The data below are the head injury readings for driver-side crash dummies for various classes of vehicles. The vehicle types are coded as 1=Compact, 2=Heavy, 3=Light, 4=Medium, 5=MPV, 6=Pickup, and 7=Van. Larger numbers indicate more serious injuries.
Injury Type 791 1 846 1 1024 1 1007 1 399 1 1279 1 407 1 1656 1 1036 1 1226 1 423 2 541 2 517 2 1328 2 471 2 533 2 863 2 786 2 551 2 1068 2 551 3 1068 3 757 3 1114 3 920 3 1809 3 1238 3 918 3 1339 3 603 3 712 4 435 4 298 4 733 4 1200 4 1701 4 707 4 790 4 800 4 480 4 1345 5 1269 5 1477 5 758 5 996 5 1306 5 968 5 943 5 1026 5 1564 5 985 6 1074 6 742 6 985 6 1342 6 1184 6 977 6 1465 6 892 6 1074 6 805 7 2613 7 903 7 949 7 1183 7 1051 7 1387 7 1320 7 1434 7 1603 7
(a) Apply the Kruskal-Wallis test to this data. State your test statistic and p-value using the approximate chi-square distribution. What is your conclusion if α = 0.05?
To test: No. of head injuries differs with the type of vehicle.
To run a Kruskal Wallis test:
First, sort the data (Injury), and rank them:
Write the corresponding ranks accross each observation in the data:
Find the sum of ranks for each group.Here, for group 1,
. Similarly, find the sum of ranks for each groups.
Let N be the total no. of observations.Here, N = 70.
The test statistic is given by:
We have more than 5 datapoints per group.Hence, we may treat H as chi square.
Substituting the values, we get the test statistic value H =
18.3. Next, we compare the test statistic value obtained with the
critical chi square value for n-1 = 8 - 1 = 7 df. ()
(Since the sample size is large, we interpret the result using the p value using the approximate chi-square distribution.)
As the calculated test statistic 18.3 > 14.07, we do not have sufficient evidence to support the null hypothesis that the no. of injuries does nor differ with the type of vehicles.Hence, reject H0 at 5% level.
Running, kruskal wallis test in SPSS,
The output is obtained as:
Since, the p value is less than 0.05, we reject H0. We may conclude that no. of injuries differs significantly, accross different class of vehicles.
The data below are the head injury readings for driver-side crash dummies for various classes of...
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Data is copied below for ease of use.
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978 31 6310 10.4
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96 0 78 73
1038 7 5400 11.6
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200 0 160 143
1071 3 6740 12.1...
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