Download The p – value represents the probability of making a type I error, or

The p – value represents the probability of making a type I error, or rejecting the null
hypothesis when it is true. The smaller the p value, the smaller is the probability that you
would be wrongly rejecting the null hypothesis.
T distribution:
Example: Suppose the t statistic = 3.05 in a 2 sided problem, where (n-1) =12. To
calculate the p – value, we will first calculate P (t <= 3.05) (this is the cumulative
probability).
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Choose Calc > Probability Distributions > t.
Choose Cumulative Probability.
The non centrality parameter will be 0.0.
Enter Degrees of freedom (12 in this example).
Choose Input Constant, and enter the test statistic.
Click OK. This will give us the cumulative probability of (t<=3.05).
Calculate (1 – cumulative probability) = (1 – 0.994958) = 0.0050424.
For a double sided test, the p value will be 2 * 0.0050424 = 0.0100847.
Normal distribution:
Example: Suppose the z statistic = 28.9 in a 2 sided problem, where mean is 24 and the
standard deviation is 4. To calculate the p – value, we will first calculate P (z <= 5.13)
(this is the cumulative probability).
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Choose Calc > Probability Distributions > Normal.
Choose Cumulative Probability.
Put in the values of Mean (24) and Standard deviation (4).
Choose Input Constant, and enter the test statistic.
Click OK. This will give us the cumulative probability of (z<=28.9).
Calculate (1 – cumulative probability) = (1 – 0.889712) = 0.110288.
For a double sided test, the p value will be 2 * 0.110288= 0.220576.
F distribution:
Example: Suppose the F statistic = 4.78, where numerator degrees of freedom =3, and
denominator degrees of freedom =2. To calculate the p – value, we will first calculate P
(F <= 4.78) (this is the cumulative probability).
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Choose Calc > Probability Distributions > F.
Choose Cumulative Probability.
The non centrality parameter will be 0.0.
Enter Degrees of freedom: Numerator =3 and denominator = 2.
Choose Input Constant, and enter the test statistic : 4.78
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Click OK. This will give us the cumulative probability of (F<=4.78).
Calculate (1 – cumulative probability) = (1 - 0.822140) = 0.17786. This is the p
value.
Chi Square distribution:
Example: Suppose the test statistic = 12.6 where (n-1) =10. To calculate the p – value, we
will first calculate P (Chi square <= 3.05) (this is the cumulative probability).
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Choose Calc > Probability Distributions > Chi square.
Choose Cumulative Probability.
The non centrality parameter will be 0.0.
Enter Degrees of freedom (10 in this example).
Choose Input Constant, and enter the test statistic.
Click OK. This will give us the cumulative probability of (chi square<=12.6).
Calculate (1 – cumulative probability) = (1 – 0.753096) = 0.246904. This is the p
value