Brian S. Everitt A Handbook of Statistical Analyses using SPSS

Table 2.1 Lifespans of Rats (in Days) Given Two Diets
a) Restricted diet (n = 105)
105 193 211 236 302 363 389 390 391 403 530 604 60.5 630 716
718 727 731 749 769 770 789 804 810 811 833 868 871 848 893
897 901 906 907 919 923 931 940 957 958 961 962 974 979 982
1101 1008 1010 1011 1012 1014 1017 1032 1039 1045 1046 1047 1057 1063 1070
1073 1076 1085 1090 1094 1099 1107 1119 1120 1128 1129 1131 1133 1136 1138
1144 1149 1160 1166 1170 1173 1181 1183 1188 1190 1203 1206 1209 1218 1220
1221 1228 1230 1231 1233 1239 1244 1258 1268 1294 1316 1327 1328 1369 1393
1435
b) Ad libitum diet (n = 89)
89 104 387 465 479 494 496 514 532 536 545 547 548 582 606
609 619 620 621 630 635 639 648 652 653 654 660 665 667 668
670 675 677 678 678 681 684 688 694 695 697 698 702 704 710
711 712 715 716 717 720 721 730 731 732 733 735 736 738 739
741 743 746 749 751 753 764 765 768 770 773 777 779 780 788
791 794 796 799 801 806 807 815 836 838 850 859 894 963
Source: Berger, Boss, and Guess, 1988. With permission of the Biometrics Society.
2.2 Methods of Analysis
Data analysis generally begins with the calculation of a number of summary
statistics such as the mean, median, standard deviation, etc., and by
creating informative graphical displays of the data such as histograms, box
plots, and stem-and-leaf plots. The aim at this stage is to describe the
general distributional properties of the data, to identify any unusual
observations (outliers) or any unusual patterns of observations that may
cause problems for later analyses to be carried out on the data. (Descriptions
of all the terms in italics can be found in Altman, 1991.)
Following the initial exploration of the data, statistical tests may be
applied to answer specific questions or to test particular hypotheses about
the data. For the rat data, for example, we will use an independent samples
t-test and its nonparametric alternative, the Mann-Whitney U-test to assess
whether the average lifetimes for the rats on the two diets differ. For the
second data set we shall apply a paired samples t-test (and the Wilcoxon
signed ranks test) to address the question of whether men and women
have different average ages at marriage. (See Boxes 2.1 and 2.2 for a brief
account of the methods mentioned.)
Finally, we shall examine the relationship between the ages of husbands
and their wives by constructing a scatterplot, calculating a number of correlation
coefficients, and fitting a simple linear regression model (see Box 2.3).
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