Hypothesis Testing Overview

Hypothesis Testing

• Hypothesis testing is a statistical method to evaluate hypotheses about a population parameter.
• It helps researchers differentiate between real and random patterns in data.

Developing a Research Question

• Four key elements:
  • Patient or Population: The subject of the research question.
  • Intervention or Exposure: The action or condition being studied.
  • Comparisons: Alternative actions or conditions.
  • Outcomes: The effects or results of the intervention.

Defining Hypotheses

• A well-defined hypothesis clarifies the research question.
• It influences how statistical tests analyze data.
• A tentative statement explaining a phenomenon or event.
• Good hypotheses are testable, potentially predictive.
• Procedures without hypotheses are not experiments.

Formatting Hypotheses

• If-then statements define relationships between variables.
  • Example: If skin cancer is linked to UV light, then high exposure leads to higher skin cancer risk.
• Include dependent and independent variables.
• Dependent variable: The result or outcome (e.g., skin cancer frequency).
• Independent variable: The factor causing the change or effect (e.g., UV light exposure).

Disproving Hypotheses

• Collect all relevant evidence.
• If evidence supports the hypothesis, keep it as provisionally true.
• If evidence refutes the hypothesis, reject it and form a new one.
• Statistical testing uses null hypotheses.
  • Null hypothesis: No difference unless an unlikely event.
  • Alternative hypothesis: There is a difference.

Statistical Hypotheses Testing

• Define the relevant problem.
• State the null hypothesis (H0).
• State the alternative hypothesis (H1).
• Collect sample data.
• Calculate a test statistic (observed value - hypothesized value / standard error).
• Determine the P-value (relation to known distribution).
• Interpret the P-value.

Defining the Problem

• Null hypothesis: Assumes no effect in the population; there's no treatment effect.
• Alternative hypothesis: Opposite of the null hypothesis; indicates a treatment effect.

Example: Hypothesis on Cranberry Juice and UTIs

• Null hypothesis: Drinking cranberry juice has no effect on UTI recurrence rates.
• Alternative hypothesis: Drinking cranberry juice reduces UTI recurrence rates.

Choosing Test Statistics

• Identify the relevant measurement (mean or proportion).
• Understand the measurement's distribution (normal or skewed).
• Determine the number of patient groups.
• Note if groups are independent or paired.

Interpretation of P-Value

• Assessing the probability of getting results as extreme as the observed sample if the null hypothesis is true.
• Indicates how likely the outcome was influenced by chance.
• Small P-values suggest unlikely chance occurrences and support the alternative hypothesis.

Example: Whale Life Expectancy

• Null hypothesis: Whale average life expectancy is 100 years.
• Alternative hypothesis: Whale average life expectancy is not 100 years.

Examples of Mean Hypothesis

• Example 1: Mean body weight of newborn babies in Saudi Arabia in 2020 was >3 kg. Pediatricians suspect the 2021 mean body weight is <3 kg. H0: μ ≥ 3 kg; Ha: μ <3 kg
• Example 2: Doctors believe the mean sleep time for teens in Saudi Arabia is no more than 10 hours. A researcher believes teens sleep longer. H0: μ ≤ 10 hours; Ha: μ > 10 hours

Examples of Proportion Hypothesis

• Example 1: A pharmaceutical company claims at least 60% of diabetes patients responded to their drug. Doctors believe the response rate is <60%. H0: p ≥ 0.60; Ha: p < 0.60
• Example 2: Breast cancer is the leading cause of cancer in Saudi Arabian women, accounting for 25% of new cases in 2018. H0: p ≤ 0.25; Ha: p > 0.25

Data and Variables

• Data are answers to questions or measurements from experiments. Variables change between subjects; height and gender are examples.
• One variable per column in tables of data

Inference

• Two methods for inference:
  • Point estimation: Single best value estimate for the population parameter (e.g., mean or proportion).
  • Interval estimation: Range of values likely containing the true population parameter.

Inferential Statistics

• Compare multiple variables or groups, using sample data to infer population values.
• Divided into two types:
  • Estimation: Determining confidence intervals.
  • Significance testing: Evaluating hypotheses.

Estimation (Confidence Intervals)

• Estimate the population parameter from a sample value with a given confidence interval (C.I).
  • Mean (95% CI): Mean ± Z α/2 * SE where SE = SD/√n.
  • Proportion (95% CI): P ± Z α/2 ∗ SE where SE = √{PQ/n}.

Example: Confidence Interval for Heights

• Sample study: Mean height of 100 students = 165 cm; standard deviation =8 cm.
• Calculate 95% confidence interval: 163.2 cm to 166.8 cm.

Example: Confidence Interval for Pain Relief

• Study: 200/300 patients experienced pain relief with a new drug.
• Calculate 95% confidence interval for the proportion experiencing relief.

Statistics vs. Parameters

• Statistics: Measurements (means, standard deviations, proportions) calculated from samples.
• Parameters: Population values(mean, standard deviation, proportion)

Estimation of Parameters

• Population: Mean (μ) is unknown.
• Sample: Point estimate (x = 50).
• Interval estimate (e.g., 40 to 60).

Standard Error

• Quantitative variable: SE(Mean) = S/√n.
• Qualitative variable: SE(p) = √p(1-p)/n.

Types of T-Tests

• One sample t-test: Compare a sample mean to a known value.
• Independent samples t-test: Compare two independent groups' means.
• Paired samples t-test: Compare two related or paired groups' means.

One Sample t-test: Assumptions

• Population distribution is normal.

Example: Normal Body Temperature

• Null hypotheses (H0): Normal body temperature = 37.6°C.
• Alternative hypotheses (H1): Normal body temperature ≠ 37.6°C.

Analysis of Variance (ANOVA)

• ANOVA analyzes variation within and between experimental groups.
• It aims to determine the contributions of different factors to the total variance.

Type of Data for ANOVA

• Independent variable: Categorical variable with multiple levels (e.g., socio-economic status).
• Dependent variable: Continuous variable (e.g., hemoglobin level).

Proportion Test

• Assess whether a particular medicine is more effective than another medicine.
• Involves comparing cure rates between different groups based on chance variation and effect variation.

Null Hypothesis (Proportion Test)

• Null hypothesis: Cure rate in one group equals the cure rate in another group (no difference).
• Alternative hypothesis: Cure rates in the two groups differ.

Conclusion (T-test)

• One sample T-test: Analyze data from a single group.
• Unpaired T-test: Compare the means of two independent samples.
• Paired T-test: Compare the means of two dependent samples.