# Links: Stat 202 Summer 2016

From Sean_Carver

## Contents

## Links

- Online textbook: http://www.macmillanhighered.com/Catalog/Product.aspx?isbn=1464133409
- Kahn Academy videos on why you divide by (n-1) instead of (n) when you compute the sample standard deviation or sample variance. Video 1: https://www.khanacademy.org/math/probability/descriptive-statistics/variance_std_deviation/v/review-and-intuition-why-we-divide-by-n-1-for-the-unbiased-sample-variance Video 2: https://www.khanacademy.org/math/probability/descriptive-statistics/variance_std_deviation/v/simulation-showing-bias-in-sample-variance
- How to interpret a Normal Quantile Plot (QQ-Plot): http://stats.stackexchange.com/questions/101274/how-to-interpret-a-qq-plot
- Spurious Correlations: http://tylervigen.com/spurious-correlations

## Practice Exams And Exams

## StatCrunch Skills We Covered, Summer 2016 (mostly copied from Summer 2015, but still relevant)

### StatCrunch Plots

- Bar Graph
- Pie Chart
- Stemplot
- Histogram
- QQ-Plot (Normal Quantile Plot)
- Scatter Plot
- Scatter Plot with Regression Line overlaid
- Residual Plot
- Boxplot

### StatCrunch Calculators

- Normal Calculator
- Binomial Calculator

### StatCrunch Statistics

- Summary Stats (Columns)
- Summary Stats (Correlation)
- Regression (Simple Linear)

### Other StatCrunch Skills

- Load Data
- Delete and Insert Rows And Columns
- Rename Columns
- Simulate Data From A Specified Distribution
- Use Fixed and Dynamic Seeds
- Apply Transformations to Data

### Sampling

- Conduct a random sample of data
- Sample if there is more than one column and you want sampled columns to correspond.
- Use fixed seeds for sampling
- Generate a sequence of numbers to use for sampling.

### Hypothesis Testing

- Z-Test
- T-Test
- Proportion Test
- One Sample
- Two Sample
- Paired
- With Data
- With Summary

### Confidence Intervals

- Z-Stats
- T-Stats
- Proportion Stats
- One Sample
- Two Sample
- Paired
- With Data
- With Summary

### Power/Sample Size

- Z-Stats
- T-Stats
- Proportion Stats
- One Sample
- Two Sample

### Confidence Interval Width/Sample Size

- Z-Stats
- T-Stats
- Proportion Stats
- One Sample
- Two Sample

## Some Other Things to Review for Summer 2016 Final

- Know how to use the 68-95-99.7 Rule.
- Be able to recognize when to use each type of test of significance listed above, and each type of confidence interval listed above.
- Know how to interpret the results of tests of significance and confidence intervals.
- Know what a p-value is. Know the definition and remember it!
- Know what a null hypothesis is, and what an alternative hypothesis is, and the difference between the two (they are not interchangeable!)
- Know that a small p-value, i.e. less than alpha, means the result is significant, which means you reject the null hypothesis, in favor of the alternative hypothesis: you have compelling evidence that an effect is there, a positive result. Traditionally alpha = 0.05.
- Know that a large p-value, i.e. greater than alpha, means the result is insignificant, which means you fail to reject the null hypothesis: you do not have no compelling evidence that an effect is there, a negative result. Again, traditionally alpha = 0.05.
- Know the difference between a one-sided alternative hypothesis and a two-sided alternative hypothesis. Know that unless you are sure that you should use a one-sided hypothesis, that you should always use a two sided hypothesis. Know that two-sided hypotheses is more conservative--significant results with a two sided hypothesis are significant with a one-sided hypothesis in the appropriate direction.
- Don't make the following mistake, WRONG: "a p-value greater than alpha means the result is significant:" THIS IS WRONG! In the past, students with this confusion made the same mistake on several problems and lost a lot of points on each, a costly mistake, but it reveals that you don't really understand tests of significance, which justifies a low grade. BE WARNED AND BE CAREFUL! You won't make this mistake if you know what a p-value is and why it needs to be small to reject the null hypothesis and find an effect. Make a habit of checking your understanding with your conclusion, each time you draw a conclusion.
- Know about the use and abuse of statistical tests (Homework 22).
- Know about statistical power, type I and type II errors, false positives and false negatives, and specificity and sensitivity. Know how to calculate these things with stat crunch.
- Know that the probability of a type I error (False Positive) is alpha. But don't just remember this fact! Know why this statement is true based on the design of a test of significance.
- Know how to use the Binomial calculator, when to use it, and how to recognize when a problem requires it.
- Know how to use the Normal calculator, when to use it, and how to recognize when a problem requires it.
- Know about sampling distributions for mean, counts and proportion. Know what is the mean of the sample means, the mean of the sample proportions, and the means of the counts. Also know about the standard deviations of these things, and when these distributions are approximately Normal. I will give you the formulas on a formula sheet in the beginning of the exam BUT know how to use them and know how to recognize when they need to be used.
- Know what a random variable is.
- Calculate the mean of a random variable, and know how this mean differs from a sample mean.

## 2016F Study Instructions

- Make sure you know the difference between a t-test and a proportions test, and when you use each kind.
- Make sure you know the difference between a 1-sample, a 2-sample and a paired test.
- Make sure you know to use a one sample test when you are comparing distributions, and you have one sample, but you know the parameters of the other distribution.
- Make sure you know how to specify your hypotheses.
- Make sure you know what a p-value is and what it is used for.
- Make sure you know how to interpret a p-value as significant or insignificant based on the level of significance of the test.
- Make sure you know the relationships between type I and type II errors and power and level of significance of tests.
- Make sure you know the definitions of specificity and sensitivity and their relationships between type I and type II errors.
- Make sure you know how to use the power sample size tool.
- Make sure you know how to compute and report a confidence interval and interpret values inside and outside the interval.
- Make sure you know what a random variable is and how to create examples of a random variable.
- Make sure you can do sampling with StatCrunch and use a fixed seed.
- Make sure you can do simulation with StatCrunch and use a fixed seed.
- STAT 203 -- Basic Stats with Calculus: There will be a calculus problem on the exam similar to one of the ones on the midterms.

## 2017XD Problems for Final

- Binomial Problem
- Concepts of Tests of Significance Problem
- Sampling Distribution Problem
- Probability Problem
- Correlation and Regression Problem
- Random Variable Problem
- Power/Difference/Sample Size Problem
- Identify Which Significance Test To Use Problem
- Confidence Interval and Interpretation Problem
- Normal Calculator/Z-Score Problem
- Possible Surprise Problem