Repeated Measures

Hypothesis Testing Homework Problem Solving Process

1. Diagram your study showing the details of the research design setup: the target population, the

sampling process, the sample group(s), the Independent variable(s) and its treatments (also

called conditions or levels), the dependent variable. Then diagram the hypothesis testing

process: the two explanations (H0 null and H1 alternative hypotheses) of your data stated in

directional (one-tail) or non-directional (two tails) language depending on the research question

being asked, the probability calculation (show the correct statistical test) based on the null

hypothesis, the two outcomes of your probability calculation showing your alpha level

(boundary between high and low probability) leading to the two decisions (based on each

probability outcome.

2. After you have completed step 1 above, then, and only then, are you ready to start using your

statistical test formula sheet to work through each step on that formula sheet. Make sure you

have the correct formula sheet based on which statistical test (i.e. probability calculation) is the

correct one to use for the type of data you are collecting and the type of research design you are

conducting (i.e. how many samples, how many independent variables, how many treatments).

a. Part I Assumptions: helps you decide which is the correct statistical test to use.

b. Part II Hypotheses: that is the same as the two explanations for your data.

c. Part III Critical Regions: this step will enable you to convert your alpha level (the

boundary defining high and low probability of obtaining your research results by

chance) into z, t, or F scores (depending on which statistical test is the correct one to

use). This step will give you your critical values (in z, t, or F scores). Diagram this step to

show the expected mean value of the sample (i.e. no sampling error) and how the

distribution of all the sampling means follows a normal curve. Show on your diagram

the high and low probability areas and whether you are focusing on one tail or two tail.

d. Part IV Calculating your test Statistic: this is usually a two or three step process

depending on the statistical test.

i. z tests: First you compute the standard error (i.e. average sampling error you

can expect by chance). Second, you compute the “calculated” z value (i.e. the

probability of getting your research results by chance).

ii. t tests: First you compute the variance (uses sample values to estimate the

populational standard deviation). Second you compute the standard error (i.e.

average sampling error you can expect by chance). Finally you compute the

“calculated” z value (i.e. the probability of getting your research results by

chance).

iii. F tests: First you compute the variance for between the groups (SS between, df

between) and the variance for within each group (SS within, df within) for all

levels of the independent variable(s). Second you compute the F ratio value(s)

for each independent variable(s).

e. Part IV Make a decision about the null hypothesis (whether it is true or not) based on

your statistical analysis

f. Part V Report your results professionally

2 Explanations 2 Outcomes 2 Decisions

Probability

calculation (calculates the

probability of

getting your

research results

by chance)

High probability

Low probability

= .05, .01, or .001

H1 Alternative Hypothesis

H0 Null Hypothesis

Accept the Null (to be true)

Reject the Null (as false)

& Accept the Alternative

M = S =

µ = σ =

Research Designs that use a z or t Test