The same test will be performed using the \(p\)-value approach in Example \(\PageIndex{3}\). Missed the LibreFest? Each can be checked with a corresponding condition. Students should not calculate or talk about a correlation coefficient nor use a linear model when that’s not true. If those assumptions are violated, the method may fail. As was the case for two proportions, determining the standard error for the difference between two group means requires adding variances, and that’s legitimate only if we feel comfortable with the Independent Groups Assumption. We can proceed if the Random Condition and the 10 Percent Condition are met. Tossing a coin repeatedly and looking for heads is a simple example of Bernoulli trials: there are two possible outcomes (success and failure) on each toss, the probability of success is constant, and the trials are independent. Again there’s no condition to check. Independent Groups Assumption: The two groups (and hence the two sample proportions) are independent. We already made an argument that IV estimators are consistent, provided some limiting conditions are met. Sample-to-sample variation in slopes can be described by a t-model, provided several assumptions are met. Matching is a powerful design because it controls many sources of variability, but we cannot treat the data as though they came from two independent groups. If, for example, it is given that 242 of 305 people recovered from a disease, then students should point out that 242 and 63 (the “failures”) are both greater than ten. Of course, in the event they decide to create a histogram or boxplot, there’s a Quantitative Data Condition as well. ●The samples must be independent ●The sample size must be “big enough” The spreadof a sampling distribution is affected by the sample size, not the population size. 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