7
Two possible types of mistakes:
Type 1 error: The null hypothesis is true but is rejected. The probability of a type 1 error is denoted by
alpha (α).
Type 2 error: The null hypothesis is false, but is it not rejected. The probability of a type 2 error is
denoted by beta (β).
A p-value represents the probability, if H
0
is actually true, that random chance could produce your observed
results. If you calculate p = 0.01, then this means that there is a 1% chance of the null hypothesis being true (no
difference between the means) given your observed results. If you calculate p = 0.57, then this means that there
is a 57% chance of the null hypothesis being true given your observed results.
To determine if you should accept your hypothesis (i.e. reject your null hypothesis), you calculate a t-statistic
and p-value.
You accept your hypothesis if p < α (greek letter alpha)
For most scientific studies, the accepted value of α is 0.05
The data support the research hypothesis if p < 0.05.
There is a statistically significant difference between the two populations.
The data fail to support the null hypothesis.
The data fail to support the research hypothesis if p > 0.05.
There is no statistically significant difference between the two populations.
The data support your null hypothesis.
For a t-test, as the difference between your calculated t-statistic and t-critical increases, the p-value decreases.
Back to the example:
t = 0.988 Is this a high or low value?
By looking at the table, you can see that this value is less than the t-critical value (2.05) and therefore it is not
significant at p = 0.05. Therefore, we reject our research hypothesis and support our null hypothesis. There is
no significant difference in robin density between urban and rural settings.
In this example, p > 0.05
But what if I’m using a computer program to analyze my data?
If you are using a computer program to calculate your statistics (which is what we normally do), then you don’t
need to figure out the t-critical value using a table. Most computer statistical programs, including the statistics
you will do in EXCEL, compute the p-value for you. In this example, p = 0.331. This value is much larger than
the accepted p-value of 0.05. This large p-value indicates that we cannot reject our null hypothesis (another
way of saying this is that we fail to support our research hypothesis).
Reporting statistics in your results section
Report the t-statistic, degrees of freedom and p-value using the following format: Sentence stating your results
(t
df
= t-stat; p-value).