Quantitative Data Interpretation – Exam Review

Quantitative Data Interpretation

  • Converts numerical data into actionable insights.
  • Relies on summarising (descriptives) and generalising (inferentials).
  • Accuracy depends on sample size, measurement validity, and context.

Quantitative Data & Types

  • Quantitative data = measurable counts/values.
  • \text{Discrete}: separate whole numbers (e.g.phones counted).
  • \text{Continuous}: any value on a scale (e.g. height, time).

Statistical Approaches

  • \text{Descriptive}: condense data (mean, SD, etc.).
  • \text{Inferential}: draw population conclusions (hypotheses, CIs, regression).

Descriptive Statistics

  • \text{Mean} = \frac{\Sigma x}{n}
  • \text{Median} = middle value.
  • \text{Mode} = most frequent.
  • \text{Range} = x{max}-x{min}
  • \text{Variance} = \frac{\Sigma (x-\bar x)^2}{n}
  • \text{SD} = \sqrt{\text{Variance}}

Inferential Statistics

  • Hypothesis tests (e.g. t, \chi^2) judge significance.
  • Confidence Interval: range likely containing true parameter (e.g. 95\% CI).
  • Regression: model relationship between predictors and outcome (linear, multiple).

Distribution Concepts

  • \text{Normal}: bell curve; empirical rule 68\%-95\%-99.7\% within 1/2/3 SD.
  • Skew: positive (right tail) vs. negative (left tail).
  • Kurtosis: leptokurtic (sharp), platykurtic (flat), mesokurtic (normal).
  • Other shapes: bimodal, multimodal, uniform.

Visualization

  • Bar chart (categorical).
  • Histogram (continuous in bins).
  • Boxplot: median, Q1, Q3, whiskers, outliers.

Correlation & Regression

  • Correlation coefficient r\in[-1,1] indicates strength/direction.
  • Positive r: variables rise together; negative r: one rises, one falls.
  • Regression predicts dependent variable; assesses influence of independents.

Hypothesis Testing & CIs

  • H0: no effect; Ha: effect exists.
  • p\text{-value} \le 0.05 ⇒ reject H_0.
  • CI example: mean 50 with 95\% CI (47,53).

Chi-Square, T-Test, ANOVA

  • \chi^2 Independence: relationship between two categorical variables.
  • t-tests: compare two means (independent vs. paired).
  • \text{ANOVA}: compare \ge 3 means; significant result ⇒ run post-hoc (e.g. Tukey).

Interpreting Results

  • Statistical significance: effect unlikely by chance (p<0.05).
  • Practical significance: magnitude matters for real-world impact.

Common Mistakes & Ethics

  • Violating test assumptions (normality, independence, equal variance).
  • Overgeneralising from small or biased samples.
  • Misreading p, ignoring effect size, selective reporting.
  • Ethical practice: avoid bias, manipulation; ensure transparency and limitations.

Key Takeaways

  • Use descriptives to summarise, inferentials to generalise.
  • Check distribution shape and visualise appropriately.
  • Combine significance with effect size for meaningful interpretation.
  • Uphold ethical standards to maintain research credibility.