T- Test Example of how to perform a t-test

Step 1 State the null hypothesis  Begin with assuming that any observed differences between the two samples means it occurred by chance and is not significant. This assumption is expressed as the NULL HYPOTHESIS.  For our example:  The mean height of stressed plants is NOT significantly different from the mean height of nonstressed plants.

Step 2 Establish the level of significance.  Alpha =0.05  This communicates the probability that the researcher erred in rejecting the null hypothesis. At 0.05 level of significance, the probability of error in rejecting the null hypothesis is less than 5%.

Step 3: Calculating the means.  Stressed plants  55  65  50  57  59  73  57  54  62  68  Nonstessed Plants  48  65  59  57  51  63  65  58  44  50

Step 3: Calculating the Means continued  X stressed = ΣX÷n  / 10= 60  X nonstressed =  / 10= 56

Step 4 Calculating the variance  S 2 =Σ(X 1 -X) 2 ÷n-1  Stressed:  =(55-60) 2 +(65-60) 2 + (50-60) 2 ……+(68-60) 2 ÷10-1=49.1  Nonstressed:  =(48-56) 2 +(65-56) 2 + (59-56) 2 …..+(50-56) 2 ÷10-1=60.7

Step 5: Calculating t  T= X 1 -X 2 ÷√s 2 1 +s 2 2 ÷n  T = 60-56÷√ ÷10  =4÷√109.8÷10  =4√10.98  =4÷3.1  =1.3

Step 6: Determining degrees of freedom  =(n-1)+(n-1)  = (10-1) )  =18  If you have more than 2 groups you must compare all of your groups.  Example group A, B, and C  You would compare A vs. B, A vs. C, and B vs. C, so you need to perform 3 t-test.

Step 7:Determine the significance of the calculated t.  At df=18, alpha of 0.05, t= 2.101; the calculated t of 1.3<2.101 and is not significant at the 0.05 level  Because the calculated value of t is NOT significant, the null hypothesis is NOT rejected.  Because the null hypothesis was NOT rejected, the research hypothesis that stressed plants would have a greater mean height than nonstressed plants was NOT supported.