# Test of Significance

#### AlexKom

##### New Member
Hello,

I performed a small experiment for my biology class, where I compared pulse rate after running on 2 legs, and pulse rate after running on 4 legs. Basicly, this was my procedure:
1. Select a person for the experiment.
2. Measure pulse rate of a person (number of pulses per one minute).
3. Measure the distance of at least 28 meters in the corridor.
4. Ask the subject to cover this distance back and forth on two legs (bipedal) as fast as he/she can.
5. Measure the pulse rate after running.
6. Record the data.
7. Let the subject rest.
8. Repeat steps 1- 8, but cover the distance, using 4 legs (quadrapedal).
9. Repeat steps 1-10 with at least three other subjects.

See attached file with the document, where I have my data recorded.

I don't know what type of test of significance I should perform, if I want to find out wheter quadrapedal running increases the pulse rate more, than bipedal running. I thought that it may be matched pairs t -test, but it does not really work. Can you please help me.

Thank you
Alex

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#### F.A.P

##### New Member
AlexKom said:
I thought that it may be matched pairs t -test, but it does not really work. Can you please help me.
You should be able to use the paired t test for this situation.
From what I see you want to test the hypothesis

H0: mean1 - mean2 = 0, against H1: mean1 - mean2 > 0

where mean1 is the mean increase in heart rate for quadrapetal running.
Denote the differences of X1i - X2i by Di and compute Dbar, the mean of those, as well as the standard deviation sD for the Di's.
An equivalent test to that above is

H0: meanD = 0, against H1: meanD > 0

and for that we have the test statistic Dbar/(sD/sqrt(n)). This should then be compared with the critical t with alpha and n-1 degrees of freedom.

Doesn't it work for you this way?

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#### AlexKom

##### New Member
Need Help

Thank you very much for your reply! Unfortunately I took AP Stat last year and I don't really remember how to perform this test. I think conditions are: Simple Random Sample, Population size > 10n. Population is normal, or large sample size or moderate sample size with moderate skewness or outliers. How do I check whether population is normal. Do I make the histogram for the distribution of mean differences?
Also I don't remember how to perform the experiment.
I believe formula is

x - mean0(which will equal 0 in this test)
---------------------------------------------- = t
s/ square root of n

What do I put for x-bar?
What for standard deviation? Standard deviation of the mean difference?

Please help me. My paper is due 12/21/06

Thank you for help...

#### F.A.P

##### New Member
AlexKom said:
x - mean0(which will equal 0 in this test)
---------------------------------------------- = t
s/ square root of n

What do I put for x-bar?
What for standard deviation? Standard deviation of the mean difference?
Instead of x-bar you put D-bar. Standard deviation you use is that for the differences Di = X1i - X2i . Di is then the different in increased heart rate for person i using different running ways.

X1i is increase in heart rate for person i with four legs.
X2i is increase in heart rate for person i with two legs.

(mean of Di's) - mean0(which will equal 0 in this test)
---------------------------------------------------- = t
(standard deviation of the Di's)/ square root of n

,where n is the number of persons in test.

This should work...I think...
I hope you found a way to solve this in time.