Data Analysis Notes

Quantitative Data Analysis

Chapter 1, 2, 3, and 12

Dotplot, Stemplot, Boxplot, Histogram

• When discussing the shape of data, use "approximately symmetrical" instead of "approximately normal."

Numerical Summary

• Includes minimum, $Q<em>1$, $Q</em>2$ (median), $Q_3$, and maximum values.

Outlier Rule

• Any number less than $Q_1 - 1.5 Imes IQR$ is considered an outlier.
• Any number greater than $Q_3 + 1.5 Imes IQR$ is considered an outlier.

Center

• Mean
• Median

Spread

• Standard deviation
• Variance
• IQR (Interquartile Range)
• Range
• $Variance = (Standard Deviation)^2$

Skewness

• Right Skew: The right tail is longer, and the mean is pulled towards the right.
• Left Skew: The left tail is longer, and the mean is pulled towards the left.

Distributions

• For symmetrical distributions, use mean and standard deviation.
• For skewed distributions, use median and IQR.

Bar Graphs

• Use percentages, especially when comparing categorical data.
• When comparing graphs, use comparison words and SOCS (Shape, Outliers, Center, Spread).

Transformations of Data

• Adding or subtracting a constant to the data set will not change measures of spread.
• Multiplying or dividing by a constant will change all measures.

Median

• The median is resistant to extreme observations (it doesn't change when the end values change).

Graphing

• When creating a graph, include a label and a scale.

Percentile Graphs

• Also known as cumulative relative frequency graphs or ogives (Chapter 2).

Scatterplots

• Explanatory variable on the x-axis.
• Response variable on the y-axis.
• Use DOFS (Direction, Outliers, Form, Strength) to describe scatterplots.

Correlation

• Represented by "r."
• Read computer output and describe properties of r.

Computer Output

• Slope
• y-intercept
• r²
• s (standard deviation of residuals)

Interpretation

• Interpret slope, y-intercept, r², r, and residuals.
• Write the equation from computer output: $\hat{y} = a + bx$
• Calculate predicted values and residuals.

Extrapolation

Transformations for Non-Linear to Linear Forms

• Only $y$ is changed to $\log y$ or $\ In y$: The original model is exponential.
• Both $x$ and $y$ are changed to $\log x$ / $\ In x$ and $\log y$ / $\ In y$: The original model is a power model.

Logarithmic Transformations

• For $\log y$, the base is 10.
  • If $\log \hat{y} = 35$, then $\hat{y} = 10^{35}$.
• For $\ In y$, the base is $e$.
  • If $\ In \hat{y} = 35$, then $\hat{y} = e^{35}$.

Residual Plots

• A pattern in the residual plot indicates the model is not linear.

Scatter Plot Analysis

• When you see a curve in the scatter plot, the model is not linear.