# Statistical Vignettes

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Correlation Coefficient

The correlation coefficient is commonly used in various scientific disciplines to quantify an observed relationship between two variables and communicate the strength and nature of the relationship. This vignette will help build a student's understanding of correlation coefficients and how two sets of measurements may vary together.

Normal Distribution

Normal Distribution is one of the fundamental probability distributions used in statistics to predict the outcomes for a set of measurements, such as the overall height of a population and is commonly known as the bell curve or Gaussian distribution. Thus, the normal distribution shows the behavior of the variable by listing all possible observed outcomes based on available data. The vignette will reinforce or establish a student's understanding of Normal Distribution, the parameters that facilitate the size and shape of the distribution (mean and standard deviation), and how it is applied to express probable outcomes and outliers for an event. The concept will be reviewed by analyzing the probability distribution for pizza delivery times and demonstrating it in a following exercise.

Linear Regression

Linear Regression is similar to the correlation coefficient in that both are utilized to understand the relationship between two sets of measurements. Regression expands this concept to create modeled predictions from the extension of the best fit line between a dependent and independent variable. This vignette will help build a student's understanding of linear regression and how to interpret R2 coefficients by analyzing lines of best fit.

Significant Figures

Significant figures are used in everyday measurements, where accurate values are needed to provide concise quantitative answers. Measuring devices such as rulers, calculators or thermometers all have limits to their precision, thus all numerical values are only as accurate as the measurement tool used to collect the data. This vignette will reinforce or establish a student's understanding of significant figures and how the "Atlantic-Pacific Rule" (Stone 1989) can be applied for any given measurement or mathematical operation.

Hypothesis Testing

Hypothesis Testing is a widely used data analysis tool to make inferences or draw conclusions about an area of interest for a population from a selected sample, such as the addition of a new course of study or to test if a new medicine is effective. A hypothesis test evaluates two types of statements for a population by comparing their results using the mean, standard deviation, and sample size. The null hypothesis can be described as the "status quo" with no changes occurring, while the alternative hypothesis expects a change to occur. The benefit of the test is that it can be used to determine the significance of the data and understand an outcome with limited information.

M3 (Mean, Median, Mode)

Mean, Median, and Mode is a simple descriptive statistical method that assist in the representation, organization, and summarization of a dataset or scores of data of any size. A score is commonly identified as the average that is used to compare groups of individuals or between sets of data. The representation of the data is defined as central tendency, where the goal is to describe a single score that best represents all the individual values within the center of a distribution.