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When do we use an unpaired t-test?
When do we use an unpaired t-test?
Remember that we cannot compare only the means of experimental groups, because there is often variability from replicate samples for each group. We use standard deviation to report this variability. If we compare mean ± standard deviation for the two groups (or look at the column graph and overlap in error bars of standard deviation), we can get a sense of how different the measurements are.:
Site A (3200 ± 540) & Site B (900 ± 80):
The mean population size of algae at Site A is quite a bit larger than the mean population size at Site B. The means are very different and the standard deviations indicate that the values in the datasets likely would not substantially overlap. Notice! These two groups have very different values for standard deviation. How is this reflected in the graph?
Site B (900 ± 80) and Site C (810 ± 70):
The mean population size of algae at Site C does not appear to be substantially different than the mean population size at Site B. The means for the two groups are similar and the standard deviations indicate that the values in the datasets likely overlap quite a bit.
In order to determine if the observed differences between your experimental groups are significant, you need to run a statistical test.
If your experimental question examines whether there are significant differences between exactly two groups (e.g. Site B vs. Site C), you will use an unpaired t-test (aka two-sample t-test) as a method to statistically compare the two samples.
To conclude that the difference between your two groups is large enough to be considered statistically significant, the p-value from your statistical test must be less than or equal to 0.05 (p ≤ 0.05).
To understand what the p-value actually means, you need to know some statistical lingo. Examine the figure and read more details below:
The t-test compares one dependent variable (e.g. population size) between exactly two groups (e.g. Site B and Site C) to determine the probability that the null hypothesis is true. What does that even mean?!?!
The null hypothesis (H0) is often called the hypothesis of "no difference." If the null hypothesis is supported, it means that any differences observed between two sample populations are due to random sampling error and variation. Stated another way, the independent variable is not responsible for the difference between the two groups.
The null hypothesis for the example above would be that there is no significant difference in algae population size between Site B and Site C.
The alternative hypothesis (HA) is the more interesting experimental hypotheses. If the alternative hypothesis is supported, it means that at least some of the difference observed between the two sample populations is due to the independent variable in the experiment.
The alternative hypothesis for the example above would be that there is a significant difference in algae population size between Site B and Site C.
The p-value tells us the probability that the null hypothesis is supported (and therefore the probability that there are no significant differences between the two populations). The p-value ranges from 0-1; the smaller the p-value, the lower the probability that the null hypothesis is true.
If p is greater than 0.05, there is more than a 5% probability that the null hypothesis is supported. Therefore, when p>0.05, we accept the null hypothesis and we conclude that there are no significant differences between the two groups.
If p is less than or equal to 0.05, there is less than a 5% probability) that the null hypothesis is supported. Therefore, when p ≤ 0.05, we can reject the null hypothesis. In other words supports the alternative hypothesis (HA) that at least some of the difference between the means of the two populations can be explained by the independent variable you are testing.
Using GraphPad to Perform an unpaired t-test
Using GraphPad to Perform an unpaired t-test
Free t-test calculator: https://www.graphpad.com/quickcalcs/ttest1/
Free t-test calculator: https://www.graphpad.com/quickcalcs/ttest1/
Watch this video overview about performing t-tests and follow the steps provided below
Watch this video overview about performing t-tests and follow the steps provided below
1. Type or copy/paste the link in your browser to go to the free GraphPad t-test calculator: https://www.graphpad.com/quickcalcs/ttest1/
2. Complete the 4-step form:
Step 1. Choose data entry format:
Select "Enter or paste up to 2000 rows."
Step 2. Enter data
Change the Labels to the names of your two groups.
Copy/paste the set of values for the replicates measured from your first group.
Copy/paste the set of values for the replicates measured from your second group.
Step 3. Choose a Test:
Select "Unpaired t-test"
Step 4. View the results:
The first paragraph of the t-test results will tell you the p-value and the statistical significance
Step 5. Record the results:
Record the t-test results in your notebook, including the p-value.
Refer to your hypothesis from your prelab to determine if it was supported by your experimental data and statistical test.
Two t-test examples
Two t-test examples
Example 1:
Example 1:
Comparing Snail size at Salem vs. Nahant
Comparing Snail size at Salem vs. Nahant
You collected 7 snails from Salem and 7 snails from Nahant. You would like to determine if there is a significant difference in shell height (in mm) between snails from the two locations.
You collected 7 snails from Salem and 7 snails from Nahant. You would like to determine if there is a significant difference in shell height (in mm) between snails from the two locations.
Example 1: t-test to compare shell size at Salem vs. Nahant
Example 1: t-test to compare shell size at Salem vs. Nahant
We copy/pasted the data for Salem and Nahant in to the t-test calculator to perform an Unpaired t-test (Left)
The t-test results (below) show that the p-value was p=0.2888. Because this value was larger than the cutoff value of p=0.05, we determine that the differences in shell size between Salem and Nahant were not significant.
Example 2: Comparing Snail size in
Example 2: Comparing Snail size in
Bar Harbor vs. Portland
Bar Harbor vs. Portland
You collected 7 snails from Bar Harbor Maine and 7 snails from Portland Maine. You would like to determine if there is a significant difference in shell height (in mm) between snails from the two locations.
Example 2: t-test to compare shell size in Bar Harbor vs. Portland
Example 2: t-test to compare shell size in Bar Harbor vs. Portland
We copy/pasted the data for Bar Harbor and Portland in to the t-test calculator to perform an Unpaired t-test (below)
The t-test results (right) show that the p-value was p=0.0001. Because this value was smaller than the cutoff value of p=0.05, we determine that the differences in shell size between Bar Harbor and Portland were statistically significant.
Describing t-test in formal results text
Describing t-test in formal results text
Watch this video overview about writing t-test paragraphs and follow the steps provided below
Watch this video overview about writing t-test paragraphs and follow the steps provided below
Results sections include 3 important components:
Figure
Properly labeled with error bars
Figure caption
Numbered in order of appearance in the text
Briefly describe the data presented in the graph. Make sure it includes:
Your model organism for the experiment
Your experimental groups (independent variable) displayed on the X-axis
What you measured (dependent variable) displayed on the Y-axis
That the columns represent means and the error bars represent standard deviations.
Results text paragraph
Briefly introduce the experimentthat is depicted in your figure.
State the data pattern presented in the figure, including whether the comparison was significant.
In parentheses: results of the statistical test
In parentheses: a reference to the figure where the comparison is displayed
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