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Difficulty: MediumStatistical Inference and Hypothesis Testing

An academic journal's editorial board is conducting statistical peer review for several manuscript submissions. The reviewers must verify that the authors selected the correct statistical tests for their study designs. Match each manuscript's methodology description with the statistical test that should be used for its primary analysis.

  • Evaluating the difference in mean hemoglobin A1c reduction between patients randomized to a novel GLP-1 agonist versus those receiving a placebo.Two-sample t-test
  • Determining whether there is an association between patient race (categorized into four groups) and readmission to the hospital within 30 days (yes or no).Chi-square test
  • Comparing the mean forced expiratory volume in 1 second (FEV1) among patients randomized to three different inhaled corticosteroid regimens.Analysis of variance (ANOVA)
  • Assessing the strength of the linear relationship between the number of pack-years smoked and the continuous measurement of carotid intima-media thickness.Pearson correlation coefficient

Answer

The novel GLP-1 vs placebo study requires a two-sample t-test. The patient race vs hospital readmission study requires a Chi-square test. The three corticosteroid regimens study requires Analysis of variance (ANOVA). The pack-years vs carotid intima-media thickness study requires the Pearson correlation coefficient.
Selecting the correct statistical test requires identifying whether the variables analyzed are continuous (quantitative) or categorical (qualitative). A two-sample t-test compares the means of a continuous variable between exactly two groups. Analysis of variance (ANOVA) is required when comparing the means of a continuous variable across three or more independent groups. The Chi-square test evaluates independence and associations between two categorical variables. The Pearson correlation coefficient measures the linear relationship between two continuous numerical variables.

Step-by-Step Solution

1
Identify the type of independent and dependent variables for each proposed manuscript.
Manuscript 1: categorical (2 groups) vs. continuous. Manuscript 2: categorical (4 groups) vs. categorical (2 groups). Manuscript 3: categorical (3 groups) vs. continuous. Manuscript 4: continuous vs. continuous.
The nature of the variables being analyzed determines the appropriate statistical hypothesis test.
2
Match the combination of variable types to the corresponding statistical test.
Continuous outcomes compared between two groups use a t-test. Associations between categorical variables use Chi-square. Continuous outcomes across three or more groups use ANOVA. Linear relationships between two continuous variables use Pearson correlation.
Applying fundamental biostatistics rules ensures valid interpretation of data and prevents methodological errors like inflated alpha levels.

Key Concept

Selection of statistical hypothesis tests based on variable type
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Topics

Statistical Inference and Hypothesis Testing

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