Hypothesis Testing and Research Questions

Hypothesis Testing

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

Developing a Research Question

• 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

Defining a Hypothesis

• 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

Formatting a Hypothesis

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

Format Examples

• 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

Disproving a Hypothesis

• 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.

Statistical Hypothesis Testing

• 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

Examples of Hypotheses

• 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

Choosing a Test Statistic

• Determine the measurement of interest (means or proportions)
• Define the distribution of measurements (Normal or skewed)
• Note the number of patient groups ( one/ two/ or more)
• Check if the groups are independent or paired

Interpreting a P-Value

• 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

Example - Whale Life Expectancy

• H₀: The average life expectancy of whales is exactly 100 years
• Hₐ: The average life expectancy of whales is not equal to 100 years

Types of T-tests

• 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)

Analysis of Variance (ANOVA)

• ANOVA analyzes variations in an experimental result
• It determines the contributions of factors to the variance
• Variance is the square of the standard deviation

Type of Data Required for Hypothesis Testing Methods

• 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)

Example - HB Levels and Socioeconomic Status

• 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.

Proportion Test

• Hypothesis testing focuses on the comparison between two or more groups, e.g., the effectiveness of different medication

Example - Cure Rates of Different Medications

• H₀: Cure rate in Drug A = Cure Rate in Drug B
• Hₐ: Cure rate in Drug A ≠ Cure rate in Drug B

Discover the fundamentals of hypothesis testing and how to develop a solid research question. This quiz covers the essential elements of a good hypothesis and the proper formatting methods. Test your understanding of these crucial concepts in research methodology.