STAT 113: EXAM 2 STUDY GUIDE COLIN REIMER DAWSON, FALL 2015 (1) - PDF document

STAT 113: EXAM 2 STUDY GUIDE COLIN REIMER DAWSON, FALL 2015 (1) Chapter 3: Inference Foundations / Bootstrap Confidence Intervals 3.1 Sampling Distributions. You should be able to • Recognize and explain the difference between a popula- tion and a sample, and between a parameter and a statis- tic. • Understand how to find good point estimates of parame- ters using a sample. • Understand what a sampling distribution is, what the cases are in a sampling distribution, and what the in- dividual values in a sampling distribution represent. • Understand what a standard error is, how it relates to standard deviation, and how it contrasts with variability of individual cases in a sample. • Recognize where a sampling distribution is typically cen- tered. • Use the ± 2 SE rule when appropriate to recognize where most sample statistics fall in a sampling distribution. • Recognize when the ± 2 SE rule is and isn’t appropriate. • Visually estimate standard error from a dot plot or his- togram of a sampling distribution / bootstrap distribution / randomization distribution • Distinguish between sample size and number of samples in a simulated sampling distribution. • Recognize the effect of sample size on variability of sample statistics. 3.2 Confidence Intervals. You should be able to • Interpret what a margin of error is telling us. Date : November 16, 2015. 1

2 COLIN REIMER DAWSON, FALL 2015 • Recognize the relationship between standard error of a sampling distribution and margin of error of an estimate. • Construct a confidence interval from a point estimate and either a margin of error or a standard error. • Interpret a confidence interval (what is likely to be within it?) • Interpret the confidence level (what happens 95% or 99% of the time?) • Recognize and avoid common misinterpretations of the confidence interval. 3.3 Boostrap Confidence Intervals. You should be able to • Understand what it means to “bootstrap resample” from a sample. • Recognize what the values in a bootstrap distribution rep- resent. • Understand where a bootstrap distribution is centered • Understand the role of the standard deviation of the boot- strap distribution. • Construct a 95% confidence interval from a point estimate and a bootstrap standard error. 3.4 Boostrap Confidence Intervals Using Percentiles. You should be able to • Identify which quantiles of a bootstrap distribution are needed for a particular confidence level • Identify what confidence level is associated with particu- lar quantiles of a bootstrap distribution (2) Chapter 4: Hypothesis Tests Using Randomization 4.1 Hypothesis Testing Basics. You should be able to • Identify when a hypothesis test is called for (vs. a confi- dence interval, vs. no need for inference) • Construct null and alternative hypotheses, in both words and statements about population parameters, from a re- search question. • Recognize the distinction between a sample having a par- ticular mean/proportion/difference/correlation and the pop- ulation having the same.

STAT 113: EXAM 2 STUDY GUIDE 3 • Recognize which sample statistics provide the strongest evidence for a particular hypothesis. • Interpret what it means that a finding is statistically sig- nificant . 4.2 P -values. You should be able to • Understand the role of a randomization distribution in hypothesis testing. • Recognize what the values in a randomization distribution represent • Recognize what is assumed when generating a random- ization distribution. • Recognize what the center of a randomization distribution is in the context of the hypothesis test. • Understand what a P -value is, as a proportion (What goes in the numerator? What goes in the denominator?) • Understand which cases in the randomization distribution to count toward the P -value in a one-tailed or two-tailed test. • Understand the tradeoff between flexibility and statistical power when deciding between a one- and two-tailed test. 4.3 Statistical Significance and Statistical Errors. You should be able to • Understand the role of the significance level ( α ) in decid- ing whether a result is statistically significant. • Understand what Type I Errors / False Discoveries are, and how the likelihood that they occur is related to the significance level, α . • Understand what a Type II Error / Missed Discovery is, and how its likelihood is related to the significance level, α , as well as to the sample size. 4.4 Constructing Randomization Distributions for Different Hypothe- ses. You should be able to • Understand / describe the process of generating a ran- domization distribution to test whether a population pro- portion is equal to a particular null value.

4 COLIN REIMER DAWSON, FALL 2015 • Understand / describe how to create a randomization dis- tribution from a bootstrap distribution to test whether a population mean is equal to a particular null value. • Understand / describe a process to generate a randomiza- tion distribution to test whether two subpopulations have different rates (proportions) of a particular categorical re- sponse variable. • Understand / describe a process to generate a randomiza- tion distribution to test whether two subpopulations have different mean levels of a particular quantitative response variable. • Understand / describe a process to generate a random- ization distribution to test whether two quantitative vari- ables are correlated in a population. 4.5 Tests and Confidence Intervals. You should be able to • Interpret confidence intervals in terms of possible null hy- potheses about a population parameter. • Use a confidence interval to make a binary decision at the approporiate significance level about whether a particular null hypothesis value can be rejected. (3) Chapter 5. Using a Normal Distribution 5.1 Normal Distributions. You should be able to • Understand the relationship between a proportion of cases in a simulated distribution, and the area under a density curve in a theoretical distribution. • Estimate tail proportions visually by looking at a density graph • Estimate quantiles visually using a density graph • Understand how to combine tail proportions to get pro- portions in intervals. • Recognize what happens to a distribution of a variable when we convert its values to z -scores. • Understand how the area/proportion past a z score in a Standard Normal relates to the area past a value that has that z score in a different (non-standard) Normal. 5.2 Confidence Intervals and P -values Using Normal Distributions. You should be able to

STAT 113: EXAM 2 STUDY GUIDE 5 • Recognize when it would be appropriate to use a Normal approximation for a bootstrap or randomization distribu- tion. • Identify the approximate z -scores corresponding to some commonly used Normal quantiles (e.g., 0.005, 0.025, 0.05, 0.95, 0.975, 0.995). • Use these z -scores, together with a point estimate and a standard error of a sample statistic, to create 90%, 95% and 99% confidence intervals • Understand / describe what we would need to do to get a confidence interval at some other confidence level. • Understand how to find the parameters (mean and stan- dard deviation) to use for a non-standard Normal approx- imation to a randomization distribution • Understand / describe what we would need to do to get a P -value from such a (non-standard) Normal approxima- tion to a randomization distribution. • Convert an observed statistic into a z -score using an ap- propriate mean and standard deviation, based on proper- ties of a randomization distribution. • Use such a z -score to give a rough estimate of a P -value (“rough” meaning “Is it less than 0.01? Between 0.01 and 0.05? Between 0.05 and 0.1? Greater than 0.1?”) (4) Chapter 6. Tests and Intervals Using Normal Theory 6.1-6.3 Inference about a Proportion. You should be able to • Recognize when it is and is not appropriate to use a Nor- mal to approximate a distribution of sample proportions. • Decide what choice of p to use in what contexts when computing the standard error for a proportion. • Use the theoretical standard error for a proportion (cal- culated using the appropriate p ), together with critical Z ∗ values, to find the margin of error for a 90, 95 or 99% confidence interval for a population proportion. • Recognize what it would take to find critical Z ∗ values for other confidence levels. • Use the theoretical standard error for a proportion (cal- culated using the appropriate p ), together with a null hy- pothesis, to convert a sample proportion into a Z statistic,