Statistical Software Reference (R, Python, Excel) Cheat Sheet

Key Facts

• The sample mean is calculated by $\bar{x} = \frac{\sum x_i}{n}$, using mean(x) in R, df['x'].mean() in Python, or =AVERAGE(range) in Excel.
• The sample standard deviation is $s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}$, using sd(x) in R, df['x'].std() in Python, or =STDEV.S(range) in Excel.
• The five-number summary includes the minimum, first quartile, median, third quartile, and maximum, often written as $\min, Q_1, Q_2, Q_3, \max$.
• Correlation measures linear association with $r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{(n - 1)s_xs_y}$, using cor(x,y), df['x'].corr(df['y']), or =CORREL(range1,range2).
• A simple linear regression model has the form $\hat{y} = b_0 + b_1x$, where $b_0$ is the intercept and $b_1$ is the slope.
• A z-score standardizes a value using $z = \frac{x - \bar{x}}{s}$, which tells how many standard deviations the value is from the mean.
• For a one-sample t statistic, use $t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$, where $\mu_0$ is the hypothesized population mean.
• Always check whether software functions use sample formulas with $n - 1$ or population formulas with $n$, especially for variance and standard deviation.

Vocabulary

Data frame

A table-like data structure with rows as observations and columns as variables, commonly used in R and Python.

Function

A named command that takes input values and returns an output, such as mean(x) or =AVERAGE(range).

Sample standard deviation

A measure of spread for sample data, calculated by $s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}}$.

Correlation

A number from $-1$ to $1$ that describes the strength and direction of a linear relationship between two quantitative variables.

Linear regression

A method for modeling a straight-line relationship between variables using $\hat{y} = b_0 + b_1x$.

P-value

The probability of getting a result at least as extreme as the observed result if the null hypothesis is true.