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bc10188..6b41f0e 100644 --- a/01/01learn_obj.tex +++ b/01/01learn_obj.tex @@ -81,7 +81,7 @@ \item If random assignment has been employed in study design, the results suggest causality. \end{itemize} \item Question confounding variables and sources of bias in a given study. -\item Distinguish between simple random, stratified, and cluster sampling, and recognize the benefits and drawbacks of choosing one sampling scheme over another. +\item Distinguish between simple random, stratified, cluster, and multistage sampling, and recognize the benefits and drawbacks of choosing one sampling scheme over another. \begin{itemize} \renewcommand{\labelitemi}{{\textcolor{dark}{{\tiny $\blacksquare$}}}} \item Simple random sampling: Each subject in the population is equally likely to be selected. diff --git a/02/02learn_obj.log b/02/02learn_obj.log index fd74316..b9aa666 100644 --- a/02/02learn_obj.log +++ b/02/02learn_obj.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 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The standard error associated with this estimate is 0.015 (1.5\%). What is the margin of error ay 95\% confidence level? Calculate a 95\% confidence interval and interpret it in context. You may assume that the point estimate is normally distributed (we'll learn how to check this later). +In a random sample of 1,017 Americans 60\% said they do not trust the mass media when it comes to reporting the news fully, accurately, and fairly. The standard error associated with this estimate is 0.015 (1.5\%). What is the margin of error for a 95\% confidence level? Calculate a 95\% confidence interval and interpret it in context. You may assume that the point estimate is normally distributed (we'll learn how to check this later). } \end{itemize} }} diff --git a/05/05learn_obj.tex b/05/05learn_obj.tex index 6d341f2..ee8b290 100644 --- a/05/05learn_obj.tex +++ b/05/05learn_obj.tex @@ -38,7 +38,7 @@ \begin{document} -{\LARGE \textcolor{oiB}{Learning Objectives \hfill Chapter 5: Inference for numerical variables}} \\ +{\LARGE \textcolor{oiB}{Learning Objectives \hfill Chapter 5: Inference for numerical data}} \\ % diff --git a/06/06learn_obj.log b/06/06learn_obj.log index 72b0caf..c1fe11c 100644 --- a/06/06learn_obj.log +++ b/06/06learn_obj.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015) (preloaded format=pdflatex 2015.5.24) 18 DEC 2015 19:23 +This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015) (preloaded format=pdflatex 2015.5.24) 7 JUL 2016 01:00 entering extended mode \write18 enabled. %&-line parsing enabled. @@ -518,7 +518,7 @@ Here is how much of TeX's memory you used: 10753 multiletter control sequences out of 15000+600000 9347 words of font info for 36 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 - 42i,5n,35p,395b,548s stack positions out of 5000i,500n,10000p,200000b,80000s + 42i,5n,35p,395b,546s stack positions out of 5000i,500n,10000p,200000b,80000s < @@ -530,7 +530,7 @@ l/texlive/2015/texmf-dist/fonts/type1/public/amsfonts/cm/cmr8.pfb> -Output written on 06learn_obj.pdf (5 pages, 138388 bytes). +Output written on 06learn_obj.pdf (5 pages, 138647 bytes). 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hypothesis test are different when dealing with proportions, since in the hypothesis test we need to assume that the null hypothesis is true -- remember: p-value = P(observed or more extreme test statistic $|$ $H_0$ true). \begin{itemize} -\item[-] For confidence intervals use $\hat{p}$ (observed sample proportion) when calculating the standard error and checking the success/failure condition: +\item[-] For confidence intervals use $\hat{p}$ (observed sample proportion) when calculating the standard error and when checking the success/failure condition: \[ SE_{\hat{p}} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \] \item[-] For hypothesis tests use $p_0$ (null value) when calculating the standard error and checking the success/failure condition: \[ SE_{\hat{p}} = \sqrt{\frac{p_0 (1-p_0)}{n}} \] \item[-] Such a discrepancy doesn't exist when conducting inference for means, since the mean doesn't factor into the calculation of the standard error, while the proportion does. \end{itemize} -\item Explain why when calculating the required minimum sample size for a given margin of error at a given confidence level, we use $\hat{p} = 0.5$ if there are no previous studies suggesting a more accurate estimate. +\item Calculate the required minimum sample size for a given margin of error at a given confidence level, and explain why we use $\hat{p} = 0.5$ if there are no previous studies suggesting a more accurate estimate. \begin{itemize} \item[-] Conceptually: When there is no additional information, 50\% chance of success is a good guess for events with only two outcomes (success or failure). \item[-] Mathematically: Using $\hat{p} = 0.5$ yields the most conservative (highest) estimate for the required sample size. @@ -117,7 +117,7 @@ \item Note that the calculation of the standard error of the distribution of the difference in two independent sample proportions is different for a confidence interval and a hypothesis test. \begin{itemize} -\item[-] confidence interval and hypothesis test when $H_0: p_1 -p_2 =$ some value other than 0: +\item[-] confidence interval (and hypothesis test when $H_0: p_1 -p_2 =$ some value other than 0): \[SE_{(\hat{p}_1 - \hat{p}_2)} = \sqrt{\frac{ \hat{p}_1 (1 - \hat{p}_1)}{n_1} + \frac{ \hat{p}_2 (1 - \hat{p}_2)}{n_2} } \] \item[-] hypothesis test when $H_0: p_1 -p_2 = 0$: \[SE_{(\hat{p}_1 - \hat{p}_2)} = \sqrt{\frac{ \hat{p}_{pool} (1 - \hat{p}_{pool})}{n_1} + \frac{ \hat{p}_{pool} (1 - \hat{p}_{pool})}{n_2} }, \] @@ -166,8 +166,8 @@ \item Use a chi-square test of goodness of fit to evaluate if the distribution of levels of a single categorical variable follows a hypothesized distribution. \begin{itemize} -\item[] $H_0:$ The distribution of observed counts follow the hypothesized distribution, and any observed differences are due to chance. -\item[] $H_A:$ The distribution of observed counts do not follow the hypothesized distribution. +\item[] $H_0:$ The distribution of the variable follows the hypothesized distribution, and any observed differences are due to chance. +\item[] $H_A:$ The distribution of the variable does not follow the hypothesized distribution. \end{itemize} \item Calculate the expected counts for a given level (cell) in a one-way table as the sample size times the hypothesized proportion for that level. @@ -176,7 +176,7 @@ \[ \chi = \sum_{i = 1}^{k} \frac{(\text{observed count} - \text{expected count})^2}{\text{expected count}}, \] where $k$ is the number of cells. -\item Note that the chi-square distribution is right skewed with one parameter: degrees of freedom. In the case of a goodness of fit test, $df = k - 1$. +\item Note that the chi-square distribution is right skewed with one parameter: degrees of freedom. In the case of a goodness of fit test, $df = \# \text{of categories} - 1$. \item List the conditions necessary for performing a chi-square test (goodness of fit or independence) \begin{enumerate} diff --git a/07/07learn_obj.log b/07/07learn_obj.log index 2201453..2075e2e 100644 --- a/07/07learn_obj.log +++ b/07/07learn_obj.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015) (preloaded format=pdflatex 2015.5.24) 18 DEC 2015 19:25 +This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015) (preloaded format=pdflatex 2015.5.24) 7 JUL 2016 01:04 entering extended mode \write18 enabled. %&-line parsing enabled. @@ -535,7 +535,7 @@ Here is how much of TeX's memory you used: 10768 multiletter control sequences out of 15000+600000 9347 words of font info for 36 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 - 42i,7n,35p,390b,602s stack positions out of 5000i,500n,10000p,200000b,80000s + 42i,7n,35p,390b,568s stack positions out of 5000i,500n,10000p,200000b,80000s < @@ -546,7 +546,7 @@ ocal/texlive/2015/texmf-dist/fonts/type1/public/amsfonts/cm/cmr6.pfb> -Output written on 07learn_obj.pdf (5 pages, 144310 bytes). +Output written on 07learn_obj.pdf (5 pages, 144379 bytes). 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diff --git a/07/07learn_obj.tex b/07/07learn_obj.tex index 017759b..cb3f3a7 100644 --- a/07/07learn_obj.tex +++ b/07/07learn_obj.tex @@ -65,11 +65,11 @@ \item[-] Note that a relationship that is nonlinear is simply called an association. \end{itemize} -\item Note that correlation coefficient ($R$, also called Pearson's $R$) the following properties: +\item Note that correlation coefficient ($r$, also called Pearson's $r$) the following properties: \begin{enumerate} \item[-] the magnitude (absolute value) of the correlation coefficient measures the strength of the linear association between two numerical variables \item[-] the sign of the correlation coefficient indicates the direction of association -\item[-] the correlation coefficient is always between -1 and 1, -1 indicating perfect negative linear association, +1 indicating perfect positive linear association, and 0 indicating no linear relationship +\item[-] the correlation coefficient is always between -1 and 1, inclusive, with -1 indicating perfect negative linear association, +1 indicating perfect positive linear association, and 0 indicating no \emph{linear} relationship \item[-] the correlation coefficient is unitless \item[-] since the correlation coefficient is unitless, it is not affected by changes in the center or scale of either variable (such as unit conversions) \item[-] the correlation of X with Y is the same as of Y with X @@ -126,7 +126,7 @@ \item Calculate the estimate for the slope ($b_1$) as \[ b_1 = R\frac{s_y}{s_x}, \] -where $R$ is the correlation coefficient, $s_y$ is the standard deviation of the response variable, and $s_x$ is the standard deviation of the explanatory variable. +where $r$ is the correlation coefficient, $s_y$ is the standard deviation of the response variable, and $s_x$ is the standard deviation of the explanatory variable. \item Interpret the slope as \begin{itemize} @@ -157,7 +157,7 @@ \item Define $R^2$ as the percentage of the variability in the response variable explained by the the explanatory variable. \begin{itemize} \item[-] For a good model, we would like this number to be as close to 100\% as possible. -\item[-] This value is calculated as the square of the correlation coefficient. +\item[-] This value is calculated as the square of the correlation coefficient, and is between 0 and 1, inclusive. \end{itemize} \end{enumerate} diff --git a/LO-PDFs.zip b/LO-PDFs.zip new file mode 100644 index 0000000000000000000000000000000000000000..4fb099bf36dc7acd251f93e99cf52a3d2874f999 GIT binary patch literal 1005376 zcmV)KK)SzBO9KQ7000000OttjNB{r;000000000000;mO08CFUP((&^FI89!06^n? zSApYwSN8!F08mQ<1QY-W00;o>p@KmG00000000000000N01yC7Pc2YHMsqJPFl=RE za&BL5VrnjMWM)-Z3;T2!i%s-zZ`vpS>-B4V_Rbga;%b4$Z((5wUu1olQ&1Ux*@^fIP) z<}MZljLZxi1phmr>BTH1pt}-X*br7Qt=lA8rPHp8 zDxtfoMY=XvChjieA~e1mrBgljPwio5`SNF`zB7H3j^+8zHMUD+rb~QZ#ZJdA@(Q>n zhw*5iS_f1-n&|yqub`8-G^_o#(Nl?h0$!?Bg6Va&;zyAkRHWvidf3QUq`4ZLqcUP5 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