# Australian Bureau of Statistics

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 CensusAtSchool Australia

CaSQ 5 - Cause and Effect: Height and Dominant Hand Reaction Time

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 How to: Get a Random Sample from CensusAtSchool Go to the CensusAtSchool Random Sampler and get a sample. Reference year: (select year) Sample size: At least 20 students Select questions: Height, Dominant Hand Reaction Time Location: Select location Year level: Select a range of year levels. To protect privacy there is a rule built into the sampler that the requested sample size cannot exceed 10% of the respondents for the parameters entered,

Please note: This task is designed to be completed by hand. It can also be completed using a computer or CAS calculator.

1. In your CensusAtSchool random sample, find the question about height, and the question about dominant hand reaction time, and enter both sets of twenty numbers as:
• two columns in Excel, or
• two separate lists in your CAS calculator, or
• as a table in your workbook

Outliers are any values which appear to be very different from the majority of the data. They are extreme values and may have been caused by an error. They should be removed from your data set and replaced with the next value from your list.

2. Create a scatter plot, with height as the explanatory or independent variable (x) and dominant hand reaction time as the response or dependent variable (y).

3. Examine the linear relationship of your scatter plot. Circle or lightly shade the correlation of your scatter plot in your table below.

4. Does your graph suggest a relationship between height and dominant hand reaction time? Explain.

Causation and association

What is causation?
A relationship between two variables, the explanatory and the response, are said to be causal if the change in the explanatory variable actually causes a change in the response variable. The explanatory variable is usually the independent variable, and that is usually graphed on the axis.

What is association or correlation?
Both of these words are used to describe relationships that exist between two or more variables. Correlation tends to be used when describing the strength of a relationship between two numerical variables (such as height and arm span).

Explaining the association
Possible explanations for the observed association are:
• The explanatory variable is actually causing a change in the response variable.
• The response variable is actually causing a change in the explanatory variable.
• Confounding: there may be causation, but there are too many uncontrolled variables.
• Common response or coincidence: no causation, the association can be explained by other variables associated with both the explanatory and response variables.

5. If someone found there was a correlation between height and dominant hand reaction time, is this the same as saying a person’s reaction time is caused by their height? Explain.

6. Identify any non-causal explanations for the association. Explain your reasoning.

7. Can height be used to predict dominant hand reaction time? Draw conclusions from your graph, and write a summary paragraph. Some key words to use are: random sample, linear, correlation, cause, effect.