Part of a usability study to assess voting machines measured the time on task (T

Question

Part of a usability study to assess voting machines measured the time on task (TOT) of voters casting ballots (efficiency). Specifically, the data are for the same ballot cast on two different voting machines at the same location (called a precinct). Your job is to perform a “t” test on these data and draw conclusions about which voting machine is better in terms of usability. A few background items: • The voters (participants/users) are a homogeneous group. • Voters were randomly assigned to the voting machines. • Thus, the two groups of voters (one group using the DRE voting machine, and the other using the OptiScan voting machine) have equal variances. • We have no advance information to indicate that one voting machine will be better than the other. If you need a refresher of the “t” test, read the “t-test description.pdf” document (attached), or check your statistics book. You do not need to do any hand calculations. Use the following site as it has a very easy to use “t” test calculator: http://www.graphpad.com/quickcalcs/ttest1.cfm. The spreadsheet (attached) contains the data and some intermediate statistical values for use in the “t” test calculator (so that you do not have to enter individual data points).

Question1 – What is the null hypothesis in this usability study?

Question 2 – How many degrees of freedom are in each group (the DRE and OptiScan groups)?

Question 3 – Which “t” test should be used – paired, unpaired/equal variance, unpaired/unequal variance?

Question 4 – Should a one-tail, or two-tailed test be used, and why?

Question 5 – What is the t value?

Question 6 – Is the t value significant at the 0.05 level, and why?

Question 7 – Is the t value significant at the 0.01 level, and why?

Question 8 – Considering the combination of the above analysis, and the number of ballots completed (see spreadsheet), which voting machine has better usability, and why?

Explanation / Answer

Question1 – What is the null hypothesis in this usability study?

The null hypothesis is

One voting machine is NOT better than other in terms of usability

Question 2 – How many degrees of freedom are in each group (the DRE and OptiScan groups)?

The degree of freedom is given as DF = N-2 , AS THE variance are equal , so if there are 10 participants in each group , then the df is 20-2 = 18 (no data given in the question)

Question 3 – Which “t” test should be used – paired, unpaired/equal variance, unpaired/unequal variance?

We can use independent samples t test , as the members are assigned to the machines randomly

Question 4 – Should a one-tail, or two-tailed test be used, and why?

As we are interested in the BETTER part of the hypothesis , hence we must use a directional t test , which would be a 1 tail t test. If the hypothesis was to test whether the values for the 2 voting machines are statisitically different or not , then we would have selected a 2 tail test

Please note that we can answer only 4 subparts at a time, as per the answering guidelines

also , attach the data in your question so that remaining questions can be answered by an expert

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