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Foundations of Inference in R

MedelnivåKunskapsnivå

Uppdaterad 2024-07

Learn how to draw conclusions about a population from a sample of data via a process known as statistical inference.

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RProbability & Statistics

4 tim

17 videor

58 Övningar

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Kursbeskrivning

One of the foundational aspects of statistical analysis is inference, or the process of drawing conclusions about a larger population from a sample of data. Although counter intuitive, the standard practice is to attempt to disprove a research claim that is not of interest. For example, to show that one medical treatment is better than another, we can assume that the two treatments lead to equal survival rates only to then be disproved by the data. Additionally, we introduce the idea of a p-value, or the degree of disagreement between the data and the hypothesis. We also dive into confidence intervals, which measure the magnitude of the effect of interest (e.g. how much better one treatment is than another).

Förkunskapskrav

Introduction to Regression in R Hypothesis Testing in R

1

Introduction to ideas of inference

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.

Welcome to the course!

Hypotheses (1)

Hypotheses (2)

Randomized distributions

Working with the NHANES data

Calculating statistic of interest

Randomized data under null model of independence

Randomized statistics and dotplot

Randomization density

Using the randomization distribution

Do the data come from the population?

What can you conclude?

Study conclusions

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.

Example: gender discrimination

Gender discrimination hypotheses

Summarizing gender discrimination

Step-by-step through the permutation

Randomizing gender discrimination

Distribution of statistics

Reflecting on analysis

Critical region

Two-sided critical region

How does sample size affect results?

Sample size in randomization distribution

Sample size for critical region

What is a p-value?

Calculating the p-values

Practice calculating p-values

Calculating two-sided p-values

Summary of gender discrimination

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.

Example: opportunity cost

Summarizing opportunity cost (1)

Plotting opportunity cost

Randomizing opportunity cost

Summarizing opportunity cost (2)

Opportunity cost conclusion

Errors and their consequences

Different choice of error rate

Errors for two-sided hypotheses

p-value for two-sided hypotheses: opportunity costs

Summary of opportunity costs

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.

Parameters and confidence intervals

What is the parameter?

Hypothesis test or confidence interval?

Bootstrapping

Resampling from a sample

Visualizing the variability of p-hat

Always resample the original number of observations

Variability in p-hat

Empirical Rule

Bootstrap t-confidence interval

Bootstrap percentile interval

Interpreting CIs and technical conditions

Sample size effects on bootstrap CIs

Sample proportion value effects on bootstrap CIs

Percentile effects on bootstrap CIs

Summary of statistical inference

Foundations of Inference in R

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