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Doing the Right Thing! … statistically speaking ... What is statistics? • Statistics is a collection of procedures and principles for gathering and analyzing sample data to learn something about a larger population. (Ch. 1). • Sample Population!!! • NOT just Sample and then !!! Population, parameters, samples and statistics • Parameters are numbers that summarize population data. – mean , proportion p, standard deviation . • Statistics are numbers that summarize the corresponding sample data. (Ch. 2) – mean , proportion p-hat, standard deviation s. • Use sample statistics to learn about population parameters. (Unit A4) Different samples produce different results • To use statistics to make decisions about parameters, we must understand how sample statistics vary by studying their sampling distributions. (Units B11, B12) • The normal curve (Unit B9) can be used to describe how sample means and sample proportions vary. Good answers come from good data…or junk in = junk out! • If want to learn about one population, use principles of good sampling and surveying. (Ch. 4) • If conducting an experiment to compare two or more populations, use principles of good randomized experiments. (Unit A3) • If performing an observational study to compare two or more populations, know limits of observational studies. (Unit A3) Two ways to learn about a population parameter • Confidence intervals (Units C1, C2) estimate parameters. – We can be 95% confident that the proportion of Penn State students who have a tattoo is between 5.1% and 15.3%. • Hypothesis tests (Ch. 11) test the value of parameters. – There is enough statistical evidence to conclude that the mean GPA of all Penn State science majors is greater than 3.0. In this class, we’ve learned about a limited set of situations • • • • • One population mean (Unit C6) Mean of paired differences (Unit C9) Comparing two population means (Unit C8) One population proportion (Ch. 10, 11) Comparing two or more population proportions (Ch. 6) Choosing the correct analysis • Depends on type of data – numerical or categorical • Depends on number of groups (populations) – 1, 2, or more • Depends on research question – Testing hypotheses: Does the parameter equal this? Or is there a difference? – Interval estimation: What is the value of the parameter? Or how different are the parameters? Use what you’ve learned here... • When conducting your own research. • When critically evaluating what you read in newspaper articles. • When critically evaluating what you read in scientific journal articles.