Example of Onetailed Two Independent Samples Student's t Test
Biostatistics BI 45, Saint Anselm College
Step 1) State the biological question. Does a new fertilizer improve plant growth by making plants grow taller?
Step 2) Translate the biological question into statistical hypotheses.
Step 3) State the alpha level: p<0.05 is considered significant
Step 4) State the statistical test.
Because we are working with two independent samples and we want to test the direction of the difference between two independent means, we use the onetailed Two Independent Samples t test.
Step 5) State the assumptions of the test.
The subjects in each sample must be randomly selected from a population. The sample data must come from a normally distributed populations of observations for the variable under study and the variances from the two samples must be equal.
Step 6) Calculate the observed t statistics from your data.

oldfert 
dold 
dold2 
ssold 

48.2 
3.71 
13.7641 
102.229 

54.6 
2.69 
7.2361 


58.3 
6.39 
40.8321 


47.8 
4.11 
16.8921 


51.4 
0.51 
0.2601 


52 
0.09 
0.0081 


55.2 
3.29 
10.8241 


49.1 
2.81 
7.8961 


49.9 
2.01 
4.0401 


52.6 
0.69 
0.4761 






Sum 
519.1 



Mean 
51.91 



n 
10 



df 
9 














newfert 
dnew 
dnew2 
ssnew 

52.3 
4.25 
18.0625 
69.2 

57.4 
0.85 
0.7225 


55.6 
0.95 
0.9025 


53.2 
3.35 
11.2225 


61.3 
4.75 
22.5625 


58 
1.45 
2.1025 


59.8 
3.25 
10.5625 


54.8 
1.75 
3.0625 
















Sum 
452.4 



Mean 
56.55 



n 
8 



df 
7 



Step 7) Find the df and critical value of t from the table of critical values.
Step 8) Compare the critical and observed t values and reject or do not reject the null hypothesis.
Find the actual P value
t_{.005(1)16}=2.921<t_{obs}=2.99<
t_{.0025(1)16}=
0.0025<P<0.005
Step 9) Interpret the results of the analysis as it relates to the biological question raised in 1). Plants grown on the new fertilizer grow significantly taller than plants on the old fertilizer (t=2.99, df=16, onetailed, p<0.005).
Blackboard at Saint Anselm College
Trademark and Disclaimers
Copyright © 2001 Jay Pitocchelli. All rights reserved. The contents of this page are the intellectual property of Dr. Jay Pitocchelli for distribution to students enrolled in Biostatistics BI 45 at Saint Anselm College. These pages may not be copied, photocopied, reproduced, translated, or published in any electronic or machinereadable form in whole or in part without prior written approval of Jay Pitocchelli. Students enrolled in Biostatistics BI 45 at Saint Anselm College have permission to print this material for their lecture notes. All formulae and critical values from: Zar, J. H. 1999. Biostatistical Analysis. (4th ed.). New Jersey, Prentice Hall.