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 

 A: 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. 
A: There is actually widespread confusion about how to interpret p-values, even among scientists. I recommend the ASA Statement on Statistical Significance and P-Values and Greenland et al. (2016) as references.
    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 

t = -1.7796 is the calculated t-statistic. df = 10.147 are the degrees of freedom. These are each calculated according to their own formulas and used with a t-distribution to derive p-value = 0.1051
p-value = 0.1051 assumes that all your assumptions are true and that you didn't mess up the research design, sampling, etc. and that $H_0$ is true, and tells you:

*

*Given that there is no actual/true difference in means, if you were to repeat your experiment over and over again, 10.51% of the time you would see the type of difference in means as in your samples, or a more extreme difference in means.

This tells you something about how compatible your data is with a statistical model that assumes the true group means are actually equal.
Typically you want the $H_0$ model to be incompatible with the data. Lower p-values mean less compatible.
When a p-value is low enough, i.e. lower than 0.05, researchers will often call it "significant". If the p-value is not low enough ($p>0.05$), researchers will often call it "not significant".
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -4.2742915  0.4742915

This tells you that, given that you assume $H_0$ is false, the true mean
may lie in the interval [-4.2742915, 0.4742915].
It's called a 95% confidence interval because, if you repeat your experiment over and over again, 95% of the time the interval will contain the true mean.
It's an interval that you can have some confidence about containing the true mean (given that all your assumptions are correct).
However, you should use alternative="greater" or alternative="less", e.g,  t.test(..., alternative="less"), if you want to test if the mean of lizard$warm is greater or less than the mean of lizard$cold. The default behavior of t.test is two-tailed, which might not be what you want.
