**Chapter P Videos**

P.1 Example [2:22]

P.1.1 Describe how the six steps of a statistical investigation apply to a particular statistical study. [8:14]

P.1.2 Think of and write research questions that could be investigated with a statistical study. [3:43]

P.1.3 Identify the observational units and variables in a statistical study. [2:12]

P.1.4 Classify variables as categorical or quantitative. [3:00]

P.2 Example [1:19]

P.2.1 Write a paragraph comparing two distributions of data on a quantitative variable as presented in dotplots, addressing aspects of shape, center, variability, and unusual observations. [6:42]

P.2.2 Compare centers between two or more distributions displayed in dotplots. [1:40]

P.2.3 Compare variability between two or more distributions displayed in dotplots. [2:21]

P.2.4 Compare shapes between two or more distributions displayed in dotplots. [1:15]

P.2.5 Make predictions about centers and means, and about variability and standard deviations, based on the context of a variable. [3:06]

**Chapter 1 Videos**

1.1 Example [2:57]

1.1.1 Student should be able to describe how to use coin tossing to simulate outcomes from a chance model of the random choice between two events. [5:31]

1.1.2 Student should be able to use the One Proportion applet to carry out the coin tossing simulation. [4:47]

1.1.3 Implement the 3S strategy: find a statistic, simulate results from a chance model, and comment on strength of evidence against observed study results happening by chance alone. [3:46]

1.1.4 Recognize the difference between parameters and statistics. [2:27]

1.1.5 Identify whether or not study results are statistically significant or if the chance model is a plausible explanation for the data. [3:21]

1.1.6 Differentiating between saying the chance model is plausible and the chance model the correct explanation for the observed data. [2:12]

1.2 Example [1:02]

1.2.1 Use appropriate symbols for parameter and statistic. [1:51]

1.2.2 State the null and the alternative hypotheses in words and in terms of the symbol π, the long-run probability. [2:48]

1.2.3 Explain how to conduct a simulation using a null hypothesis probability that is not 50-50. [3:10]

1.2.4 Use the One Proportion applet to obtain the p-value after carrying out an appropriate simulation. [2:47]

1.2.5 Interpret the p-value. [1:24]

1.2.6 Explain why a smaller p-value provides stronger evidence against the null hypothesis. [1:54]

1.2.7 State a conclusion about the alternative hypothesis and null hypothesis based on the p-value. [3:08]

1.2.8 Anticipate the location of the center of the null distribution and how it changes based on whether you are using proportion or count as the statistic. [1:42]

1.3 Example [2:35]

1.3.1 Find a standardized statistic from the observed proportion of "successes", the hypothesized mean and SD of the null distribution as produced by the One Proportion applet. [2:09]

1.3.2 Describe what the standardized statistic means. [2:01]

1.3.3 State a conclusion about the alternative hypothesis (and null hypothesis) based on the magnitude of the standardized statistic. [1:36]

1.3.4 Recognize that standardized statistic is an alternative to p-value, and that both p-value and standardized statistic summarize strength of evidence. [1:25]

1.4 Example [2:05]

1.4.1 Recognize when a two-sided test/alternative hypothesis is suggested by the research question. [2:56]

1.4.2.1 Anticipate and explain why when everything else remains the same, the p-value is smaller if the observed proportion of successes is farther away from the hypothesized value of the long-run probability π. [1:09]

1.4.2.2 Anticipate and explain why when everything else remains the same, the p-value is smaller if the sample size is larger. [2:32]

1.4.2.3 Anticipate and explain why when everything else remains the same, the p-value is smaller if the alternative hypothesis is two-sided.[4:17]

1.5 Example [1:38]

1.5.1 Predict the mean and SD of the null distribution of sample proportions, as π and , respectively when the sample size is large enough. [4:33]

1.5.2 Explain when simulation and theory will yield different answers. [2:30]

1.5.3 Use the One Proportion applet to find the One Proportion z test (theory-based; normal approximation-based) p-value and standardized statistic, z. [1:53]

**Chapter 2 Videos**

2.1a Example [0:53]

2.1a.1 Identify the (finite) population and the sample in a statistical study. [1:33]

2.1a.2 Identify parameters and statistics in a statistical study. [2:23]

2.1a.3 Describe how to select a random sample and recognize that one advantage of a random sample is that it is likely to be representative of the population. [2:42]

2.1a.4 Identify whether a sampling method is likely to be biased and describe the likely direction of the bias and state what sampling bias means and how it might be present in a specific sampling plan. [3:05]

2.1a.5 Recognize that the types of statistics and graphs used for categorical and quantitative variables differ, and be able to identify which statistics (proportions, means, sds) and graphs (bar graph, dotplot, histogram) are appropriate for each type of variable. Construct graphs and calculate statistics with use of technology, and interpret appropriately. [2:20]

2.1a.6 Apply conclusions about random sampling methods (unbiased) to both categorical and quantitative variables. [2:27]

2.1a.7 Fill in a data-table where rows are the observational units and columns are the variables. [0:46]

2.1a.8 State that collecting a representative sample from a population allows for generalizing results of inference procedures from the sample statistic(s) to the population parameter(s). [1:17]

2.1a.9 Recognize that small random samples can be representative of the population; you do not have to have a large proportion of the population in your sample to be representative. [2:23]

2.1b Example [0:55]

2.1b.10 Apply simulation- and theory-based inference methods for a population proportion to research studies involving random samples from finite populations. [3:24]

2.1b.11 Set up null and alternative hypotheses, and correctly identify the parameter of interest, for statistical studies involving sampling from a (finite) population. [1:14]

2.2 Example [2:21]

2.2.1 Conduct a simulation-based analysis to conduct a single test involving the mean of a single quantitative variable. [5:38]

2.2.2 Carry out a theory-based analysis (one-sample t-test) involving the mean of a single quantitative variable, including checking relevant validity conditions. [4:21]

2.2.3 Use the size and direction of the difference in the mean and median to infer something about the skewness of the distribution and vice versa. [6:11]

2.2.4 Interpret information revealed by a histogram of a distribution (shape, variability, center, unusual observations). [2:17]

2.2.5 Anticipate the impact of the addition of an additional data value or change in data values on the mean, median and standard deviation. [2:11]

2.2.6 Anticipate the relative magnitude of the standard error of a sampling distribution of sample means based on the formula s/√n. [2:00]

2.3.1 State, justify, and explain the reasoning behind a test decision about rejecting the null hypothesis or not, depending on the significance level and p-value of a test. [3:25]

2.3.2 and 2.3.3 Describe what a Type I & a Type II Error means in a particular context and describe consequences of making such an error in that context. [4:10]

2.3.4 Recognize that the significance level is the probability of a Type I error, assuming the null hypothesis is true. [2:31]

2.3.5 Recognize that decreasing the probability of one type of error typically means increasing the probability of the other type of error, unless the sample size or other factors also change. [3:49]

2.3.6 Recognize which error could have been made after drawing a conclusion in a test of significance. [1:34]

**Chapter 3 Videos**

3.1 Example [2:05]

3.1.1 Complete multiple two-sided tests of significance, using the same value for the sample proportion but changing the value under the null, and obtain an interval of plausible values for the population parameter. [4:21]

3.1.2 Interpret an interval of plausible values as estimating the population parameter and as a confidence interval. [1:27]

3.1.3 Based on the results of a test of significance, infer whether or not a value is in the confidence interval and vice versa. [2:40]

3.2 Example [0:45]

3.2.1 Compute a confidence interval for a proportion written in terms of its endpoints from a confidence interval written in terms of center plus or minus the margin of error and vice versa. [1:41]

3.2.2 Approximate a 95% confidence interval for a proportion by using the 2SD method. [3:12]

3.2.3 Compute a confidence interval for a proportion using a theory-based approach, including checking validity conditions. [3:43]

3.2.4 Infer the relative width of a confidence interval when changing the confidence level. [2:18]

3.3 Example [1:04]

3.3.1 Approximate a 95% confidence interval for a mean by using the 2SD method. [3:13]

3.3.2 Compute a confidence interval for a mean using a theory-based approach, including checking validity conditions. [2:21]

3.4.1.1 Recognize that all other things being equal, as the confidence level increases, the width of the confidence interval increases. [1:20]

3.4.1.2 Recognize that all other things being equal, as the sample size increases, the width of the resulting confidence interval decreases. [4:43]

3.4.1.3 Recognize that all other things being equal, as the sample proportion gets farther from 0.5 the standard error decreases and thus a resulting confidence interval will be narrower. [3:32]

3.4.1.4 Recognize that all other things being equal, as the standard deviation of the quantitative variable increases, the resulting confidence interval will be wider. [2:23]

3.4.2 Apply the idea that the confidence level of an interval corresponds to its coverage probability (the proportion of confidence intervals containing the true parameter value across many, many random samples) in the interpretation of confidence intervals. [3:46]

3.5 Example [1:50]

3.5 Example B [1:10]

3.5.1 Articulate that gathering truly random samples is difficult. [3:02]

3.5.2 Understand that numerous factors may impact variable values making them less accurate than researchers hope for (e.g., wording of questions, ordering of questions, social desirability, inaccurate measurement instrument, lying, etc.). [2:47]

3.5.3 Recognize that the margin of error does not protect against sampling or non-sampling errors. [3:22]

3.5.4 Recognize the distinction between statistical significance and practical importance, understand that this issue is especially relevant with large sample sizes, and know that p-values address the issue of statistical significance while confidence intervals help to assess practical importance. [3:17]

3.5.5 Describe what the power of a test means in a particular situation and also comment on factors that affect power and in what direction: sample size, significance level, magnitude of difference between hypothesized and actual values of the parameter. [5:25]

**Chapter 4 Videos**

4.1 Example [1:15]

4.1.1 Identify which variable is the explanatory variable and which is response in a study involving two variables. [1:42]

4.1.2 Interpret conditional proportions as to whether they give any indication of an association between the explanatory and response variables. [2:16]

4.1.3 Identify potential confounding variables and explain how they provide an alternative explanation for the observed association between the explanatory and the response variable. [1:46]

4.1.4 and 4.1.5 Draw a diagram to show how the confounding variable provides an alternative explanation for the observed association between the explanatory and the response variable. [2:35]

4.2 Example [1:22]

4.2.1 Identify a study as observational or experimental. [1:47]

4.2.2 Explain that random assignment gives us the ability to draw cause-effect conclusions because it ensures that treatment groups have similar characteristics. [3:40]

4.2.3 Identify whether a study uses random assignment and/or random sampling and the implications of these design decisions on the conclusions that can be drawn. [2:34]

4.3 Example [1:09]

4.3.1 [1:39]

4.3.2 [1:59]

**Chapter 5 Videos**

5.1 Example [0:57]

5.1.1 Organize counts into a two-way table, when data are available on two categorical variables for the same set of observational units. [3:41]

5.1.2 Calculate conditional proportion of successes, for different categories of the explanatory variable, and use these conditional proportions to decide whether there is preliminary evidence of an association between the explanatory and response variables. [3:14]

5.1.3 Create a segmented bar chart to display data available on two categorical variables for the same set of observational units. [1:55]

5.1.4 Calculate and interpret relative risk. [2:54]

5.2 Example [1:55]

5.2.1 State the null and the alternative hypotheses in terms of "no association" versus "there is an association" as well as in terms of comparing probability of success for two categories of the explanatory variable (that is, π1 and π2) when exploring the relationship between two categorical variables. [2:55]

5.2.2 and 5.2.3 Describe how to use cards to simulate what outcomes (in terms of difference in conditional proportions and/or relative risk) are to be expected in repeated random assignments, if there is no association between the two variables; AND Use the Two Proportions applet to conduct a simulation of the null hypothesis when and be able to read output from the Two Proportions applet. [6:56]

5.2.4 Implement the 3S strategy: find a statistic, simulate, and compute the strength of evidence against observed study results happening by chance alone. [2:39]

5.2.5 Find and interpret the standardized statistic and the p-value for a test of two proportions. [2:31]

5.2.6 State a complete conclusion about the alternative hypothesis (and null hypothesis) based on the p-value and/or standardized statistic and the study design including statistical significance, estimation (confidence interval), generalizability and causation. [3:14]

5.2.7 Use the 2SD method to find a 95% confidence interval for the difference in long-run probability of success for two "treatment" groups, and interpret the interval in the context of the study. Interpret what it means for the 95% confidence interval for difference in proportions to contain zero. [3:22]

5.3 Example [1:06]

5.3.1 Identify a theory-based approach would be valid to find the p-value or a confidence interval when evaluating the relationship between two categorical variables. [2:18]

5.3.2 Use the Theory-Based Inference applet to find theory based p-values and confidence intervals. [2:19]

5.3.3 Understand the impacts of confidence level and sample size on confidence interval width for a confidence interval on the difference in two proportions. [2:17]

**Chapter 6 Videos**

6.1 Example [0:48]

6.1.1 Calculate or estimate the mean, median, quartiles, five number summary and inter-quartile range from a data set and understand what these are measuring. [5:18]

6.1.2 When comparing two quantitative distributions, identify which has the larger mean, median, standard deviation, and inter-quartile range. [2:06]

6.1.3 Identify if there is likely an association between a binary categorical variable and a quantitative response variable. [1:26]

6.2 Example [1:17]

6.2.1 State the null and the alternative hypotheses in terms of “no association” versus “there is an association” as well as in terms of comparing means for two categories of the explanatory variable (that is, μ1 and μ 2) when exploring the relationship between two categorical variables. [2:19]

6.2.2 Describe how to use cards to simulate what outcomes (in terms of difference in means or median) are to be expected in repeated random assignments, if there is no association between the two variables. [3:23]

6.2.3 Use the Multiple Means applet to conduct a simulation of the null hypothesis and be able to read output from the Multiple Means applet. [3:19]

6.2.4 Implement the 3S strategy to compare two means: find a statistic, simulate, and compute the strength of evidence against observed study results happening by chance alone. [2:29]

6.2.5 Find and interpret the standardized statistic and the p-value for a test of two means. [2:34]

6.2.6 State a complete conclusion about the alternative hypothesis (and null hypothesis) based on the p-value and/or standardized statistic and the study design including statistical significance, estimation, generalizability and causation. [2:03]

6.2.7 Use the 2SD method to find a 95% confidence interval for the difference in population means for two "treatment" groups, and interpret the interval in the context of the study. Interpret what it means for the 95% confidence interval for difference in means to contain zero. [1:57]

6.3 Example [1:05]

6.3.1 Identify when a theory-based approach would be valid to find the p-value or a confidence interval when evaluating the relationship between one binary and one quantitative variable. [1:55]

6.3.2 Use the Theory-Based Inference applet to find theory based p-values and confidence intervals for a test of two means. [2:39]

**Chapter 7 Videos**

7.1 Example [2:07]

7.1.1 Identify or a study design as having pairing or independent groups. [3:33]

7.1.2 Identify a study design as paired using repeated measures or paired using matching. [4:25]

7.2 Example [1:14]

7.2.1 Understand the difference between independent samples and paired samples in terms of the study design and how variability can be lower in a paired design and how this can influence the strength of evidence. [1:56]

7.2.2 Complete a simulation-based test of significance of a paired design by writing out the hypothesis, determining the observed statistic, computing the p-value, and writing out an appropriate conclusion. [3:39]

**Chapter 8 Videos**

8.1 Example [1:14]

8.1.1 Compute the MAD (mean absolute value of the differences) statistic from a data set when comparing multiple proportions. [3:30]

8.1.2 Understand that larger values of the MAD statistic suggest stronger evidence against the null hypothesis. [3:43]

8.1.3 Explain why the simulated null distribution of the MAD statistic looks different from other simulated null distributions presented thus far. [2:03]

8.1.4 Use the multiple proportions applet to carry out an analysis using the MAD statistic to compare multiple proportions. [2:08]

8.1.5 [3:37]

8.1.6 [3:02]

8.2 Example [1:51]

8.2.1 Find the value of the chi-square test statistic using the multiple proportions applet, recognize that larger values of the statistic mean more evidence against the null hypothesis and why the distribution of the chi-squared statistic is positive and skewed right. [4:47]

8.2.2 Identify whether or not a chi-square test meets appropriate validity conditions. [1:53]

8.2.3 Conduct a chi-square test of significance using the multiple proportions applet, including appropriate follow-up tests. [3:03]

**Chapter 9 Videos**

9.1 Example [2:32]

9.1.1 Apply the MAD (mean absolute value of the differences) statistic to a data set, including the relationship with the statistic comparing two means. [2:19]

9.1.2 Understand that larger values of the MAD statistic suggest stronger evidence against the null hypothesis. [2:24]

9.1.3 Understand why the simulated null distribution of the MAD statistic looks different from other simulated null distributions presented thus far. [1:48]

9.1.4 Use the multiple means applet to carry out an analysis using the MAD statistic to compare multiple means. [1:44]

9.1.5 [2:48]

9.1.6 [2:14]

9.2 Example [2:09]

9.2.1 Find the value of the ANOVA F statistic using the multiple means applet, recognize that larger values of the statistic mean more evidence against the null hypothesis and why the distribution of the F statistic is positive and skewed right. [4:27]

9.2.2 Identify whether or not an ANOVA (F) test meets appropriate validity conditions. [2:31]

9.2.3 Conduct an ANOVA using the multiple means applet, including appropriate follow-up tests. [2:41]

**Chapter 10 Videos**

10.1 Example [0:45]

10.1.1 Summarize the characteristics of a scatterplot by describing its direction, form, strength and whether there are any unusual observations. [2:35]

10.1.2 Estimate the value of the correlation coefficient within +/- 0.3 by looking at a scatterplot. [4:07]

10.1.3 Recognize that the correlation coefficient is appropriate only for summarizing the strength and direction of a scatterplot that has linear form. [1:51]

10.1.4 Recognize that a scatterplot is the appropriate graph for displaying the relationship between two quantitative variables, and create a scatterplot from raw data. [1:30]

10.1.5 Recognize that a correlation coefficient of 0 means that there is no linear association between the two variables and that a correlation coefficient of -1 or 1 means that the scatterplot is exactly a straight line. [1:39]

10.1.6 Understand that the correlation coefficient is not robust to extreme observations. [1:44]

10.2 Example [1:16]

10.2.1 Apply the 3-S strategy when evaluating the hypothesis of linear association using the correlation coefficient as the statistic. [4:06]

10.2.2 Articulate how to conduct a tactile simulation to implement the 3-S strategy for testing a correlation coefficient. [1:25]

10.2.3 Define the p-value in the context of the 3-S strategy using simulated correlation coefficients under the null hypothesis of no association. [1:25]

10.3 Example [1:00]

10.3.1 Understand that one way a scatterplot can be summarized is by fitting the best-fit (least squares regression) line and interpret both the slope and intercept of a best-fit line in the context of the two variables on the scatterplot. [1:42]

10.3.2 Find the predicted value of the response variable for a given value of the explanatory variable. [1:27]

10.3.3 Understand the concept of residual and find and interpret the residual for an observational unit given the raw data and the equation of the best fit (regression) line. [1:52]

10.3.4 Understand the relationship between residuals and strength of association and that the best-fit (regression) line this minimizes the sum of the squared residuals. [1:12]

10.3.5 Find and interpret the coefficient of determination (r2) as the squared correlation and as the percent of total variation in the response variable that is accounted for by changes (variation) in the explanatory variable. [2:38]

10.3.6 Understand that extrapolation is when a regression line is used to predict values outside of the range of observed values for the explanatory variable; Using the y-intercept as a prediction of the value of the response variable when the explanatory variable is 0 is often (but not always) an example of extrapolation. [1:03]

10.3.7 Understand that slope=0 means no association, slope<0 means negative association, slope>0 means positive association, and that the sign of the slope will be the same as the sign of the correlation coefficient. [1:35]

10.3.8 Understand that influential points can substantially change the equation of the best-fit line and that observations with extreme values of the explanatory variable may potentially be influential. [1:49]

10.4 Example [1:33]

10.4.1 Apply the 3-S strategy when evaluating the hypothesis of association using the slope as the statistic. [2:21]

10.4.2 Articulate how to conduct a tactile simulation to implement the 3-S strategy for testing a slope. [2:04]

10.4.3 Define the p-value in the context of the 3-S strategy using simulated slopes under the null hypothesis of no association. [1:37]

10.4.4 Know that a test of association based on slope is equivalent to a test of association based on a correlation coefficient. [1:54]

10.5 Example [0:56]

10.5.1 Realize that both simulation based approaches to testing correlation coefficients and slopes can, when certain conditions are met, be well-predicted by a theory-based approach; namely, a t-test. The test predicts the null distribution of t-statistics not the distribution of slopes or correlation coefficients. [1:33]

10.5.2 Evaluate a scatterplot for the two validity conditions for a theory-based test of correlation coefficients/slopes. Namely, check to see if there are approximately equal numbers of points above and below the regression line (symmetry) and check to see if the variability of the points around the regression line is consistent for all values of the explanatory variable. Recognize that when the validity conditions are not met simulation can be used or a variable transformation may be appropriate. [2:41]

10.5.3 Interpret a confidence interval for the population slope. [1:33]

10.5.4 State hypotheses in terms of population slopes and correlations. [1:50]