PSYCH 2220 CH. 7 Hypothesis Testing with Z Tests

cleaning "dirty" data

1. Judgment calls need to be made. Should data be kept or omitted? When? Other possible solutions? 2. When you "clean" data, be clear in your reporting about what you did and why so that other researchers can assess your choices and the corresponding tradeoffs. 3. Clean replications of studies that show the same results can give us greater confidence in those results.

Assumptions of the Z-Test

1. The dependent variable is measured as a scale variable. (not nominal or ordinal variables) 2. participants are randomly selected. 3. The independent variable is nominal.

Hypothesis testing - general Assumptions?

1. characteristics we want our population to have. 2. meeting the assumptions helps us to make accurate inferences. 3. Always check the assumptions before running your test (assuming that you have a parametric test).

steps of hypothesis testing

1. identify the population, distribution, and assumptions, and then choose the appropriate hypothesis test. 2. state the null and research hypotheses, in both words and symbolic notations. 3. determine the characteristics of the comparison distribution. 4. determine the critical values or cutoffs, that indicate the points beyond which we will reject the null hypotheses. 5. calculate the test statistic. 6. decide whether to reject or fail to reject the null hypothesis.

Critical Value or a cutoff

A test statistic value beyond which we reject the null hypothesis.

Z table

Appendix B-1. It gives us: percentage between z score and the mean. percentage in the tail base on a given z score.

Parametric tests vs. nonparametric tests

Are there assumptions about the characteristics of the population?

What percentage of scores are at least as extreme as a target score?

It is asking the percentage not between but greater and lesser than the given z scores.

Critical region

The area in the tail(s) of the comparison distribution in which the null hypothesis can be rejected.

misleading data

The famous butterfly ballot used in Florida during the 2000 presidential election showed the importance of the arrangement of items on a page. Instead of one page at a time. They combine the whole table in two pages. so people had to jump from one page to another.

how do we calculate the test statistic?

[sample mean (M) - population mean (µM)] / σM.

How do we determine the characteristics of the comparison distribution?

calculate standard error and identity population mean.

Z formula

convert back and forth between raw scores (x) and standardized scores (Z).

Two-tailed tests or nondirectional tests

critical region divided between the two tails of the distribution. (α=0.05, put 0.025 or 2.5% in each tail). we would want 2.5% of scores falling beyond z in either tail of the distribution (5% total).

One tailed tests or directional tests

critical region in one tail of the distribution. (α=0.05 or 5% in the tail).

what does Z scores allow us to do?

fair comparison. standardized scores allow us to compare different populations with the same measured variable; different sections of the same class with different instructors.

Parametric tests

inferential statistical tests based on assumptions about a population.

Nonparametric tests

inferential statistical tests not based on assumptions about the population.

What do we want to know when we conduct a study?

know if our sample appears to have a different population mean relative to a specific comparison population or the general population. Thus, we want to compute a Z statistics using standard error and the mean from our sample.

important note about meeting the assumptions.

meeting the assumptions improves the quality of the research. However, not meeting the assumptions does not necessarily invalidate the research. Some tests are fairly robust(accurate even if you violate the assumptions).

"dirty data"

missing data, misleading data, and outliers.

H0: µ1 = µ2 H1: µ1 ≠ µ2

null hypothesis states that there is no differences. alternative hypothesis states that there are differences. populations - two-tailed test.

H0: µ1 ≤ µ2 H1: µ1 > µ

one tail test- we expect the mean of population 1 to have a higher outcome than the mean of population 2.

H0: µ1 ≥ µ2 H1: µ1 < µ2

one tail test- we expect the mean of population 2 to have a higher outcome than the mean of population 1.

σM

standard error. = σ/√N

One-tailed vs two tailed tests

two tailed is more conservative. Reduces power for a particular tail (relative to a one tailed test.

Recall hypothesis-testing criteria

we tend to have a 5% rate for Type I errors (alpha or p level).

alpha (α) or p level

we usually set our "acceptable" risk of a Type I error when we run a study and conduct analyses to 0.05 or 5%.