Response – variable of interest; variable you collect - #Fish, %Coral cover, temperature, salinity, etc Factor – variable by which response is divided; categorical - location, Date, Gender, Species Level – components of factor; - Location (Puako, Hilo Bay), Date (Jan, Feb), Gender (♂, ♀) Means tests

Parametric Means tests – have defined assumptions including normally distributed data Nonparametric Means tests – have few/no assumptions Parametric vs. Nonparametric

Parametric means tests – require data to be normal, etc (assumptions) Nonparametric tests – do not require data to be normal (assumptions) Parametric vs. Nonparametric

Parametric means tests – include 2 sample t-test, ANOVA Nonparametric means tests – include Mann Whitney (t-test), Kruskal Wallace (ANOVA) Parametric vs. Nonparametric

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 (H 0 ) represents Null hypothesis Symbol (μ) represents Mean H 0 : μ 1 = μ 2 (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 not equal to the mean number of urchins in the Shallow region H 0 : μ urchins deep = μ urchins shallow In means tests – the null is always that means at equal

Testing…Testing…One…Two Alternative hypothesis (research hypothesis) – a hypothesis to be considered as an alternative to the null hypothesis (H a ) (H a : μ 1 ≠ μ 2 )(Alt. hypothesis = Mean 1 ≠ Mean 2)

Testing…Testing…One…Two Research Question – Is there a difference in urchin densities across habitat types? Alternative hypothesis (research hypothesis) – a hypothesis to be considered as an alternative to the null hypothesis (H a ) H a : μ urchins deep = μ urchins shallow

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 not equal to the mean number of urchins in the Shallow region H 0 : μ urchins deep = μ urchins shallow In means tests – the null is always that means at equal

Testing…Testing…One…Two Hypothesis testing is all about taking scientific questions and translating them into statistical hypotheses with “yes/no” answers

Testing…Testing…One…Two Important terms: Test statistic – answer unique to each statistical test; (t-test – t, ANOVA – F, correlation – r, regression – R 2 ) Alpha (α) – critical value; represents the line in the sand 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 - the smallest significance level for which the observed sample data results in rejection of H 0 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