Bivariate Data

Bivariate Data Overview

Investigating associations between two variables, including:

• response and explanatory variables and their role in investigating associations between variables

• contingency (two-way) frequency tables, two-way frequency tables and their associated bar charts (including percentaged segmented bar charts) and their use in identifying and describing associations between two categorical variables

• back-to-back stem plots, parallel dot plots and boxplots and their use in identifying and describing associations between a numerical and a categorical variable • scatterplots and their use in identifying and qualitatively describing the association between two numerical variables in terms of direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak)

• answering statistical questions that require a knowledge of the associations between pairs of variables

• Pearson correlation coefficient, r, its calculation and interpretation • cause and effect; the difference between observation and experimentation when collecting data and the need for experimentation to definitively determine cause and effect

• non-causal explanations for an observed association including common response, confounding, and coincidence; discussion and communication of these explanations in a particular situation in a systematic and concise manner.

Investigating and modelling linear associations, including:

• least squares line of best fit y = a + bx, where x represents the explanatory variable and y represents the response variable; the determination of the coefficients a and b using technology, and the formulas y x s b r s = and a y bx

Investigating and modelling linear associations, including:

• least squares line of best fit y = a + bx, where x represents the explanatory variable and y represents the response variable; the determination of the coefficients a and b using technology, and the formulas y x s b r s = and a y bx = −

• modelling linear association between two numerical variables, including the: – identification of the explanatory and response variables – use of the least squares method to fit a linear model to the data

• interpretation of the slope and intercepts of the least squares line in the context of the situation being modelled, including: – use of the rule of the fitted line to make predictions being aware of the limitations of extrapolation – use of the coefficient of determination, r2 , to assess the strength of the association in terms of explained variation – use of residual analysis to check quality of fit

• data transformation and its use in transforming some forms of non-linear data to linearity using a square, log or reciprocal transformation (on one axis only)

• interpretation and use of the equation of the least squares line fitted to the transformed data to make predictions

Assessment Tasks Overview

• Chapter Tests
• Combined SAC (At the end of Chapter 6)

Learning Goals/Success Criteria

Chapter3: Investigating Associations between two variables

Chapter 4: Regression: Fitting lines to data

Chapter 5: Data Transformation