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Merge pull request #55 from open-resources/vrbiki-patch-1
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firasm authored Jun 2, 2024
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Expand Up @@ -202,4 +202,32 @@ Multiple and logistic regression:
- The general idea behind forward-selection is to start with only one variable and adding one variable at a time until the ideal model is reached.
- Adjusted $R^2$ method is more computationally intensive, but it is more reliable, since it doesn't depend on an arbitrary significant level.
- List the conditions for multiple linear regression as; (1) linear relationship between each (numerical) explanatory variable and the response - checked using scatterplots of $y$ vs. each $x$, and residuals plots of $residuals$ vs. each $x$, (2) nearly normal residuals with mean 0 - checked using a normal probability plot and histogram of residuals, (3) constant variability of residuals - checked using residuals plots of $residuals$ vs. $\hat{y}$, and $residuals$ vs. each $x$, (4) independence of residuals (and hence observations) - checked using a scatterplot of $residuals$ vs. order of data collection (will reveal non-independence if data have time series structure).
- Note that no model is perfect, but even imperfect models can be useful.
- Note that no model is perfect, but even imperfect models can be useful.

# Topic Break

Sampling and Design
Topic Outcome:
- Explain the purpose and importance of sampling in statistics.
- Assess the representativeness of a sample and identify and avoid sources of sampling bias and nonsampling errors.
- Critically evaluate statistical studies for issues related to sample selection, sample size, and potential biases.
- Apply appropriate rounding techniques to data values.
- Define and differentiate between the four levels of measurement: nominal, ordinal, interval, and ratio.
- Differentiate between descriptive and inferential statistics.
- Define and differentiate between key terms such as population, sample, parameter, statistic, variable, and data.
- Use appropriate symbols (e.g. $\bar x$) to represent data values.
- Design and conduct simple surveys or experiments to collect and analyze data, ensuring ethical considerations.
- Distinguish between sampling errors and nonsampling errors.
- Discuss the use of graphs in presenting data and the importance of selecting the most informative graph based on the data and context.
- Identify the population, sample, experimental units, explanatory variable, response variable, and treatments in a study.
- Recognize the importance of proper experimental design to ensure reliable and accurate data.
- Define and explain the purpose of randomized experiments.
- Define lurking variables and understand their potential impact on experimental results.
- Explain how random assignment helps control for lurking variables and ensures that treatment groups are comparable.
- Define blinding and double-blinding in the context of experiments.
- Understand the role of placebo treatments and control groups in reducing the power of suggestion.
- Interpret the results of experiments and identify cause-and-effect relationships between variables.
- Recognize and explain unethical behavior in the context of statistical studies.
- Design an experiment to test a specific hypothesis, including identifying variables, treatments, and methods for random assignment.
- Critically evaluate the design and execution of experiments to identify strengths and weaknesses and determine the validity and reliability of the results.
- Explain the key protections mandated by law for research involving human participants, including informed consent and data privacy.

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