Introduction to
Hypothesis Testing
MARE 250
Dr. Jason Turner
Hypothesis Testing
We use inferential statistics to make
decisions or judgments about data values
Hypothesis testing is the most commonly
used method
Hypothesis testing is all about taking
scientific questions and translating them into
statistical hypotheses with “yes/no” answers
Hypothesis Testing
Start with a research question
Translate that question into a hypothesis
- statement with a “yes/no” answer
Hypothesis crafted into two parts:
Null hypothesis and Alternative
Hypothesis – mirror images of each other
Hypothesis Testing
Hypothesis testing – used for making
decisions or judgments
Hypothesis – a statement that something
is true
Hypothesis test typically involves two
hypothesis:
Null and Alternative Hypotheses
Testing…Testing…One…Two
Null hypothesis – a hypothesis to be tested
Symbol (H0) represents Null hypothesis
Symbol (μ) represents Mean
H0: μ1 = μ2 (Null hypothesis = Mean 1 =
Mean 2)
Testing…Testing…One…Two
Research Question – Is there a difference in
urchin densities across habitat types?
Null hypothesis – The mean number of
urchins in the Deep region are equal to the
mean number of urchins in the Shallow
region
H0: μurchins deep = μurchins shallow
In means tests – the null is always that
means at equal
Testing…Testing…One…Two
Three choices for Alternative hypotheses:
1. Mean is Different From a specified value –
two-tailed test
Ha: μ ≠ μ0
2. Mean is Less Than a specified value –
left-tailed test
Ha: μ < μ0
3. Mean is Greater Than a specified value –
right-tailed test
Ha: μ > μ0
Testing…Testing…One…Two
Testing…Testing…One…Two
Critical Region-Defined
We need to determine the critical value (s) for
a hypothesis test at the 5% significance level
(α=0.05) if the test is (a) two-tailed, (b) left
tailed, (c) right tailed
0.025
0.025
0.05
0.05
{
{
{
{
Testing…Testing…One…Two
Alternative hypothesis (research
hypothesis) – a hypothesis to be considered
as an alternative to the null hypothesis (Ha)
(Ha: μ1 ≠ μ2 )(Alt. hypothesis = Mean 1 ≠
Mean 2)
Testing…Testing…One…Two
Research Question – Is there a difference in urchin
densities across habitat types?
Null hypothesis – The mean number of urchins in
the Deep region are equal to the mean number of
urchins in the Shallow region
H0: μurchins deep = μurchins shallow
Alternative hypothesis - The mean number of
urchins in the Deep region are not equal to the
mean number of urchins in the Shallow region
Ha: μurchins deep ≠ μurchins shallow
Testing…Testing…One…Two
Important terms:
Test statistic – answer unique to each statistical
test; (t-test – t, ANOVA – F, correlation – r,
regression – R2)
Alpha (α) – critical value; represents the line
between “yes” and “no”; is 0.05
P-value – universal translator between test statistic
and alpha
Hold on, I have to p
P-value approach – indicates how likely (or
unlikely) the observation of the value obtained
for the test statistic would be if the null
hypothesis is true
A small p-value (close to 0) the stronger
the evidence against the null hypothesis
It basically gives you odds that you
sample test is a correct representation of
your population
Didn’t you go before we left
P-value – equals the smallest significance
level at which the null hypothesis can be
rejected
Didn’t you go before we left
P-value – equals the smallest significance
level at which the null hypothesis can be
rejected
- the smallest significance level for which the
observed sample data results in rejection of
H0
If the p-value is less than or equal to the
specified significance level (0.05), reject
the null hypothesis, otherwise, do not (fail
to) reject the null hypothesis
No, I didn’t have to go then
How to we use p?
Compare p-value from test to
specified significance level (alpha,
α=0.05)
If the p-value is less than or equal to
α=0.05, reject the null hypothesis,
Otherwise, do not reject (fail to) the null
hypothesis
No, I didn’t have to go then
p< 0.05 – Reject Null Hypothesis
p> 0.05 – Fail to Reject (Accept) Null
0.05 – value for
Alpha (α)with
fewest Type I and
Type II Errors
Testing…Testing…One…Two
Important terms:
Test statistic – answer unique to each statistical
test; (t-test – t, ANOVA – F, correlation – r,
regression – R2)
Alpha (α) – critical value; represents the line
between “yes” and “no”; is 0.05
P-value – universal translator between test statistic
and alpha
Testing…Testing…One…Two
Three steps:
1) You run a test (based upon your
hypothesis) and calculate a Test statistic – T
= 2.05
2) You then calculate a p value based upon
your test statistic and sample size – p =
0.0001
3) Compare p value with alpha (α) (0.05)
Testing…Testing…One…Two
Research Question – Is there a difference in urchin
densities across habitat types?
Null hypothesis – The mean number of urchins in
the Deep region are equal to the mean number of
urchins in the Shallow region
H0: μurchins deep = μurchins shallow
Alternative hypothesis - The mean number of
urchins in the Deep region are not equal to the
mean number of urchins in the Shallow region
Ha: μurchins deep ≠ μurchins shallow
Testing…Testing…One…Two
Means test is run
Output: T = 2.15 df = 59 p = 0.0001
Do we accept or reject the null
hypothesis?
Testing…Testing…One…Two
p< 0.05 – Reject Null Hypothesis
Output: T = 2.15 df = 59 p = 0.0001
Since P<0.05 – we reject the null that
H0: μurchins deep = μurchins shallow
and accept the alternative that
Ha: μurchins deep ≠ μurchins shallow
Testing…Testing…One…Two
Therefore we reject the Null hypothesis and
accept the Alternative hypothesis that:
The mean number of urchins in the Deep
region are Significantly Different than the
mean number of urchins in the Shallow
region