# Biology

BIO A01H3 Y Fall 2017

Guide to Preparing and Interpreting the Result of your Student’s t-Test

You can either do the t-tests on licensed statistical programs on computers in UTSC’s computer stats

labs or you can use free online ‘plug-in’ programs such as the one found at

http://www.graphpad.com/quickcalcs/ttest1.cfm?Format=C

The step-by-step instructions below are based on the latter graph pad program. Read the website

thoroughly, and consider what boxes should be selected given the data set.

Step 1: What is your H1? What is your H0? The standard rule for a t-test is that if your Sample

statistic falls within 95% of the range of values expected for H0 , then you fail to reject H0, and

there is no difference between your value and the value expected under H0. Remember that if

your Sample statistic falls beyond the 95% range, in the “tails” of the expected distribution,

then you reject H0 because it is unlikely that your Sample statistic is drawn from the same

range of values as H0. In other words, the two groups you are comparing in your t-test are

different. Just because your data is different does not necessarily mean that the finding

supports H1. Whether or not H1 is supported by your data is an interpretation that you should

address in your Discussion!

Step 2: Find your degrees of freedom (df) in Table 2 below. Go across that row to find the

Critical t-value under α= 0.05. Note this value in your Worksheet.

Step 3: Compare your Calculated t-test statistic to the Critical t-test value. Is larger or

smaller? Follow the guidelines under Table 1 below to draw your statistical conclusion.

Table 1: Table of Critical t Values of Student’s t Distribution with df Degrees of Freedom.

α (2 tail) = 0.2 0.1 0.05 0.02 0.01

df

1 3.078 6.314 12.706 31.819 63.655

2 1.886 2.920 4.303 6.965 9.925

3 1.638 2.353 3.182 4.541 5.841

4 1.533 2.132 2.776 3.747 4.604

5 1.476 2.015 2.571 3.365 4.032

6 1.440 1.943 2.447 3.143 3.707

7 1.415 1.895 2.365 2.998 3.500

8 1.397 1.860 2.306 2.897 3.355

9 1.383 1.833 2.262 2.821 3.250

10 1.372 1.812 2.228 2.764 3.169

11 1.363 1.796 2.201 2.718 3.106

12 1.356 1.782 2.179 2.681 3.055

13 1.350 1.771 2.160 2.650 3.012

14 1.345 1.761 2.145 2.625 2.977

15 1.341 1.753 2.131 2.603 2.947

16 1.337 1.746 2.120 2.584 2.921

17 1.333 1.740 2.110 2.567 2.898

18 1.330 1.734 2.101 2.552 2.878

19 1.328 1.729 2.093 2.540 2.861

20 1.325 1.725 2.086 2.528 2.845

21 1.323 1.721 2.080 2.518 2.831

22 1.321 1.717 2.074 2.508 2.819

23 1.319 1.714 2.069 2.500 2.807

24 1.318 1.711 2.064 2.492 2.797

25 1.316 1.708 2.060 2.485 2.787

26 1.315 1.706 2.056 2.479 2.779

27 1.314 1.703 2.052 2.473 2.771

28 1.313 1.701 2.048 2.467 2.763

29 1.311 1.699 2.045 2.462 2.756

30 1.310 1.697 2.042 2.457 2.750

31 1.309 1.696 2.040 2.453 2.744

32 1.309 1.694 2.037 2.449 2.739

33 1.308 1.692 2.035 2.445 2.733

34 1.307 1.691 2.032 2.441 2.728

35 1.306 1.690 2.030 2.438 2.724

36 1.306 1.688 2.028 2.435 2.720

37 1.305 1.687 2.026 2.432 2.715

38 1.304 1.686 2.024 2.429 2.712

39 1.304 1.685 2.023 2.426 2.708

40 1.303 1.684 2.021 2.423 2.705

Table 2. Guide for interpreting Calculated t Values and Probability Values from Excel.

Method 1

Method 2

Conclusion

if

t

>

t

Critical (in Table 2)

if

p < 0.05

then

reject Ho

if t < t Critical (in Table 2) if p > 0.05 then fail to reject Ho