RESULTS AND CONCLUSIONS FOR t TEST
WHEN SHOULD YOU USE THE t-TEST?
Quantitative data
Comparing the MEAN of TWO groups only
Sample data
Heights of Phaseolus vulgaris after 30 Days
Stressed Plants(cm) Unstressed Plants(cm)
55.21 48.04
65.33 64.56
50.50 59.11
57.12 57.25
59.14 51.66
73.00 63.22
57.82 64.78
54.24 58.36
61.92 44.27
67.03 49.99
Step 1: State the null hypothesis.
The mean height of stressed plants is not significantly different from the mean height of
unstressed plants.
Step 2: Establish the level of significance (0.05)
probability of error in rejecting null hypothesis is 5/100
Step 3: Calculate the t statistics using Excel or the graphing calculator (see end of this document)
Results from Excel: Results from TI-84:
t-Test: Two-Sample Assuming Equal VariancesStressed Plants (cm) / Unstressed Plants (cm)
Mean / 60.131 / 56.124
Variance / 45.61141 / 52.78344889
Observations / 10 / 10
Pooled Variance / 49.19742944
Hypothesized Mean Difference / 0
df / 18
t Stat / 1.277418316
P(T<=t) one-tail / 0.108842951
t Critical one-tail / 1.734063592
P(T<=t) two-tail / 0.217685901
t Critical two-tail / 2.100922037
2-SampTTest
m 1 > m 2
t = 1.277418316
p = .1088854109
df = 17.90487128
x1 = 60.131
x2 = 56.124
Sx1 = 6.75362199
Sx2 = 7.26522187
n1 = 10
n2 = 10
Step 4: Compare the calculated value for t to the critical value for t.
TI-84: Look at a table of critical values of t
Excel: Choose the appropriate critical t from your table of results
m 1 > m 2 -- One-tail t-test (Mean of one group > mean of other group)
m 1 m 2 -- Two-tail t-test (Means of two groups not equal)
Step 5: Decide to reject or not reject the null hypothesis
Calculated t < critical t → null hypothesis not rejected
Calculated t critical t → null hypothesis is rejected
At df = 18, critical t at 0.05 level.= 1.73; calculated t of 1.28 < 1.73
The null hypothesis is not rejected.
Step 6: Determine whether the statistical findings support the research hypothesis.
IF Null hypothesis was rejected = research hypothesis was supported
(unless research hypothesis IS a null hypothesis)
IF Null hypothesis not rejected = research hypothesis was not supported
Because the null hypothesis was not rejected, the research hypothesis that stressed plants
would have a greater mean height than unstressed plants was not supported.
Step 7: Construct a data table that communicates all statistics
Table A: Effect of Stress on the Mean Height of Phaseolus vulgaris After 30 Days
Stressed group / Unstressed groupMean
Standard deviation
1SD
2SD
Number / 60.13 cm
6.75 cm
53.38 – 66.88 cm
46.63 – 73.63 cm
10 / 56.12 cm
7.27 cm
48.85 – 63.39 cm
41.58 – 70.66 cm
10
t = 1.28
df = 18 / t of 1.28 < 1.73 p = 0.11
Step 8: Write a paragraph describing results
¨ Write a topic sentence stating the independent and dependent variables, and a reference to
tables and graphs.
Effects of stress on the height of Phaseolus vulgaris plants are summarized in Table A.
¨ Write sentences comparing the means and standard deviation of the groups.
Stressed plants exhibited a greater mean height (60.13 cm) than unstressed plants (56.12 cm). Variations within the groups were similar, with stressed plants having a standard deviation of 6.75 and unstressed plants a standard deviation of 7.27. Ninety-five percent of the stressed plants fell within the range of 46.63 to 73.63 cm, as opposed to unstressed plants, which ranged from 41.58 to 70.66 cm.
¨ Write sentences describing the statistical test, level of significance, and null hypothesis.
The t test was used to test the following null hypothesis at the 0.05 level of
significance: The mean height of stressed plants is not significantly different from the mean
height of unstressed plants.
¨ Write sentences comparing the calculated t value with the critical value and make a
statement about rejection of the null hypothesis.
The null hypothesis was not rejected (t = 1.28 < 1.73 at df = 18; p =0.11)
¨ Write sentences stating support of the research hypothesis by the data.
The data did not support the research hypothesis that stressed plants would have a greater
mean height after planting than unstressed plants.
Step 9: Construct a box-and-whiskers plot to illustrate the variation for each group.
Step 10: Write an appropriate conclusion.
· What was the purpose of the experiment?
The effect of stress on the growth of Phaseolus vulgaris plants was investigated by comparing the height of ten plants subjected to stress for 15 days with the heights of ten unstressed plants.
· What were the major findings? (Focus on results of the statistical test)
No significant difference existed between the mean height of stressed plants and unstressed plants 30 days after transplanting.
· Was the research hypothesis supported by the data?
The research hypothesis that stressed bean plants would have a greater mean height than unstressed bean plants was not supported.
· How did your findings compare (similarities and differences) with your preliminary research?
In contrast, Japanese farmers found that hitting and pulling rice plants were beneficial.
(Osaki 57)
· What possible explanations can you offer for similarities and/or differences between your results and other researchers?
Possible explanations include differences in the methods of administering stress or the type of plant, for example, monocots (rice) versus dicots (beans).
· What recommendations do you have for further study and for improving the experiment?
Additional investigations using various sources of stress at more frequent intervals with
both monocots and dicots should be conducted. Improved experimental design techniques should be implemented, including a larger sample size, more frequent measurement, and a longer growing period.
NOTE: You should be able to write much more than I did. After all, you did an extensive literature review before experimentation and you are the “expert” for your topic.
How to do t-Test with Excel or calculator
t-Test with Excel
Statistical procedures are found in the Data Analysis Tools, which are included with Microsoft Excel.
You need to first verify that Data Analysis tools are installed:
· Open Microsoft Excel
· Select File ® Options ® Add-Ins.
· In the Add-Ins dialog box that appears, select the Analysis ToolPak and Analysis ToolPak – VBA check boxes from the Add-Ins Available list and click the OK button.
· Exit Microsoft Excel (to save the selections)
You should only need to do this once. (School computers are an exception)
1. Enter your data into columns on the spreadsheet. The first cell of each column should have your column heading.
2. Select Tools ® Data Analysis and in the dialog box select t-Test: Two-Sample Assuming Equal Variances and click OK.
3. In the t-Test dialog box, click on the icon in the Variable 1 Range box, then highlight the whole column (including the heading) for the first set of data. Click on the icon again to return to the t-Test dialog box.
4. Repeat Step 3 for Variable 2 Range box, using the second column of data.
5. Enter 0 as the Hypothesized Mean Difference and leave Alpha as 0.05.
6. Check the Labels box to include your column headings as labels.
7. Select the Output Range option, and and choose a cell away from your data (E1 or F1).
8. Click OK.
9. Results appear in the columns next to your data.
10. Change the width of the columns to view all contents.
Note: If the two groups of data being compared are related, you will need to do a paired t-test. An example of this would be comparing the blood pressure taken on 35 patients by two different nurses.
t-Test with Graphing Calculator
Enter data onto lists:
1. STAT
2. Select “EDIT”, then ENTER
3. Add numbers from your data to the lists (L1, L2, . . . )
Perform the t-test:
1. STAT
2. Select “TESTS”
3. Select “4: 2-SampTTest”
4. ENTER
5. Make sure the lists with your data are chosen for List1 and List2.
6. Move the cursor down to “Calculate”
7. ENTER
Results will be given.
t is the value for your t-test df is the degrees of freedom
x1 is the mean from list 1 n1 is the number of values in list 1
x2 is the mean from list 2 n2 is the number of values in list 2
Sx1 is the standard deviation for list 1 (square this number to get the variance)
Sx2 is the standard deviation for list 2