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 two-

tailed 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.