RCT Statistical Inference and Data Types

Tutorial 5 - RCT (2)

• Focuses on statistical inference, hypothesis testing, and statistical tests.
• Reviews the graphical representation of data.

Data Types

• Two main data types: numerical (continuous) and categorical (ordinal, nominal, proportions).
• For categorical data, bar charts are appropriate for visually graphing categorical variables.
• Bar charts represent proportions/frequencies of different categories, for easily comparing how groups (e.g., race or sex) are distributed within interventions.
• Using the wrong type of figure can obscure data and can lead to misunderstanding.

Graphical Representation Questions

• Question 1a: For the "Race" row in the table, a bar chart is the appropriate graphical representation because race is a categorical variable.
• Question 1b: For the "Antihypertensive medication classes" row in the table, a bar chart is the correct choice since medication classes are categorical.
• Question 1c: For the "Education" characteristic, a bar chart is suitable because education levels are categorical.
• Question 1d: For the "Age" characteristic, a box plot is more appropriate as age is a numerical variable.

Statistical Inference Basics

• Statistical inference uses a small sample to make an educated guess about the entire population.
• It involves the process of sampling from a population to make inferences about that population.

Measurement Errors

• Two types of errors in measurement: systematic and random.
• Systematic error: occurs in the same direction and magnitude every time.
• Systematic error can be an error in the measurement tool/process.
• Random error: shifts each measurement from its true value by random amount and direction.
• Random error is an inherent part of all measurement processes.
• Increased diversity can amplify random error.
• Increasing sample size and repeating measurements can reduce random error.

Systematic vs. Random Errors

• Systematic Errors: Characterized by inaccuracy, skewing measurements away from true value and leading to inability to draw valid conclusions.
• Random Errors: Characterized by imprecision, creating variability around the true value, but averaging can cancel the variability to get closer.
• Systematic errors are addressed through study designs (crosssectional, cohort, casecontrol, intervention studies).
• Random errors are addressed via statistical inference (hypothesis testing, confidence intervals).

Understanding Statistical Inference

• Statistical inference may not be needed if you can calculate a population parameter from the birthdate of every citizen, which can be derived if there's access to ALL of the population data.
• Statistical inference is used in research studies because access to the entire population is often infeasible, so inferences have to be made from samples.

Consolidating Key Concepts

• Measurements of a giraffe's height (true height is 5m) yield measurements of 4.8m, 5.1m, and 5.3m. This is an example of random error.
• Random error can be reduced through repeated measurements.
• Researchers can reduce systematic error via training in correct measurement processes.
• Increasing sample size does not fix systematic error. Systematic error cannot be fixed by changing the sample size

Random Error Summary

• Represents natural fluctuations in data that occur without specific cause.
• Introduces variability in study results, obscuring effects, affecting statistical power, and potentially leading to misleading conclusions.
• Can only be reduced by increasing sample size.
• Can be estimated using statistical methods such as hypothesis testing and confidence intervals.

Hypothesis Testing - an Overview

• Hypothesis testing: Step 1, Identify the Question, Step 2, Select the Statistical Test, Step 3, Compare the Evidence, Step 4, Make your Conclusions

Setting up Hypothesis Testing

• Question: Does Intervention A (IA) lead to statistically significant weight loss compared to Intervention B (IB).
• Null hypothesis (H0): No difference in weight loss between IA and IB.
• Alternative hypothesis (H1): There is a difference in weight loss between IA and IB.

Defining Hypotheses

• HO ("null" hypothesis): Suggests no difference between your observations.
• H1: Suggests a real difference between observations.
• Example Question "Do people in Town A have a different mean BMI compared to people in Town B?” requires an independent t-test.
  • There is no difference in the mean BMI between Town A and Town B (H0).
  • H1: There is a difference in the mean BMI between Town A and Town B.

Hypothesis Testing in Practice

• Question: "Class A and Class B have a mix of girls and boys. The mean IQ scores of students in both classes were measured. Do mean IQ scores differ between Class A and Class B?". The correct H0 is, "There is no difference in the mean IQ scores between Class A and Class B."
• Question: "Do children from families with a higher income have a different incidence of dental caries than children from families with a lower income?" The correct H1 is, "There is a difference in the incidence of caries between children from families of different income."

"Proving" Your Hypothesis

• Statistical proof assumes the null hypothesis is true and seeks evidence against it. That's the baseline for hypothesis testing.
• Insufficient evidence to reject the null hypothesis: Unable to reject the null hypothesis.
• Sufficient evidence to reject the null hypothesis: Able to reject the null hypothesis.

Hypothesis Testing Details

• The evidence needed to reject or not reject HO comes from the study. E.g., the mean height of men in Town A is 2 cm taller than in Town B.
• Assess how sure of the results are. A key way is to repeat the study again and again: will one find the 2cm difference or is the first study a once-off.
• Convention: Accept up to a 5% probability that the observed result is by chance (aka significance level).
• Quantify the difference in the study and check whether the data meets the 5% significance level, via statistical tests.

Beginning Statistical Tests

• One needs to identify the outcome variable (or Y variable).
• Determine the number of groups in the independent variable (or X variable).
• If the outcome variable is numerical, one should check for normality.

Statistical Tests Flowchart

• Numerical Data ("Continuous," Comparing means):
  • 1 group: One-sample t-test, Wilcoxon Signed-Rank test
  • 2 groups: Paired t-test, Wilcoxon Signed Rank test (Paired); Two-sample t-test, Mann-Whitney U test (Independent)
  • >2 groups: One-way ANOVA, Kruskal-Wallis test (Independent)
• Categorical Data ("Comparing Proportions"):
  • 1 group: Binomial test
  • 2 groups: McNemar's test (Paired); Chi-square test, Fisher's Exact test (Independent)
  • >2 groups: Chi-square test (Independent)

Parametric vs Non-Parametric Tests

• Parametric tests: Applies only to continuous data and refers to data distribution.
• If the data distribution is "normal" then parametric tests can be used.
• If the data distribution is not normal, then non-parametric tests should be used.
• All tests for ordinal and nominal (categorical) data are non-parametric.
• The Fisher's exact test caters to small sample sizes where could expect small cells

Statistical Tests - Practice Questions

• To test the null hypothesis: “There is no difference between the mean age of having their first cigarette between boys and girls", a Two sample T-test is used.
• For the null hypothesis: “There is no difference between the prevalence of diabetes between Town A and Town B", one should use a Chi-Square test.
• For the null hypothesis: “There is no difference in the resting heart rate in the study subjects at 6am and 6pm”, one should use a Paired T-test.
• For the statement: “There is a difference in the incidence of cavities when they are 6 years of age...”, an ANOVA is most appropriate.

Week 6: 95% Confidence Interval

• 95% Confidence Interval: Range of values to estimate a population parameter, and used to check p-values, as well as statistical vs clinical significance

Learning Objectives

• Understand the concept of a 95% confidence interval (CI).
• Learn how confidence intervals (CI) help quantify random error.
• Explore factors that influence the width of a confidence interval (CI).
• Learn how to interpret confidence intervals (CIs) in research.

Confidence Intervals

• Range of values to estimate a population parameter.
• Provides an interval estimate around a sample statistic, and indicates how accurate the estimates are likely to be.

Understanding 95% CI

• The 'true value' will fall within each of the intervals; an assumption to be measured to see just how often this is truthful.
• In 100 samples, 95 of those had intervals that contained the true value.
• Random variants and measuring how often tests work affects the true value being derived.

Quantifying Random Error

• The width of the confidence interval signifies and determines uncertainty and the random error.

Factors Influencing CI Width

• Influenced by sample size, variability, and confidence level.
• Larger sample size reduces the width of a CI and the uncertainty.
• Small sample size increases the width of a CI.
• Low data variability reduces the width of the confidence interval.
• Large data variability increases the width of the interval.

Confidence Level Explained

• Lower confidence levels can be measured for various data points. For example, 90%, 95%, and 99%. However, 95% is most often used.

Applying 95% CIs: Examples

• A study has the mean systolic blood pressure to be 120 mmHg with a 95% confidence interval between 115 - 125 mmHg. Which means that 95% confident that the true population mean blood pressure lies between 115 and 125 mmHg.

Summarizing 95% Confidence Intervals

• 95% Means that if the study is repeated many times, it will produce a series of intervals.
• Those intervals will estimate the 'true population parameter' through all the numbers being generated.
• These Intervals will contain Width as influenced of sample size, Variability, and a confidence level.
• 95% of those generated will be a good representation.

Understanding P-Values

• P-value helps us find the 'meaning' of the data set.
• Pillars that represent: understanding, interpretation, understanding 95% CI's and p-values, the differences Between 95%CI's and p-values, and the significance among clinical studies.

P-Value Definitions

• The assumption that any differences is due to random error
• measure of extreme observed data, assuming the null is true
• P-value: Helps to determine if data is surprising if random is applied