Inference Sample Statistic Population Parameter Hypothesis/Significance Testing assess evidence the data gives against a hypothesis about a parameter Confidence Regions provide a range (region) believed to contain the parameter with a certain believability (confidence) Confidence Intervals

The Scientific Method Make Observation Construct Hypothesis Make Predictions from Hypothesis Gather Observations / Experiment Compare Observations to Predictions Match, gain belief in hypothesis Don’t match, lose belief in hypothesis Inference Concepts

The Scientific Method Statistical hypothesis testing is at center Compares predictions to observations in the face of sampling variability Make Observation Make Predictions from Hypothesis Gather Observations / Experiment Compare Observations to Predictions Match, gain belief in hypothesis Don’t match, lose belief in hypothesis Construct Hypothesis Statistical hypothesis testing follows same logic Compares observations to predictions from a hypothesis Inference Concepts

Two Main Hypothesis Types Research Hypothesis a general statement of an effect Statistical Hypothesis (two types) Alternative Hypotheses (HA) a mathematical representation of the research hypothesis one of HA: parameter <,>, specific value Null Hypotheses (Ho) the “no effect” or “no difference” situation always Ho: parameter = specific value Inference Concepts

What are the null and alternative hypotheses … “The mean density of Canada yew (Taxus canadensis) in areas not exposed to Moose (Alces alces) on Isle Royale will be more than 1 stem per m2” HA: m>1 vs. H0: m=1 Where m is the mean density of Canada Yew in ALL areas not exposed to Moose on Isle Royale. Inference Concepts

What are the null and alternative hypotheses … “The percentage of Ashland residents over the age of 40 whose parents were born in Ashland is greater than 35%.” HA: p>0.35 vs. H0: p=0.35 Where p is the proportion of ALL Ashland residents over the age of 40 whose parents were born in Ashland Inference Concepts

What are the null and alternative hypotheses … “The mean age of medical college students (Homo sapien) is less than 24 years” HA: m<24 vs. H0: m=24 Where m is the mean age of ALL medical college students. Inference Concepts

What are the null and alternative hypotheses … “The mean longevity of employees at the company is different than 10 years” HA: m10 vs. H0: m=10 Where m is the mean longevity for ALL employees at the company. Inference Concepts

What are the null and alternative hypotheses … “A research paper claims that the mean fetal heart rate is 137 bpm. A doctor feels that the mean rate is lower for women admitted to her clinic.” HA: m<137 vs. H0: m=137 Where m is the mean fetal heart rate for ALL pregnant women admitted to her clinic. Inference Concepts