From b1d0d325946ed0960523a3311aefdeddea893657 Mon Sep 17 00:00:00 2001 From: Christina Yang Date: Thu, 31 Aug 2023 19:01:30 -0700 Subject: [PATCH 1/3] add 4.1.1.12 (cdf + pmf) --- outputs_csv/LO_stats.csv | 1 + 1 file changed, 1 insertion(+) diff --git a/outputs_csv/LO_stats.csv b/outputs_csv/LO_stats.csv index 8dce91b..c992d20 100644 --- a/outputs_csv/LO_stats.csv +++ b/outputs_csv/LO_stats.csv @@ -50,6 +50,7 @@ Numbered Topic,Topic,Subtopic,Subsubtopic,Learning Outcome,Code 004.Distributions of random variables,Distributions of random variables,Topic Outcome,,Calculate probability of a given number of successes in a given number of trials using the binomial distribution $P(k = K) = \frac{n!}{k!~(n - k)!}~p^k~(1-p)^{(n - k)}$.,4.1.1.9 004.Distributions of random variables,Distributions of random variables,Topic Outcome,,Calculate the expected number of successes in a given number of binomial trials $(\mu = np)$ and its standard deviation $(\sigma = \sqrt{np(1-p)})$.,4.1.1.10 004.Distributions of random variables,Distributions of random variables,Topic Outcome,,"When number of trials is sufficiently large ($np \ge 10$ and $n(1-p) \ge 10$), use normal approximation to calculate binomial probabilities, and explain why this approach works.",4.1.1.11 +004.Distributions of random variables,Topic Outcome,,Cumulative density function and probability mass functions.,4.1.1.12 005.Foundations for inference,Foundations for inference,Topic Outcome,,"Define sample statistic as a point estimate for a population parameter, for example, the sample proportion is used to estimate the population proportion, and note that point estimate and sample statistic are synonymous.",5.1.1.0 005.Foundations for inference,Foundations for inference,Topic Outcome,,"Recognize that point estimates (such as the sample proportion) will vary from one sample to another, and define this variability as sampling variation.",5.1.1.1 005.Foundations for inference,Foundations for inference,Topic Outcome,,"Calculate the sampling variability of the proportion, the standard error, as $SE = \sqrt{\frac{p(1-p)}{n}}$, where $p$ is the population proportion.",5.1.1.2 From 0436fb68fdb558cf58e06ce364bc2d3828dc4826 Mon Sep 17 00:00:00 2001 From: Christina Yang Date: Thu, 31 Aug 2023 19:13:10 -0700 Subject: [PATCH 2/3] Revert "add 4.1.1.12 (cdf + pmf)" This reverts commit b1d0d325946ed0960523a3311aefdeddea893657. --- outputs_csv/LO_stats.csv | 1 - 1 file changed, 1 deletion(-) diff --git a/outputs_csv/LO_stats.csv b/outputs_csv/LO_stats.csv index c992d20..8dce91b 100644 --- a/outputs_csv/LO_stats.csv +++ b/outputs_csv/LO_stats.csv @@ -50,7 +50,6 @@ Numbered Topic,Topic,Subtopic,Subsubtopic,Learning Outcome,Code 004.Distributions of random variables,Distributions of random variables,Topic Outcome,,Calculate probability of a given number of successes in a given number of trials using the binomial distribution $P(k = K) = \frac{n!}{k!~(n - k)!}~p^k~(1-p)^{(n - k)}$.,4.1.1.9 004.Distributions of random variables,Distributions of random variables,Topic Outcome,,Calculate the expected number of successes in a given number of binomial trials $(\mu = np)$ and its standard deviation $(\sigma = \sqrt{np(1-p)})$.,4.1.1.10 004.Distributions of random variables,Distributions of random variables,Topic Outcome,,"When number of trials is sufficiently large ($np \ge 10$ and $n(1-p) \ge 10$), use normal approximation to calculate binomial probabilities, and explain why this approach works.",4.1.1.11 -004.Distributions of random variables,Topic Outcome,,Cumulative density function and probability mass functions.,4.1.1.12 005.Foundations for inference,Foundations for inference,Topic Outcome,,"Define sample statistic as a point estimate for a population parameter, for example, the sample proportion is used to estimate the population proportion, and note that point estimate and sample statistic are synonymous.",5.1.1.0 005.Foundations for inference,Foundations for inference,Topic Outcome,,"Recognize that point estimates (such as the sample proportion) will vary from one sample to another, and define this variability as sampling variation.",5.1.1.1 005.Foundations for inference,Foundations for inference,Topic Outcome,,"Calculate the sampling variability of the proportion, the standard error, as $SE = \sqrt{\frac{p(1-p)}{n}}$, where $p$ is the population proportion.",5.1.1.2 From 7f66269d654680bef9c27d0773711491980c5758 Mon Sep 17 00:00:00 2001 From: Christina Yang Date: Thu, 31 Aug 2023 19:14:06 -0700 Subject: [PATCH 3/3] fix move to yml --- LO_stats.yml | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/LO_stats.yml b/LO_stats.yml index 790ab73..4a0d4a5 100644 --- a/LO_stats.yml +++ b/LO_stats.yml @@ -66,6 +66,7 @@ Distributions of random variables: - Calculate probability of a given number of successes in a given number of trials using the binomial distribution $P(k = K) = \frac{n!}{k!~(n - k)!}~p^k~(1-p)^{(n - k)}$. - Calculate the expected number of successes in a given number of binomial trials $(\mu = np)$ and its standard deviation $(\sigma = \sqrt{np(1-p)})$. - When number of trials is sufficiently large ($np \ge 10$ and $n(1-p) \ge 10$), use normal approximation to calculate binomial probabilities, and explain why this approach works. + - Cumulative density function and probability mass functions. # Topic Break @@ -113,7 +114,7 @@ Inference for categorical data: - Note that the reason for the difference in calculations of standard error is the same as in the case of the single proportion; when the null hypothesis claims that the two population proportions are equal, we need to take that into consideration when calculating the standard error for the hypothesis test, and use a common proportion for both samples. - 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. - 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. - - Calculate the chi-square test statistic. + - Calculate the chi-square test statistic. - Note that the chi-square distribution is right skewed with one parameter; degrees of freedom. In the case of a goodness of fit test, $df = \# \text{of categories} - 1$. - List the conditions necessary for performing a chi-square test (goodness of fit or independence). - Describe how to use the chi-square table to obtain a p-value. @@ -124,7 +125,7 @@ Inference for categorical data: - Use simulation methods when sample size conditions aren't met for inference for categorical variables. - In hypothesis testing; for one categorical variable, generate simulated samples based on the null hypothesis, and then calculate the number of samples that are at least as extreme as the observed data. For two categorical variables, use a randomization test. - Use bootstrap methods for confidence intervals for categorical variables with at most two levels. - + # Topic Break Inference for numerical data: @@ -159,7 +160,7 @@ Introduction to linear regression: Topic Outcome: - Define the explanatory variable as the independent variable (predictor), and the response variable as the dependent variable (predicted). - Plot the explanatory variable ($x$) on the x-axis and the response variable ($y$) on the y-axis, and fit a linear regression model. - - When describing the association between two numerical variables, evaluate direction, form and strength. + - When describing the association between two numerical variables, evaluate direction, form and strength. - Define correlation as the linear association between two numerical variables. - Note the correlation coefficient ($r$, also called Pearson's $r$) and its following properties. - Recall that correlation does not imply causation. @@ -170,7 +171,7 @@ Introduction to linear regression: - Interpret the slope. - Note that the least squares line always passes through the average of the response and explanatory variables ($\bar{x},\bar{y}$). - Use the above property to calculate the estimate for the slope ($b_0$) as $b_0 = \bar{y} - b_1 \bar{x}$, where $b_1$ is the slope, $\bar{y}$ is the average of the response variable, and $\bar{x}$ is the average of explanatory variable. - - Interpret the intercept. + - Interpret the intercept. - Predict the value of the response variable for a given value of the explanatory variable, $x^\star$, by plugging in $x^\star$ in the linear model. - Define $R^2$ as the percentage of the variability in the response variable explained by the the explanatory variable. - Define a leverage point as a point that lies away from the center of the data in the horizontal direction.