Introduction to Applied Statistics for the Health Sciences

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Applied Statistics for the Health Sciences

Overview

This guide introduces fundamental concepts in applied statistics, focusing on their use in health sciences. Key topics include descriptive and inferential statistics, sampling and populations, sampling methods, hypothesis testing, and confidence intervals.

Descriptive Statistics vs. Inferential Statistics

Definitions and Differences

Descriptive statistics summarize the features of a dataset, such as mean, median, mode, and standard deviation. They describe the data collected from a sample or population.
Inferential statistics allow conclusions to be drawn about a population based on data from a sample. They use probability theory to make generalizations beyond the observed data.

Descriptive Statistics	Inferential Statistics
Summarize data	Draw conclusions about populations
Mean, median, mode, SD	Hypothesis testing, confidence intervals
Describe sample or population	Generalize from sample to population

Example: Calculating the average height of a sample of students (descriptive) vs. using that average to estimate the average height of all students in a university (inferential).

Samples and Populations

Definitions

Population: The entire group of individuals with a particular characteristic of interest (e.g., all adults with hypertension).
Sample: A subset of the population selected for study (e.g., 100 adults with hypertension from a specific city).

Researchers use samples because:

They are cheaper and faster than investigating entire populations.
They are more practical and manageable.
They allow for estimation of population parameters.

Statistics refer to values calculated from samples (e.g., sample mean), while parameters refer to values from populations (e.g., population mean).

Example: Studying a sample of 200 patients to estimate the average blood pressure in all patients with hypertension.

Sampling Methods

Types of Sampling

Simple random sampling: Every member of the population has an equal chance of being selected. Example: Randomly selecting 50 patients from a hospital database.
Opportunity sampling: Selecting participants who are readily available. Example: Surveying people in a shopping mall.
Snowball sampling: Existing study subjects recruit future subjects from among their acquaintances. Example: Studying a rare disease by asking current participants to refer others.
Volunteer sampling: Participants self-select to be part of the study. Example: Posting an online advertisement for study volunteers.

Sampling Method	Advantages	Disadvantages
Simple random	Unbiased, representative	May be time-consuming, costly
Opportunity	Quick, easy	May not be representative
Snowball	Useful for hard-to-reach populations	Potential for bias
Volunteer	Easy to recruit	May not be representative

Additional info: The representativeness of the sample is crucial for generalizing results to the population.

Null Hypothesis Testing

Concepts and Process

Null hypothesis (H0): Assumes no effect or no difference exists in the population.
Alternative hypothesis (H1): Assumes there is an effect or a difference.
Statistical tests are used to determine whether to reject H0 in favor of H1.

Type I error (α): Incorrectly rejecting the null hypothesis when it is true (false positive).

Type II error (β): Failing to reject the null hypothesis when it is false (false negative).

	H0 True	H0 False
Reject H0	Type I error	Correct
Do not reject H0	Correct	Type II error

Statistical significance is often determined by a p-value less than 0.05, indicating strong evidence against H0.

Example: Testing whether a new drug lowers blood pressure compared to a placebo.

Confidence Intervals

Definition and Interpretation

A confidence interval (CI) provides a range of values within which the true population parameter is likely to fall, with a specified level of confidence (commonly 95%).
The formula for a 95% confidence interval for the mean is:

Where is the sample mean, is the z-score for the desired confidence level (1.96 for 95%), is the sample standard deviation, and is the sample size.
Confidence intervals can be visualized using error bars in graphs.

Example: A 95% CI for the mean systolic blood pressure is 120–130 mmHg, meaning we are 95% confident the true mean lies within this range.

Calculating Confidence Intervals Using SPSS

SPSS can calculate the margin of error and the lower and upper limits of the confidence interval around the sample mean.
Steps include selecting the appropriate analysis, specifying the confidence level, and interpreting the output.
Graphical representation can be created by plotting means with error bars indicating the confidence intervals.

Additional info: Confidence intervals provide more information than a single point estimate by indicating the precision of the estimate.