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?

VOTING MACHINE BRAND DRE 532 OptiScan 499      Time to vote (in seconds) 513 405 Voting Machine Brand DRE OptScan      referred to time on task 573 391      or TOT 500 354 Mean TOT (in seconds) 633.84314 429.2381 880 650 TOT Standard Deviation (SD) 166.5041 156.45615 757 350 TOT Standard Error of the Mean 23.3152 24.1417 956 358 Completion Task Rate (of voters) 50 of 51 42 of 42 461 463 430 321 512 409 998 391 651 457 349 394 754 323 610 181 623 285 615 449 1185 330 528 261 497 292 718 366 648 359 589 398 421 806 490 380 591 954 758 344 776 375 498 356 498 399 623 383 621 464 594 618 594 524 602 304 458 342 567 576 865 277 546 390 714 818 729 387 785 645 581 804 661 710 668 660 251 810 572

Explanation / Answer

We are allowed to do 4 subparts question at a time. Post again for more subparts of question.

a) Null: DRE is better than opticscan

Then ALt hypothesis becomes: DRE is not better than optiscan.

b) Dof DRE = 51 - 1 = 50

Optiscan = 42 - 1 = 40

c) Unpaired and equal variance.

d) One tail

as we are not just trying to see if there is any difference between the machines but we are trying to see which one is better.

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