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Cited by 61Probability and Statistical ResearchStatistics Education and MethodologiesStatistical Methods and Applications

Independent Samples T-Test

Ross, Amanda, Willson, Victor L.·2017·Basic and Advanced Statistical Tests
DOI 10.1007/978-94-6351-086-8_3
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Abstract

An independent samples t-test compares the means of two groups. The data are interval for the groups. There is not an assumption of normal distribution (if the distribution of one or both groups is really unusual, the t-test will not give good results with unequal sample sizes), but there is an assumption that the two standard deviations are equal. If the sample sizes are equal or very similar in size, even that assumption is not critical.

AI snapshot

Written from the paper’s full text.

TL;DR

This chapter demonstrates an independent samples t-test using a clinical example comparing therapy versus no therapy on PHQ-9 depression scores. It reports that therapy significantly reduced depression scores, \(t(16) = -3.95\), \(p < .05\), \(d = -1.86\), 95% CI \([-22.50, -6.80]\).

Key findings

  • In the worked example, the no-therapy group had \(M = 23.40\), \(SD = 8.20\), and the therapy group had \(M = 8.75\), \(SD = 7.50\); therapy scores were significantly lower, \(t(16) = -3.95\), \(p < .05\), \(d = -1.86\), 95% CI \([-22.50, -6.80]\).
  • The chapter outlines eight hypothesis-testing steps: choose the test, check assumptions, state hypotheses, report sample stats/graph, compute the t-test, compute effect size, compute confidence interval, and write an APA results statement.
  • It identifies three statistical pillars: null hypothesis testing/statistical significance, effect size/practical significance, and confidence interval.
  • Assumptions listed are independence of data, appropriate measurement (IV nominal, DV interval/ratio), normality (\(N > 30\)), and homogeneity of variance (\(SD_1 = SD_2\)).

Methods

  • Design: between-groups design with two groups measured once; IV is therapy (no therapy vs. therapy), and DV is depression score (PHQ-9).
  • Sample: people recently diagnosed with a depression disorder; the scenario states \(N = 18\), but one sample-stats table lists \(n = 15\) per group while a later table lists \(n = 9\) per group.
  • Analysis: independent samples t-test using pooled variance/SEM, df computation, effect size, and 95% confidence interval; the results statement reports \(t(16) = -3.95\), \(p < .05\), \(d = -1.86\), 95% CI \([-22.50, -6.80]\).

Limitations

  • Not stated in the paper.
  • Evident from the text: sample size is inconsistent across the chapter (\(N = 18\), then \(n = 15\) per group, then \(n = 9\) per group), though the reported \(df = 16\) aligns with \(N = 18\).
  • Evident from the text: the chapter’s own normality assumption says \(N > 30\), but the example uses \(N = 18\); the homogeneity assumption says \(SD_1 = SD_2\), but reported SDs are 8.20 and 7.50. Formulas and images are also not fully rendered, limiting verification of computations.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1007/978-94-6351-086-8_3

Cites

Statistics

Nothing to recompute.

Claims the paper makes

  • Findingown data
    § Step 8 Results Statement · p. 40

    The no therapy group had a mean PHQ-9 score of 23.40 (SD = 8.20).

    “those who did not receive therapy (M = 23.40, SD = 8.20)”
    • Also stated in: § Sample Stats Step 4 · p. 13 · plain
      “| No Therapy | 23.40 | 8.20 | 15 |”
    Quote in the paperSubstantial claim
  • Findingown data
    § Step 5 Statistical Significance · p. 30

    The result was statistically significant at p < .05.

    “The results are statistically signi f icant!”
    • Also stated in: § Step 8 Results Statement · p. 40 · plain
      “p&lt;.05”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The data points are independent (each from a different person).
    • The authors state this as an assumption: The independent variable is nominal and the dependent variable is interval/ratio.
    • The authors state this as an assumption: The data are normally distributed (or the sample size is greater than 30).
    • The authors state this as an assumption: The variances of the two groups are equal (homogeneity of variance).
  • Findingown data
    § Step 8 Results Statement · p. 40

    The therapy group had significantly lower PHQ-9 depression scores than the no therapy group.

    “the depression scores (PHQ-9) of those who received therapy (M = 8.75, SD = 7.50) were signi f icantly lower than those who did not receive therapy (M = 23.40, SD = 8.20)”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The data points are independent (each from a different person).
    • The authors state this as an assumption: The independent variable is nominal and the dependent variable is interval/ratio.
    • The authors state this as an assumption: The data are normally distributed (or the sample size is greater than 30).
    • The authors state this as an assumption: The variances of the two groups are equal (homogeneity of variance).
  • Findingown data
    § Step 8 Results Statement · p. 40

    The 95% confidence interval for the difference in PHQ-9 scores was [-22.50, -6.80].

    “95[-22.50, -6.80]”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The data points are independent (each from a different person).
    • The authors state this as an assumption: The independent variable is nominal and the dependent variable is interval/ratio.
    • The authors state this as an assumption: The data are normally distributed (or the sample size is greater than 30).
    • The authors state this as an assumption: The variances of the two groups are equal (homogeneity of variance).
  • Findingown data
    § Step 8 Results Statement · p. 40

    The independent samples t-test yielded t(16) = -3.95.

    “t(16) = -3.95”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The data points are independent (each from a different person).
    • The authors state this as an assumption: The independent variable is nominal and the dependent variable is interval/ratio.
    • The authors state this as an assumption: The data are normally distributed (or the sample size is greater than 30).
    • The authors state this as an assumption: The variances of the two groups are equal (homogeneity of variance).

  • The authors state this as an assumption.

    The data points are independent (each from a different person).

    “1. Independence of data”
    “1. Each data point from 1 person”

  • The authors state this as an assumption.

    The independent variable is nominal and the dependent variable is interval/ratio.

    “2. Appropriate measure of variables”
    “2. IV: nominal DV: interval/ratio”

  • The authors state this as an assumption.

    The data are normally distributed (or the sample size is greater than 30).

    “3. Normality”
    “3. N &gt; 30”

  • The authors state this as an assumption.

    The variances of the two groups are equal (homogeneity of variance).

    “4. Homogeneity of variance”
    “4. SD1 = SD2”
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Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Hypothesis names anxiety instead of depression

    Minor

    The stated hypothesis concerns anxiety scores, while the scenario identifies the dependent variable as depression score.

  • Critical-value description reverses the 5% threshold

    Minor

    The critical-value description says scores beyond it have a greater-than-5% chance of occurring naturally, whereas the reported significant result uses p < .05.

2 of 2

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Related

Authors
Ross, A., & Willson, V. L.
Affiliations
Texas A&M University (US)
ORCID
Venue
Basic and Advanced Statistical Tests
Publisher
SensePublishers
Published
2017
Pages
13-16
DOI
10.1007/978-94-6351-086-8_3
OpenAlex
W2782461265
Semantic Scholar
7c7c42e20715b2fa84557a5e8b32d04299d143e7
Cited by
61
References
0
Citations by year
2026: 13 · 2025: 13 · 2024: 18 · 2023: 7 · 2022: 3 · 2021: 4 · 2020: 1 · 2019: 1 · 2017: 1
FWCI
2.71
Type
book chapter
Language
en
Open access
closed
Licence
www.springer.com/tdm (unspecified)
Locations
SensePublishers eBooks (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
  • Physical Sciences › Mathematics › Statistics and Probability › Statistics Education and Methodologies
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Keywords
independent samples t-test, comparison of group means, interval data, sample size, hypothesis testing

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