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Statistics of Two Variables. Linear Correlation. Learning Goals. I can use vocabulary related to two variable data including, scatter plots, split-bar graph, dependent variable, independent variable, trend, linear correlation, etc.
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Statistics of Two Variables Linear Correlation
Learning Goals • I can use vocabulary related to two variable data including, scatter plots, split-bar graph, dependent variable, independent variable, trend, linear correlation, etc. • I can identify if there is a correlation between two variables, and what type it is (linear, quadratic, etc.)
Statistics of Two Variables Does smoking cause lung cancer? Is job performance related to marks in high school? Do pollution levels affect the ozone layer in the atmosphere? Often the answers to such questions are not clear-cut. However, inferences have been made based on analyzing the relationships between such variables. In this unit, we aim to detect the strength of a relationship between two variables.
Qualitative Data Analysis For qualitative data, we often use a split-bar graph. It helps us distinguish a relationship between two variables. In the example below, we are comparing the relationships between students and parents. What can we conclude?
Quantitative Data Analysis For quantitative data, we use scatter plots to graph our data. The data is an ordered pair, an x and a y variable, (x,y). A scatter plot shows the relationship between two variables with the independent (one which we control) variable on the horizontal axis and the dependent variable on the vertical. With a scatter plot, we can determine both the type of relationship as well as the strength of the relationship.
Type of relationship - Correlation We use the term correlation to explain the three types of relationships that exist. For time being, we will focus on only linear correlations – ie. data trends which can be described using a straight line. We can have a positive correlation. In this case, when our independent variable increases, so too does the dependent variable. We can have a negative correlation. In this case, when our independent variable increases, our dependent variable decreases. We can have no correlation. Here there is no definable pattern in our graph.
Example #1 Classify the relationships between X and Y.
Strength of a Relationship – Correlation Coefficient To determine the strength of a relationship, we use the correlation coefficient (r). The correlation coefficient gives a quantitative measure of the strength of the correlation. When analyzing linear relationships, the correlation coefficient indicates how closely the data points cluster around the line of best fit.
Example #2 Examining Two Training Programs A study examines two new obedience-training methods for dogs. The dogs were randomly selected to receive from 5 to 16 hours of training in one of the two training programs. The dogs were assessed using a performance test graded out of 20. Determine the more successful training program.
