PSYCH 625 Time to Practice Week 4 guide: t-tests, ANOVA
Eleven Part A problems on t-tests and ANOVA plus four conceptual questions in Part B. This guide covers the independent-versus-dependent decision that runs through all of them, the one-tailed test question one flags, why p = .000 is never correct, and the arithmetic behind preferring ANOVA to repeated t-tests.
Editorial process
Last reviewed · August 6, 2026
The one decision that runs the whole worksheet
Almost every question on this worksheet reduces to one decision made before any arithmetic happens: what design produced these numbers. Question five asks it directly across five scenarios, and questions one, four, six, seven and nine each require the same judgement silently. The rule is narrower than most students think. Use a dependent-means test when every score in one condition is paired with a specific score in the other — the same people measured twice, or deliberately matched pairs. Use an independent-means test when the two sets of scores come from different people with no such pairing. The deciding question is whether you could draw a line from each score on the left to exactly one score on the right. If you cannot, the samples are independent, whatever the topic looks like. Do that classification pass first, on paper, before opening SPSS.
Question one flags its own trap and it is worth taking seriously. The research hypothesis is that boys raise their hands more often than girls, which is directional, so this is a one-tailed test — and the question tells you to decide that first because the critical value and therefore the conclusion depend on it. A two-tailed critical value at the same alpha is larger, so using it can turn a significant result into a non-significant one on the same data. Say in your answer which tail you used and why the hypothesis dictated it. Doing this by hand, as instructed, is also worth the time: the by-hand questions exist so that the SPSS questions later are checkable rather than mysterious. Doing the by-hand questions properly also builds the intuition that makes the SPSS output later readable rather than merely copyable, which is why the worksheet insists on them.
One thing to check before you start: its opening line says to complete Parts A, B and C, and the copy circulating online contains only Parts A and B. Check your own worksheet for Part C before you submit, because a missing section is not something a marker will read as a formatting choice. It is worth ten seconds and it is the only requirement on this worksheet you cannot recover after the deadline. Everything else here is arithmetic you can redo; a section you never knew existed is not. Ask a classmate or the instructor rather than assuming the instruction line is a leftover, since worksheets are reused across terms and sections are added and removed between them.
The design | The test | The tell in the wording |
|---|---|---|
Two separate groups | t-test, independent means | Different people in each condition |
Same people, two times | t-test, dependent means | Tested twice, before and after, pre and post |
Matched pairs | t-test, dependent means | Matched, paired, littermates, twins |
Three or more groups, one factor | One-way ANOVA | Three levels of one thing |
Two or more factors crossed | Factorial ANOVA | Two levels of X and two of Y |
Two reporting conventions will cost marks quietly if you paste output without reading it. The first is that a probability of .000 does not exist. SPSS rounds to three decimal places, so .000 means smaller than .0005, and the correct report is p < .001. Question six asks for the exact probability of the outcome, which makes this the exact question where copying the cell verbatim goes wrong. The second is that SPSS labels its significance column as two-tailed by default, so a one-tailed hypothesis needs the reported value halved, and you should say that you did it. Both are small edits and both are the difference between pasted output and reported results. Read every cell you paste rather than treating the output block as an image, and the conventions take care of themselves.
Question eight's table is about vocabulary as much as design. The grouping variable is the factor — the thing that defines which condition a participant is in — and the test variable is the outcome being measured. The worked example makes it explicit: four levels of training hours is the grouping variable, typing accuracy is the test variable. The error to avoid is confusing levels with factors. A three-factor design needs three separate grouping variables crossed with one another, not one variable with three levels — the example given, two levels of training by two of gender by three of income, is three factors. Write each of your examples in that same shape and the table checks itself. It also makes question eleven straightforward, since a 2 by 3 design is two factors with two and three levels respectively, giving six cells.
Part B's last question has a numerical answer and giving it is far stronger than describing the principle. Comparing three groups pairwise means three t-tests, and if each runs at an alpha of .05 the probability of at least one false positive across the set is one minus .95 cubed, or about fourteen per cent rather than five. With four groups and six comparisons it is over a quarter. That inflation of the familywise error rate is the whole reason the analysis of variance exists: one test, one alpha, across all the groups at once. Quote the arithmetic in your answer. It converts a memorised justification into a demonstration, which is what the question is checking for. Then add the second reason in a clause: a single omnibus test also answers a question the pairwise comparisons never ask, which is whether the groups differ at all.
Likely learning objectives
Inferred from the brief — check these against your own rubric.
- 01Identify from a description whether a design produces independent or paired observations.
- 02Choose a one- or two-tailed test from the direction of the research hypothesis.
- 03Report probabilities and test statistics to convention rather than copying software output.
- 04Explain the familywise error argument for ANOVA numerically rather than descriptively.
Read the full question
Review every instruction before using the planning guidance that follows.
What Parts A and B each require
- 01Part A questions 1 to 11, including hand calculations where specified and SPSS output where specified.
- 02A decision, for each scenario in question 5, of independent or dependent means.
- 03SPSS output copied and pasted into the worksheet for questions 4, 6, 7 and 9.
- 04A completed ANOVA design table with three one-way, two two-factor and one three-factor example.
- 05A drawing or plan for a 2 x 3 factorial design, with independent and dependent variables identified.
- 06Part B: four written answers on independent samples, dependent-samples t-tests, when to use ANOVA, and why not repeated t-tests.
- 07Sources cited consistent with APA guidelines.
Working the worksheet in a sensible order
Before anything: classify each design
Go through every question and label it independent, dependent, or more than two groups.
The hand calculations
Work questions 1, 2, 3 and 7 by hand as instructed, showing the steps.
The SPSS questions
Run 4, 6 and 9, and paste legible output with the reported values converted to convention.
The ANOVA design table
Write six examples in the same shape as the worked ones.
The 2 x 3 design
Draw the design and name the independent and dependent variables.
Part B's four written answers
Answer each with a definition, an example, and the deciding piece of information.
Where the test-selection rules and reporting conventions live
Recommended databases
- Course textbook and Sage student resources
- PubMed / NCBI Bookshelf
- APA Style
- IBM SPSS documentation
Search sequence
- 1.Confirm the test-selection rules from a reference source before starting, since every question depends on them.
- 2.Check the reporting conventions for probabilities and test statistics before pasting any output.
- 3.Look up the familywise error formula so the final Part B answer can be quantified.
- 4.Read the ANOVA entry for the factor-versus-level distinction the design table turns on.
Reference shortlist
These are authoritative starting points, not a ready-made bibliography. A qualified reviewer must confirm that each source fits the assignment and supports the claim beside which it is cited.
Nothing here is cleared for citation until you have read it.
- 01
T Test
StatPearls, NCBI Bookshelf, US National Library of Medicine · 2023
The three forms — one-sample, two-sample and two-sample paired — set out side by side. This is the reference for justifying each test choice in question five rather than asserting it.
- 02
Comparing the Means of Independent Groups: ANOVA, ANCOVA, MANOVA, and MANCOVA
StatPearls, NCBI Bookshelf, US National Library of Medicine · 2024
When ANOVA applies and what it compares. Use it for the Part B question on when an ANOVA is appropriate, and for the factor-versus-level distinction the design table needs.
- 03
Types of Variables and Commonly Used Statistical Designs
StatPearls, NCBI Bookshelf, US National Library of Medicine · 2023
States directly that ANOVA is preferable to conducting multiple t-tests because it reduces the likelihood of a Type I error — the claim the last Part B question asks you to make, with a source behind it.
- 04
Hypothesis Testing, P Values, Confidence Intervals, and Significance
StatPearls, NCBI Bookshelf, US National Library of Medicine · 2023
What a probability value is and what it is not. Read it before reporting anything as .000, and before writing a conclusion about the null hypothesis in questions one, four and six.
- 05
APA Style
American Psychological Association · 2026
The reporting conventions for statistics — decimal places, leading zeros, and the rule that probabilities below .001 are reported as p < .001 rather than as an exact figure.
Before the worksheet is uploaded
Common mistakes
- Choosing a paired test because the topic is the same rather than because the observations are paired.
- Running question one as a two-tailed test when the hypothesis is directional.
- Reporting p = .000 straight from the SPSS output.
- Using the two-tailed significance column for a one-tailed hypothesis without halving it.
- Swapping the grouping and test variables in the ANOVA table.
- Treating three levels of one variable as a three-factor design.
- Pasting SPSS output at a size or crop that cannot be read.
- Answering the final Part B question with a principle when it has a number.
- Submitting Parts A and B without checking whether your worksheet also contains the Part C the instructions name.
Submission checklist
- Each test choice can be justified by whether the observations are paired.
- Question one states which tail was used and why.
- No probability is reported as .000 anywhere in the worksheet.
- One-tailed results say explicitly that the two-tailed value was halved.
- The ANOVA table's grouping and test columns are the right way round.
- The three-factor example has three factors.
- All pasted SPSS output is legible.
- The familywise error answer contains the arithmetic.
- Part C has been located in your own worksheet, or confirmed not to exist in it.
Use this guide to plan and review your own work. Follow your institution's rules and read our academic-integrity policy.
Written by
Aaron Bishop
MA, Education
assignment interpretation and research-methods coaching across disciplines
Aaron leads the EssayCrackers editorial desk. He works on how assignment briefs are read — what a rubric is actually asking for, and where students most often answer a different question than the one set.
Reviewed by
Dr. Nathan Cole
PhD, Rhetoric & Composition
Argumentation and thesis development
Nathan teaches first-year composition and directs a university writing center. He reviews EssayCrackers guides for argumentative soundness and citation accuracy.