Post on 31-Dec-2015
description
Introduction to Hypothesis Testing
MARE 250Dr. Jason Turner
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
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…TwoNull 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…TwoResearch 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
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
Testing…Testing…One…Two
Critical Region-DefinedWe 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…TwoAlternative 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…TwoResearch 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…TwoImportant 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 pP-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 leftP-value – equals the smallest significance level at which the null hypothesis can be rejected
Didn’t you go before we leftP-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
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
No, I didn’t have to go then
0.05 – value for Alpha (α)with fewest Type I and Type II Errors
Testing…Testing…One…TwoImportant 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…TwoThree 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…TwoResearch 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…TwoMeans test is run
Output: T = 2.15 df = 59 p = 0.0001
Do we accept or reject the null hypothesis?
Testing…Testing…One…Twop< 0.05 – Reject Null Hypothesis
Output: T = 2.15 df = 59 p = 0.0001
Since P<0.05 – we reject the null thatH0: μurchins deep = μurchins shallow
and accept the alternative that Ha: μurchins deep ≠ μurchins shallow
Testing…Testing…One…TwoTherefore 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