Hypothesis Testing and Research Questions

Study Notes

Key elements of a research question:
- Patient or population: Identifies who or what the study is about
- Intervention or exposure: Describes what is done to the population or patients
- Comparisons: Indicates alternative interventions or approaches
- Outcomes: Describes how the intervention affects the population or patients

A well-defined hypothesis clarifies the research question and guides the statistical tests
It is a tentative statement proposing a possible explanation for a phenomenon
A useful hypothesis is testable and can include a prediction

Hypotheses have an "if-then" structure:
- "If" part describes a tentative relationship between variables
- "Then" part states the expected outcome based on that relationship

Dependent variable:
- Example: If skin cancer is related to UV light then people exposed to high UV light will have increased skin cancer rates
Independent variable:
- Example: If some students eat breakfast and others don't then students who eat breakfast will have better grades

Collect all evidence related to the hypothesis
If evidence supports the hypothesis, treat it as provisionally true
If evidence does not support the hypothesis, refute the hypothesis and form a new one.

Define the problem
State the null hypothesis (H₀): there is no effect
State the alternative hypothesis (H₁): there is an effect
Collect sample data to gather evidence
Calculate test statistics
- Subtract the hypothesized value from the observed value
- Divide by the standard error of the observed value
Relate test statistics to known distributions to find a p-value
Interpret the p-value

Example 1 (mean hypothesis): In 2020, the average weight of new-born babies in Saudi Arabia was over 3kg, with a standard deviation of 1.2kg, and a pediatrician believes that the birth weight of 2021 babies is less than 3kg because of unbalanced diets among Saudi women.
- H₀: μ ≥ 3 kg
- Hₐ: μ < 3 kg
Example 2 (mean hypothesis): Doctors believe that the average sleep duration for teens in Saudi Arabia is no more than 10 hours per night, but a researcher believes that teens sleep longer than 10 hours a night.
- H₀: μ ≤ 10 hours
- Hₐ: μ > 10 hours
Example 3 (proportion hypothesis): A pharmaceutical company reported that at least 60% of diabetes patients responded to Diabex (Metformin), but doctors in a specified hospital claim that the response rate is lower than the reported rate.
- H₀: p ≥ 0.60
- Hₐ: p < 0.60

The p-value is the probability of observing results as extreme or more extreme than those currently observed if the null hypothesis is actually true.
A small p-value suggests that the observed results are unlikely to be due to chance, providing evidence against the null hypothesis
A p-value < .05 usually considered statistically significant

One-sample T-test: Compares sample mean to a theoretical mean
Independent sample T-test (unpaired): Used to compare two independent groups
Paired samples test: Used to compare two related groups (e.g., same people tested before and after an intervention)

Independent Variable: One nominal variable (e.g., Socio-economic status has 3 levels: low, medium, high)
Dependent Variable: A continuous variable (normally distributed; e.g., blood pressure)

Researchers study Hb levels in relation to socio-economic status.
Various status levels (e.g., low, medium, high) are grouped and analyzed in this study
- The variation between the mean Hb levels within the groups (between-group variability), compared to the variation within those same groups (within-group variability) is used to determine possible differences between the group means.