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# When I use proc univariate for hypothesis testing the t value and p values do not make sense

The data comes from the data table: marchflights.sas7bdat   (airplane flights and the corresponding weights of "freight" - the variable)

Freight (variable)

Mean=333.95, Standard deviation=98.11.  Number of observations=635

Below is the code:

/**Hypothesis Testing**/
proc univariate data=certprep.marchflights mu0 = 333.95;
var freight;
run;

I believe that the t statistic should be much higher than 0.000283,

and the p value should be very low, looking like 0.0040 or something like that, but it is 0.9998

Results are below:

Tests for Location: Mu0=333.95

 0.000283 0.9998 t statistic p value

Can the results of the t statistic and the p value actually be correct? I don't think so.

Is there anything I'm missing here? Is there something wrong with the code?

Thank you.

jtflynn33

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Solution
‎02-03-2018 11:04 AM
Super User
Posts: 23,713

## Re: When I use proc univariate for hypothesis testing the t value and p values do not make sense

Posted in reply to jtflynn33

I think you're misunderstanding hypothesis testing.

The null hypothesis is that the mean is equal to 333.95. If p<Alpha then you would reject the null hypothesis.

Since the P-value is 1, this means you fail to reject the null hypothesis and the mean is not significantly different than 333.95.

Usually you're looking to reject a null hypothesis, in this case you're looking to confirm your null hypothesis.

jtflynn33 wrote:

The data comes from the data table: marchflights.sas7bdat   (airplane flights and the corresponding weights of "freight" - the variable)

Freight (variable)

Mean=333.95, Standard deviation=98.11.  Number of observations=635

Below is the code:

/**Hypothesis Testing**/
proc univariate data=certprep.marchflights mu0 = 333.95;
var freight;
run;

I believe that the t statistic should be much higher than 0.000283,

and the p value should be very low, looking like 0.0040 or something like that, but it is 0.9998

Results are below:

Tests for Location: Mu0=333.95

 0.000283 0.9998 t statistic p value

Can the results of the t statistic and the p value actually be correct? I don't think so.

Is there anything I'm missing here? Is there something wrong with the code?

Thank you.

jtflynn33

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Super User
Posts: 10,778

## Re: When I use proc univariate for hypothesis testing the t value and p values do not make sense

Posted in reply to jtflynn33

It looks right.  If you want p value be small (significant) , then t statistic must be big enough.

t statistic measured the deviation of H0 statistical (when H0 is assuming right) .

New Contributor
Posts: 3

## Re: When I use proc univariate for hypothesis testing the t value and p values do not make sense

Thanks, your answer really helped me.
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Respected Advisor
Posts: 3,011

## Re: When I use proc univariate for hypothesis testing the t value and p values do not make sense

[ Edited ]
Posted in reply to jtflynn33

t = (xbar - mu) / (s / sqrt(n))

xbar and mu are both 333.95 (well, xbar probably has a few more decimal places), so t close to zero is correct.

When you have a t close to zero, you have a p value close to 1

--
Paige Miller
New Contributor
Posts: 3

## Re: When I use proc univariate for hypothesis testing the t value and p values do not make sense

Posted in reply to PaigeMiller
Thanks for your help!!
Solution
‎02-03-2018 11:04 AM
Super User
Posts: 23,713

## Re: When I use proc univariate for hypothesis testing the t value and p values do not make sense

Posted in reply to jtflynn33

I think you're misunderstanding hypothesis testing.

The null hypothesis is that the mean is equal to 333.95. If p<Alpha then you would reject the null hypothesis.

Since the P-value is 1, this means you fail to reject the null hypothesis and the mean is not significantly different than 333.95.

Usually you're looking to reject a null hypothesis, in this case you're looking to confirm your null hypothesis.

jtflynn33 wrote:

The data comes from the data table: marchflights.sas7bdat   (airplane flights and the corresponding weights of "freight" - the variable)

Freight (variable)

Mean=333.95, Standard deviation=98.11.  Number of observations=635

Below is the code:

/**Hypothesis Testing**/
proc univariate data=certprep.marchflights mu0 = 333.95;
var freight;
run;

I believe that the t statistic should be much higher than 0.000283,

and the p value should be very low, looking like 0.0040 or something like that, but it is 0.9998

Results are below:

Tests for Location: Mu0=333.95

 0.000283 0.9998 t statistic p value

Can the results of the t statistic and the p value actually be correct? I don't think so.

Is there anything I'm missing here? Is there something wrong with the code?

Thank you.

jtflynn33

☑ This topic is solved.

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