Identify two variables. Classify them as explanatory or response and quantitative or explanatory.

Transcription

1 OLI Module 2 - Examining Relationships Objective Summarize and describe the distribution of a categorical variable in context. Generate and interpret several different graphical displays of the distribution of a quantitative variable (histogram, stemplot, boxplot) Definitions Example 1 The explanatory variable (also commonly referred to as the independent variable)- the variable that claims to explain, predict or affect the response; and The response variable (also commonly referred to as the dependent variable)- the outcome of the study. Identify two variables. Classify them as explanatory or response and quantitative or explanatory. 1. How is the number of calories in a hot dog related to (or affected by) the type of hot dog (beef, meat or poultry)? In other words, are there differences in the number of calories among the three types of hot dogs? 2. Is there a relationship between the type of light a baby sleeps with (no light, night-light, lamp) and whether or not the child develops nearsightedness? 3. How well can we predict a student's freshman year GPA from his/her SAT score? Four Cases Types of Graphs and Summaries Case Type of Graph Summaries C Q Side-by-Side Boxplots OR 2- histograms with the same scale Shape, Center (Mean or Median), Spread (standard deviation or IQR), Outliers (2 standard deviations or 1.5 IQR). C C Segmented/Stacked Bar Chart Contingency Table with Conditional Relative Frequencies Q Q Scatterplot Correlation

2 Case 1 C Q Side-by-Side Boxplots OR 2- histograms with the same scale Example 1: Students wanted to investigate whether the distance a male student can jump is affected by having a target to jump toward. The students decide to perform an experiment comparing two groups. One group will have male students jumping toward a fixed target, and the other group will have male students jumping without a fixed target. There are 28 male students available for the experiment. S.O.C.S. with comparison Based on the boxplots, how do the lengths of the jumps compare for the two groups. Make sure to compare center, variability, and shape. Center: The median distance of those without a target (about 169 cm) was greater than the median distance of the jumpers with a target (about 157cm). Variability: The IQR of 30cm (180cm 150cm) for those with no target is also larger than those with a target who had an IQR of 17cm (167cm 150 cm), showing more variability among the middle 50% of jumpers. Shape: The distribution of jumping distances with a target appear to be skewed to the left (most jumping over 150cm, only 25% jumping between 110 and 150cm) while the distribution of those with NO target are more symmetric (50% jumping between 125cm and 169cm, and 50% jumping between 169cm and 200cm). This experiment seems to be trying to show that those without a target will jump further than those without. Practice Compare center and spread of the distribution of marathon times for men and women below.

3 Case 2 C C Segmented Bar Chart Contingency Table with Conditional Relative Frequencies Contingency Table: Gender versus Weight Feel Just Right Overweight Underweight Female Male Prefer not to Say Segmented Bar Chart: Gender vs. Weight Feel Case 3 Q Q Scatterplot Correlation For the following scatterplots, describe the relationship, using words like strong, weak, positive, negative, linear. Strong positive linear relationship between husband s age and wife s age with no apparent outliers. Moderately strong negative linear relationship between driver s age and vision distance with no apparent outliers. There is a weak positive linear relationship between scores on exam 1 and scores on exam 2, with perhaps one outlier where an individual scored a 86 on exam 1 and a 45 on exam 2 (since there is less variability among higher scores).

4 There is a moderately weak positive linear relationship between longevity (lifespan) and gestation, with an outlier at about 40 year lifespan and about 650 day gestation. Practice 3 Describe the relationship between time spent on the exam and the grade scored. Definition A lurking variable is a variable that is not among the explanatory or response variables in a study, but could substantially affect your interpretation of the relationship among those variables. Fire Damage: The scatterplot below illustrates how the number of firefighters sent to fires (X) is related to the amount of damage caused by fires (Y) in a certain city. A government study collected data on the death rates in nearly 6,000 hospitals in the United States. Here is an example of 2 of them:

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