook) . We want this probability to be very low.

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