Question

Why does the two-sided t-test table include only the upper half of the data (p from 0.5 to 0.001) and the chi-square probability table include the entire range (p from .995 to .005)?

Answer 1

The two sided t-test table is a probability distribution table which follows a symmetric bell shaped curve. The area of the probabilitiy distribution curve is exactly divided into half with t = 0 at the centre. The probabilities are equal which is.0.5 for - infinity to zero and 0.5 form zero to infinity. Hence the table consists for upper half of the data.

For example the probability for t greater than 1 is exactly equal to probability less than - 1. Hence we consider negative values of t for left tailed test from the table.

Foe chi-squared distribution there is no such case which means there is no negative values because it the probability distribution for square of the random variable X. Hence negative values are not possible and the distribution is for 0 to infinity and also the distribution is not symmetric hence in the statistical table we have probability values for entire range.