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DQ 2 :Using the “Determining the Appropriate Sample Size,” Topic Material, perform a sample size calculation to determine how large your sample should be

The design is paired and the brief says so twice. That changes the arithmetic, because a paired test is powered on the variability of the change scores, not on the variability of the population.

Editorial process

Last reviewed · August 23, 2026

01

Paired means the arithmetic changes

Two clauses in the prompt are doing all the work, and they say the same thing twice: the same people take both surveys, and the analysis is a paired t-test. That makes this a within-subjects design, and the consequence is easy to state and easy to get wrong. An independent-samples calculation is powered on the variability between people, but a paired calculation is powered on the variability of the difference scores within each person, and because each person acts as their own control, that variability is usually much smaller. The practical result is that a paired design needs a substantially smaller sample than a between-groups design to detect the same change, which is precisely why quality improvement projects use it. If your calculation reports a number that looks like a two-group trial's, you have almost certainly used the wrong standard deviation and the post will say so to anyone who reads it carefully.

Set out your four inputs explicitly and defend each with a citation, because the brief asks you to justify the calculation rather than merely to produce a number. Alpha is conventionally set at 0.05 two-tailed and power at 0.80, and saying why 0.80 rather than 0.90 is worth a sentence, because it is a decision about tolerating a Type II error. The effect size is the input that actually requires judgement: state the smallest change in your survey score that would be clinically meaningful in your setting, not the largest one you hope to see, and cite a prior study or a minimal important difference if one exists for your instrument. Add an attrition allowance, since the same people must return for the second survey. Close on validity honestly: an underpowered study risks a false negative, an overpowered one detects trivial differences and wastes participant burden, and neither is an external validity problem, which is a separate question.

Likely learning objectives

  • Recognise a within-subjects design from the analysis named in a brief.
  • Use the standard deviation of difference scores for a paired calculation.
  • Justify alpha, power and effect size as decisions rather than defaults.
  • Distinguish power problems from external validity problems.

Assignment instructions

Read the full question

Review every instruction before using the planning guidance that follows.

DNP 830 Topic 4 DQ 2 DQ 2 :Using the “Determining the Appropriate Sample Size,” Topic Material, perform a sample size calculation to determine how large your sample should be Assume you want to do a project that compares the survey results before an intervention to those after an intervention in the same sample (the same people will take both surveys). You plan to use a paired t-test to analyze your results. Using the “Determining the Appropriate Sample Size,” Topic Material, perform a sample size calculation to determine how large your sample should be. Justify your sample size calculation with citations. Discuss how your sample size may affect the validity of your study.

02

What DNP 830 Topic 4 DQ 2 asks for

  1. 01A sample size calculation using the topic material provided.
  2. 02Justification of the calculation with citations.
  3. 03A discussion of how the sample size may affect the validity of the study.
03

Inputs, calculation, then the validity discussion

01

Identifying the design

State that the same-sample structure and the paired t-test make this within-subjects.

What the assessor is likely looking for

The design named from the brief's own clauses.

02

The four inputs

Set out alpha, power, effect size and variability with a justification for each.

What the assessor is likely looking for

Each input defended rather than assumed.

03

Choosing the effect size

Define the smallest clinically meaningful change on your instrument.

What the assessor is likely looking for

A minimal important difference rather than an optimistic estimate.

04

The calculation itself

Show the working using the topic material and report the resulting n.

What the assessor is likely looking for

Working shown, not just a number.

05

Attrition allowance

Inflate the sample for participants who will not complete the second survey.

What the assessor is likely looking for

A stated attrition rate with a reason for it.

06

Validity implications

Discuss Type II error, over-powering, and the separate question of representativeness.

What the assessor is likely looking for

Internal and external validity kept apart.

04

Where power and sample size are documented

Recommended databases

  • NCBI Bookshelf
  • PubMed Central
  • GCU Library
  • CINAHL

Search sequence

  1. 1.Read the topic material's worked example before substituting your own numbers.
  2. 2.Look up statistical power to justify the 0.80 convention rather than asserting it.
  3. 3.Search your instrument's name with minimal important difference for the effect size.
  4. 4.Find an attrition rate from a comparable pre-post study in your setting.
05

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.

T Test

StatPearls, NCBI Bookshelf · 2023

Review before citing

The t test, for the paired versus independent-samples distinction.

Statistical Significance

StatPearls, NCBI Bookshelf · 2023

Review before citing

Statistical versus clinical significance, for the effect size argument.

Human Subjects Research Design

StatPearls, NCBI Bookshelf · 2023

Review before citing

Research design, for the internal and external validity distinction.

06

Before you post to the Topic 4 forum

Common mistakes

  • Using an independent-samples formula for a paired design.
  • Estimating the effect size from what you hope to find rather than what would matter.
  • Reporting a number without stating alpha, power and effect size.
  • Forgetting attrition, when both surveys must be completed by the same people.
  • Treating sample size as an external validity issue rather than a power issue.

Submission checklist

  • Have you stated that the design is within-subjects and why that matters?
  • Is your standard deviation the one for the difference scores?
  • Are alpha, power and effect size each given with a justification?
  • Have you allowed for attrition between the two surveys?
  • Does the validity discussion separate power from representativeness?

Use this guide to plan and review your own work. Follow your institution's rules and read Brinevia's academic-integrity policy.

Written by

Maren Caldwell

MSN, RN, CNE

Medical-surgical nursing, pharmacology and NCLEX preparation

Maren is a registered nurse with over 15 years of clinical and educational experience in medical-surgical nursing. She writes on NCLEX preparation, patient care fundamentals, pharmacology and evidence-based practice.

Reviewed by

Dr. Tessa Redmond

DNP, RN, CNE

Evidence-based practice and clinical education

Tessa is a doctorally-prepared nurse educator. She reviews Brinevia content for clinical accuracy and alignment with current evidence-based guidelines.

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