Advanced Statistical analysis – Bivariate data analysis

This lesson comprises two (2) master classes focusing on:

• Classifying data
• Organising and representing data
• Measures of central tendency and spread
• Bivariate scatter plots
• Lines of best fit
• Pearson's correlation coefficient
• Describing bivariate data sets
• Limitations of interpolation and extrapolation

Content:

MA-S2.1

• Classify data relating to a single random variable
• Organise, interpret and display data into appropriate tabular and/or graphical representations including Pareto charts, cumulative frequency distribution tables or graphs, parallel box-plots and two-way tables
  • compare the suitability of different methods of data presentation in real-world contexts
• Summarise and interpret grouped and ungrouped data through appropriate graphs and summary statistics
• Calculate measures of central tendency and spread and investigate their suitability in real-world contexts and use to compare large datasets
  • investigate real-world examples from the media illustrating appropriate and inappropriate uses or misuses of measures of central tendency and spread
• Identify outliers and investigate and describe the effect of outliers on summary statistics
  • use different approaches for identifying outliers, for example consideration of the distance from the mean or median, or the use of below \( Q_1−1.5 \times IQR \) and above \( Q_3+1.5 \times IQR \) as criteria, recognising and justifying when each approach is appropriate
  • investigate and recognise the effect of outliers on the mean, median and standard deviation
• Describe, compare and interpret the distributions of graphical displays and/or numerical datasets and report findings in a systematic and concise manner

MA-S2.2

• Construct a bivariate scatterplot to identify patterns in the data that suggest the presence of an association
• Use bivariate scatterplots (constructing them where needed), to describe the patterns, features and associations of bivariate datasets, justifying any conclusions
  • describe bivariate datasets in terms of form (linear/non-linear) and in the case of linear, also the direction (positive/negative) and strength of association (strong/moderate/weak)
  • identify the dependent and independent variables within bivariate datasets where appropriate
  • describe and interpret a variety of bivariate datasets involving two numerical variables using real-world examples in the media or those freely available from government or business datasets
• Calculate and interpret Pearson's correlation coefficient (r) using technology to quantify the strength of a linear association of a sample
• Model a linear relationship by fitting an appropriate line of best fit to a scatterplot and using it to describe and quantify associations
  • fit a line of best fit to the data by eye and using technology
  • fit a least squares regression line to the data using technology
  • interpret the intercept and gradient of the fitted line
• Use the appropriate line of best fit, both found by eye and by applying the equation of the fitted line, to make predictions by either interpolation or extrapolation
  • distinguish between interpolation and extrapolation, recognising the limitations of using the fitted line to make predictions, and interpolate from plotted data to make predictions where appropriate
• Solve problems that involve identifying, analysing and describing associations between two numeric variables
• Construct, interpret and analyse scatterplots for bivariate numerical data in practical contexts
  • demonstrate an awareness of issues of privacy and bias, ethics, and responsiveness to diverse groups and cultures when collecting and using data