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.
  • Discrete\text{Discrete}: separate whole numbers (e.g.phones counted).
  • Continuous\text{Continuous}: any value on a scale (e.g. height, time).

Statistical Approaches

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

Descriptive Statistics

  • Mean=Σxn\text{Mean} = \frac{\Sigma x}{n}
  • Median\text{Median} = middle value.
  • Mode\text{Mode} = most frequent.
  • Range=x<em>max−x</em>min\text{Range} = x<em>{max}-x</em>{min}
  • Variance=Σ(x−xˉ)2n\text{Variance} = \frac{\Sigma (x-\bar x)^2}{n}
  • SD=Variance\text{SD} = \sqrt{\text{Variance}}

Inferential Statistics

  • Hypothesis tests (e.g. tt, χ2\chi^2) judge significance.
  • Confidence Interval: range likely containing true parameter (e.g. 95%95\% CI).
  • Regression: model relationship between predictors and outcome (linear, multiple).

Distribution Concepts

  • Normal\text{Normal}: bell curve; empirical rule 68%−95%−99.7%68\%-95\%-99.7\% within 1/2/31/2/3 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, Q<em>1Q<em>1, Q</em>3Q</em>3, whiskers, outliers.

Correlation & Regression

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

Hypothesis Testing & CIs

  • H<em>0H<em>0: no effect; H</em>aH</em>a: effect exists.
  • p-value≤0.05p\text{-value} \le 0.05 ⇒ reject H0H_0.
  • CI example: mean 5050 with 95%95\% CI (47,53)(47,53).

Chi-Square, T-Test, ANOVA

  • χ2\chi^2 Independence: relationship between two categorical variables.
  • tt-tests: compare two means (independent vs. paired).
  • ANOVA\text{ANOVA}: compare ≥3\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 pp, 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.