Hypothesis testing

Descriptive statistics

• Describes and summarizes your sample data

• Uses  numbers, tables, graphs, and charts

• 3 Key Types:

  • Measures of location (e.g. mean, median)

  • Measures of spread (e.g. range, standard deviation)

  • Graphs/charts (e.g. bar charts, histograms)

• It tells you about the data you have — not about anything outside your sample.

Inferential Hypothesis

• Makes predictions or generalisations about a whole population based on a sample

• Random selection or random assignment

• Two Main Tools:

  • Hypothesis Testing – Is there a real effect or difference?

  • Confidence Intervals – Estimate the range a true value lies within

Statistical hypothesis

• Testing if the sample supports or rejects these kinds of claims.

• A statement about one or more study populations
  Hypothesis testing checks if study results are real or just due to chance

• Uses

  • p-values: tells if the result is statistically significant

  • Confidence intervals: estimate the likely range of the true effect

Types of hypothesis

Null Hypothesis (H₀)

• There is no difference or no association

E.g. Drug A and Drug B work the same.”

Alternative Hypothesis (Hₐ)

• There is a difference or an association

E.g.  “Drug A works better than Drug B.”

Two-Sided Hypothesis (most common in medicine)

• Null: No difference

• Alternative: There is a difference (can be better or worse)

One-Sided Hypothesis (used when direction is known)

Option 1: Negative direction

• Null: No difference or positive difference

• Alternative: Only a negative difference

Option 2: Positive direction

• Null: No difference or negative difference

Alternative: Only a positive difference

Type I error (false positive)

• Definition: Rejecting H₀ when it's actually true

• Meaning: You think something is happening, but it’s not

• Example: Doctor says a man is pregnant

• Symbol: α (alpha)

• Fixed by: Choosing a significance level (e.g. 0.05)

Type II error (false negative)

• Definition: Not rejecting H₀ when it's actually false

• Meaning: You miss something that’s actually happening

• Example: Doctor says a pregnant woman is not pregnant

• Symbol: β (beta)

Testing

• Power = 1 − β

• Meaning: The chance of detecting an effect when there is one

• Higher power = fewer Type II errors

• Improved by:

  • Larger sample size

  • Higher significance level (α)

  • True effect being stronger

P-Values

Less than 0.05 = statistically significant

• Unlikely to happen just by chance