The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences The Language of Statistical Decision Making Lecture 2 Section 1 3 Example Hypotheses Example Statistical Significance Example Assignment Robb T Koether Hampden Sydney College Fri Aug 29 2008 Outline The Language of Statistical Decision Making 1 Populations and Samples 2 Inferences Example 3 Hypotheses Example 4 Statistical Significance Example 5 Assignment Robb T Koether Populations and Samples Inferences Example Hypotheses Example Statistical Significance Example Assignment Study Low Carb Diets The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Example Hypotheses Example Statistical Significance Example Assignment Article Study Low carb diet gets best results What is the relevant information here What is known to be true and what is conjecture Are there any weaknesses to this study Populations and Samples The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Definition Population The population is the set of all individuals of interest to the study Example Hypotheses Example Statistical Significance Example Assignment Definition Sample A sample is a set of individuals in the population from which data were obtained Their characteristics were observed or measured Inferences The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Example Hypotheses Example Statistical Significance Example Assignment Definition Statistical inference A statistical inference is a conclusion that is drawn about the population based on what was observed in the sample Samples and Inferences The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Example Hypotheses Example Statistical Significance Example Assignment Population Samples and Inferences The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Population Example Hypotheses Example Statistical Significance Select a sample Example Assignment Sample Samples and Inferences The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Population Example Hypotheses Example Statistical Significance Select a sample Make the observations Example Assignment Sample Data Samples and Inferences The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Population Inference Example Hypotheses Draw an inference Example Statistical Significance Select a sample Make the observations Example Assignment Sample Data Samples and Inferences The Language of Statistical Decision Making Robb T Koether Refers to the population Populations and Samples Inferences Population Inference Example Hypotheses Draw an inference Example Statistical Significance Select a sample Make the observations Example Assignment Sample Data Example The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Example Hypotheses Example Statistical Significance Example Assignment Example Samples and Inferences Is the earth getting warmer How can we tell Example The Language of Statistical Decision Making Example Samples and Inferences Robb T Koether Populations and Samples Inferences Example Hypotheses Example Statistical Significance Example Assignment All points on the earth s surface Population Example The Language of Statistical Decision Making Example Samples and Inferences Robb T Koether Populations and Samples Inferences Example All points on the earth s surface Population Hypotheses Example Statistical Significance Example Select a sample Assignment A few points Sample Example The Language of Statistical Decision Making Example Samples and Inferences Robb T Koether Populations and Samples Inferences Example All points on the earth s surface Population Hypotheses Example Statistical Significance Example Select a sample Assignment A few points Sample Measure the temperature Temperature readings Data Example The Language of Statistical Decision Making Example Samples and Inferences Robb T Koether Populations and Samples Inferences Example The earth is getting warmer Inference All points on the earth s surface Population Hypotheses Example Statistical Significance Example Draw an inference Select a sample Assignment A few points Sample Measure the temperature Temperature readings Data Example The Language of Statistical Decision Making Example Samples and Inferences Robb T Koether Populations and Samples Inferences Example All points on the earth s surface Population Refers to the entire earth The earth is getting warmer Inference Hypotheses Example Statistical Significance Example Draw an inference Select a sample Assignment A few points Sample Measure the temperature Temperature readings Data Hypotheses The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Definition Hypothesis A hypothesis is often a statement that is proposed to explain a phenomenon that is known to be true Example Hypotheses Example Statistical Significance Example Assignment In statistics the phenomenon is that which was observed in the sample The hypothesis is a statement about the population that explains the phenomenon Hypotheses The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Example Hypotheses Example Statistical Significance Example Assignment Suppose we observe that when we roll a die the number 6 comes up unusually often One hypothesis could be that the die is not properly balanced thereby making the number 6 more likely What is another plausible hypothesis Null Hypothesis The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Example Definition Null Hypothesis The null hypothesis is the conventional belief about the population or the status quo or the neutral position Hypotheses Example Statistical Significance Example Assignment It requires no special justification That is it receives the benefit of the doubt Alternative Hypothesis The Language of Statistical Decision Making Robb T Koether Populations and Samples Inferences Example Definition Alternative Research Hypothesis The alternative hypothesis is an alternative to the null hypothesis Hypotheses Example Statistical Significance Example Assignment It requires evidence for its justification That is it bears the burden of proof The Language of
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