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  3. Foundations of Inference in R
  • 1

    Introduction to ideas of inference

    Gratuit

    In this chapter, you will investigate how repeated samples taken from a population can vary. It is the variability in samples that allow you to make claims about the population of interest. It is important to remember that the research claims of interest focus on the population while the information available comes only from the sample data.

  • 2

    Completing a randomization test: gender discrimination

    In this chapter, you will gain the tools and knowledge to complete a full hypothesis test. That is, given a dataset, you will know whether or not is appropriate to reject the null hypothesis in favor of the research claim of interest.

  • 3

    Hypothesis testing errors: opportunity cost

    You will continue learning about hypothesis testing with a new example and the same structure of randomization tests. In this chapter, however, the focus will be on different errors (type I and type II), how they are made, when one is worse than another, and how things like sample size and effect size impact the error rates.

  • 4

    Confidence intervals

    As a complement to hypothesis testing, confidence intervals allow you to estimate a population parameter. Recall that your interest is always in some characteristic of the population, but you only have incomplete information to estimate the parameter using sample data. Here, the parameter is the true proportion of successes in a population. Bootstrapping is used to estimate the variability needed to form the confidence interval.

Initializing

Exercice

p-value for two-sided hypotheses: opportunity costs

The p-value measures the likelihood of data as or more extreme than the observed data, given the null hypothesis is true. Therefore, the appropriate p-value for a two-sided alternative hypothesis is a two-sided p-value.

To find a two-sided p-value, you simply double the one sided p-value. That is, you want to find two times the proportion of permuted differences that are less than or equal to the observed difference.

The opp_perm data frame, containing the differences in permuted proportions, and the original observed statistic, diff_orig, are available in your workspace.

Instructions

100 XP

Use opp_perm to compute the two-sided p-value, or twice the proportion of permuted differences that are less than or equal to the original difference.