QM 12 Statistical Tables (Appendices A-E)

This table gives the cumulative probability N(x), the area under the standard normal curve to the left of a value x, so it answers the question of how likely a standard normal variable is to fall at or below x. To read it, find the row for the value of x to one decimal place, then move across to the column for the second decimal place, and the cell where they meet is the probability. The first table covers values of x that are zero or positive, and the second covers values that are zero or negative.

This table gives upper-tail critical values of the Student t distribution for one-tailed probabilities. Each row is a number of degrees of freedom, and each column is a tail probability p. The cell value is the point beyond which probability p remains in the right tail. For a one-tailed test at significance level a, read the column p equal to a; for a two-tailed test at level a, read the column p equal to a divided by 2.

This table gives critical values of the chi-square distribution, which is used for tests about a variance and for goodness-of-fit and independence tests. Each row is a number of degrees of freedom, and each column heading is the probability that remains in the right tail. The cell is the chi-square value beyond which that tail probability lies. Because the chi-square distribution is not symmetric, both small upper-tail probabilities and large ones are tabulated.

This table gives critical values of the F distribution, which is used to compare two variances and to test the overall significance of a regression. Each panel is set for a single right-tail area, and within a panel the columns are the numerator degrees of freedom (df1) while the rows are the denominator degrees of freedom (df2). To find a critical value, choose the panel for the tail area you want, then read the cell where your df1 column meets your df2 row. Four panels are provided, for right-tail areas of 0.05, 0.025, 0.01, and 0.005.

This table gives critical values for the Durbin-Watson statistic, which tests for first-order serial correlation in the residuals of a regression, all at a significance level of 0.05. Rows are the number of observations n, and the columns are grouped by K, the number of slope parameters in the model. Each K group has a lower bound d-lower and an upper bound d-upper. A calculated statistic below d-lower signals positive serial correlation, one above d-upper signals no positive serial correlation, and a value between the two bounds is inconclusive.