Hypothesis Testing with z Tests Chapter 7 The z Table > Benefits of standardization: allowing fair comparisons > z table: provides percentage of scores between the mean and a given z score Raw Scores, z Scores, and Percentages > Step 1: Convert raw score to z score > Step 2: Look up area in Table • The table presents area between the Mean and z and beyond the mean and z. From Percentages to z Scores > Step 1: Use the z table in reverse, taking a percentage and converting it into a z score. > Step 2: Convert the z score to a raw score using the formula. Sketching the Normal Curve > The benefits of sketching the normal curve: • Stays clear in memory; minimizes errors • Practical reference • Condenses the information The Standardized z Distribution Calculating the Percentile for a Positive z Score Calculating the Percentage Above a Positive z Score Calculating the Percentage at Least as Extreme as Our z Score Calculating the Percentile for a Negative z Score Calculating the Percentage Above a Negative z Score Calculating the Percentage at Least as Extreme as Our z Score Calculating a Score from a Percentile Check Your Learning > If the population mean is 10 and the standard deviation is 2: • What is the percentile rank of a sample mean of 6? of 11? • What percentage of the samples would score higher than a score of 6? of 11? The Assumptions and the Steps of Hypothesis Testing > Requirements to conduct analyses • Assumption: characteristic about a population that we are sampling necessary for accurate inferences Parametric v. Nonparametric Tests > Parametric tests: inferential statistical test based on assumptions about a population > Nonparametric tests: inferential statistical test not based on assumptions about the population An Example of the z Test > The z test • When we know the population mean and the standard deviation > The z test • The six steps of hypothesis testing > H0, H1 > One-tailed vs. two-tailed tests Determining Critical Values for a z Distribution – One tailed or twotailed test for significance? Making a Decision Check Your Learning > IQ scores are designed to have a mean of 100 and a standard deviation of 15. • Assume the class mean is 114. • Go through the six steps of hypothesis testing. “Dirty” Data > “Dirty” Data: Missing data, misleading data, and outliers > Misleading data: The famous butterfly ballot used in Florida during the 2000 presidential election showed the of the arrangement of items on a page. Cleaning “Dirty” Data > Judgment calls need to be made. > The best solution is to report everything so that other researchers can assess the trade-offs. > The best way to address the problem of dirty data is replication.