252conts 01/15/01
Roger Even Bove
ECO 252 SUPPLEMENTARY MATERIALS AND TABLES
Please bring this material and your text to classes and exams! Corrections are in red. Tables 10 and
11 will be distributed with the outline.
CONTENTS
pg. 1
Article
Confidence Limits and Hypothesis testing for Variances
pg. 6
Table 1
Chi-Square Distribution
pg. 7
Table 2
F Distribution
pg. 17
Table 3
Formulas for Confidence Intervals and Hypothesis Tests
pg. 19
Table 4
Critical Values of r in the Runs Test
pg. 20
Table 5
Simplified Wilcoxon Rank Sum Test for Two Independent Samples
pg. 22
Table 6
Critical Values of the Wilcoxon Rank Sum Test for Two Independent Samples
pg. 23
Table 7
Critical Values for the Wilcoxon Signed Rank Sum Test for two Matched
Samples
pg. 24
Table 8
Table of p-values Associated with Values of  F2 in the Friedman Two-Way
Analysis of Variance by Ranks
pg. 25
Table 9
Table of p-values for the Kruskal-Wallis Test Statistic for Three Samples for OneWay Analysis of Variance by Ranks
Table 10
Critical Values of for the Kolmogorov-Smirnov One-Sample Test for
Goodness of Fit
Table 11
Critical Values for the Lilliefors Test for Normality
pg. 27
Table 12
Critical Values of s in the Kendall Test For Concordance
pg. 27
Table 13
Critical Values of the Spearman Rank Correlation Coefficient
pg. 28
Table 14
Poisson Distribution
pg. 38
Table 15
Cumulative Binomial Distribution
pg. 46
Table 16
Confidence Intervals for Binomial Sampling
pg. 47
Table 17
Standard Normal Distribution
pg. 48
Table 18
Values of the t Distribution
pg. 50
Table 19
What Method Should I Use?
pg. 51
Article
Formulas For Functions of Random Variables
pg. 61
Problems
pg. 67
Things That You Should Never Do on a Statistics Exam (or Anywhere Else) !
(i)
REFERENCES
William H. Beyer, ed, CRC Standard Probability and Statistics Tables and Formulae, CRC Press,
1991.
David J. Sheskin, Handbook of Parametric and Nonparametric Statistical Procedures, CRC Press,
1997.
Sidney Siegel, Nonparametric Statistics: for the Behaviorial Sciences, McGraw - Hill, 1956.
(ii)
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TABLE 1
TABLE 2
TABLE 3
TABLE 4
TABLE 5
TABLE 6
TABLE 7
TABLE 8
TABLE 9
TABLE 10
TABLE 11
TABLE 12
TABLE 13
TABLE 14
TABLE 15
TABLE 16
TABLE 17
TABLE 18
TABLE 19
TABLE 20
TABLE 21
TABLE 4
Critical Values of r for the Runs Test
Reject The Null Hypothesis of Randomness at the 5% level if the value of r is less than or equal to the
value in Table 4a or greater than or equal to the value in Table 4b.
TABLE 5
Simplified Wilcoxon-Mann-Whitney Rank Sum Test for Two Independent Samples
This table gives the p-value corresponding to the rank sum W of the smaller sample when ranking is done
starting from the end where the smaller sample is concentrated.
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
 F2
p-value
TABLE 8
Table of p-values Associated with Values of  F2 in the Friedman Two-Way Analysis of Variance using
Ranks
Note: k = c(number of columns in the usual format); n= number of rows.
TABLE 9a
Table of p-values for the Kruskal-Wallis Test Statistic for Three Samples for One-Way Analysis of
Variance by Ranks.
Note: On this table ‘Critical Value’ is a value of H , and ' ' is a p-value.
TABLE 9b
Table of p-values for the Kruskal-Wallis Test Statistic for Three Samples (Continued).
Note: On this table ‘Critical Value’ is a value of H , and ' ' is a p-value.
TABLE 12
Critical Values of Kendall’s s as a Measure of Concordance.
TABLE 13
Critical Values of rs , Spearman’s Rank Correlation Coefficient
TABLE 16
Confidence Intervals for the Binomial Distribution
X
 p
Note:
N
95% Confidence Level
99% Confidence Level
TABLE 17
The Standard Normal Distribution