# R- Welch Two Sample t-test (t.test) interpretation help

I calculated a Welch two sample t-test in R and am very confused on how to interpret my results. The calculation was based off of a very small dataset (two groups each with 7 samples). The "alternative hypothesis" line is especially throwing me off. Looking to determine if there is a significant difference between the averages of the two groups.

    Welch Two Sample t-test

data:  lizard$cold and lizard$warm
t = -1.7796, df = 10.147, p-value = 0.1051
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-4.2742915  0.4742915
sample estimates:
mean of x mean of y
5.894286  7.794286

• The null (baseline) hypothesis for this test is that the two means, of something related to "cold" and "warm" lizards I assume, are the same. The alternative is that the two means are different. This latter statement expands to "the difference in means is not equal to 0", which means the same as "the difference between the two means is not equal to 0", but is slightly more grammatically correct: english.stackexchange.com/questions/106642/…... – jbowman Apr 8 '18 at 2:41
• The p-value is 0.1051, which is not typically considered sufficiently small for statistical significance. – jbowman Apr 8 '18 at 2:41
• The line in the output is not telling whether they differ, it's explaining the alternative hypothesis your code caused to be tested (though I don't like the particular phrasing there myself). To decide whether to reject the null, you could compare the p-value with your significance level (reject if it's less than or equal to the significance level). – Glen_b -Reinstate Monica Apr 8 '18 at 6:43

The t-test is testing two competing hypotheses:

$$H_0: \text{There is no difference between the (true) averages of the two groups}$$

$$\text{versus}$$

$$H_a: \text{There is a difference between the (true) averages of the two groups}.$$

It is not clear what averages you are comparing for the two groups (e.g., average weights), so I stated the two hypotheses in a vague fashion – you will need to fill in the missing information yourself.

The p-value associated with the test is 0.1051, so we cannot reject the null hypothesis ($H_0$) of no difference between the (true) averages of the two groups since the p-value is greater than the usual significance level alpha = 0.05. Based on these data, we conclude that there is not enough evidence of a difference between the (true) averages of the two groups at the usual significance level of alpha = 0.05. (You might want to consider a larger significance level of alpha = 0.10 with such small sample sizes, though.)

The conclusion holds provided the assumptions underlying the test are verified by the data. See Wikipedia: Welch's t-test for details on the test assumptions.

Here, the word "true" is used to refer to the averages you would get in each group if you had access to all the possible samples, not just the 7 samples per group you included in your study.

• You're welcome, Victoria! You should compute and compare the standard deviations of the two groups to see if you really need to assume different variability in each group. If the standard deviations are roughly comparable, then you should set the option var.equal of t.test to TRUE when performing the t-test. – Isabella Ghement Apr 8 '18 at 3:18
• Or maybe you should decide, which t-test to use, before you look at the data because some would consider everything else cheating. – Bernhard Apr 8 '18 at 19:44