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all statistical tests starts with the premise that the data are the result of chance variation
Reject or fail to reject this hypothesis
There is no difference or relationship among groups |
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There is an existing difference or relationship among groups
The research hypothesis, the question the study was designed to answer
Cannot prove this hypothesis |
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| rejecting the null hypothesis when it is true |
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| failing to reject the null hypothesis when the alternative hypothesis is true |
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sets up to reject the null hypothesis in the instance that the result falls in only one of the tails
You expect one of the tx to be better/worse than the other |
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the null hypothesis will be rejected if there is a result that falls at either tail
You do not expect one tx to be better than the other |
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| A single number that assesses the compatibility of the data with the null hypothesis |
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| The critical value is the value of the test statistic that delineates the specified significance level i.e. 5% |
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| used when population standard deviation is known |
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| Comparing means between groups when the population standard deviation is not known |
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Comparing proportions in 2 or more groups
used for categorical data
• A common analysis is whether Disease X occurs as much among individuals in Group A as it does among individuals in Group |
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used for continuous data
Use a t-test for comparing 2 groups
Use an f-test for comparing 3 or more groups
Both tests result in a p-value |
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| used for logistic/linear regression |
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| when the sample size is greater than 100 and expected cell counts are greater than 10 |
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| when the sample size is greater than 30 but less than 100 and the expected cell counts are greater than 5 but less than 10 |
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If the chi-square statistic is small, the observed and expected data were not very different and the p-value will be large
If the chi-square statistic is large, this generally means the p-value is small, and the difference could be statistically significant |
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Tells you if it is appropriate to use the ANOVA test
Produces a p-value
If Bartlett’s p-value >0.05, (not significant) OK to use ANOVA results
Bartlett’s p-value <0.05, variances in the groups are NOT the same and you cannot use the ANOVA results |
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Used only if Bartlett’s test reveals variances dissimilar enough so that you can’t use ANOVA
• Does not make assumptions about variance, examines the distribution of values within each group
Generates a p-value
If p-value >0.05 there is not a significant difference between group
If p-value < 0.05 there is a significant difference between groups |
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| Multivariable Linear Regression |
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• Several predictor variables analyzed simultaneously
Allows you to consider the impact of a set of predictor variables together and individually |
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used when the outcome variable (i.e. sick or not sick) and predictor variable (i.e. exposed or not exposed) are both dichotomous
Logit (Outcome) = EXPOSURE + CONFOUNDER1 + CONFOUNDER2 + CONFOUNDER3 + … (etc) |
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| How to Narrow the Confidence Interval |
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increase the sample size
small standard deviation of sample data |
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The probability of correctly rejecting H0 when it is false
When there is a true treatment effect and we do not reject H0 – Type II Error
Power = 1- β = 1 - .2 = .8 |
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| Probability of Type I Error |
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If alpha = 0.05 then the probability of Type I error is 5%
If I reject the null hypothesis due to the data from my sample there is a 5% probability that in the actual population there really is no significant difference |
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| Probability of Type II Error |
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If beta = 0.20 then the probability of Type II error is 20% and Power = 80%
If I fail to reject the null hypothesis due to the data from my sample there is a 20% probability that in the actual population there really is a significant difference |
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