Statistics and Sampling Quiz

Biostatistics Introduction

• Biostatistics is the application of mathematical statistics to biological sciences and medicine involving data collection, organization, summarization, and analysis.
• It's a growing field with numerous applications in areas like epidemiology, medical sciences, health sciences, educational research, and environmental sciences.
• A key concern for biostatistics is the collection, organization, summarization, and analysis of data to draw inferences about a larger body of data even when only a portion is observed.

Purposes of Statistics

• Statistics is used to describe and summarize information, reducing it down to more meaningful sets of data.
• Statistics enables predictions about occurrences based on observations.
• Identifying relationships and differences between observations is another important function of statistics.

Data

• Data consists of measurements or counted values.
• Biostatistics centers around interpreting the data and communicating information derived from the data.

Populations and Samples

• A population is the complete set of values a variable can take.
• A sample is a part of a larger population.
• Samples are used to analyze the population, and are used effectively in cases where a population is too large for an analysis.

Population and Sampling

• Sampling is the process of choosing a portion of the population for study.
• Representativeness is a major characteristic of a good sample that ensures the sample characteristics closely match those of its larger population.
• Sampling bias occurs when a subject is excluded from the sample without a sound scientific rationale, or it fails to fulfill the major inclusion and exclusion criteria.

Example

• Studying self-esteem and academic achievement among college students.
• Population: all college level students.
• Sample: students from the University of Jordan.

What is Sampling?

• Sampling is the process of selecting a group of study units or subjects from a larger, defined population.
• It is a key element in efficient, cost-effective research.

Questions to Consider

• The reference population for the research.
• The group of people used for drawing the sample.
• The size needed for the sample.
• The appropriate method needed for selecting the sample.

Sampling - Populations

• A reference population is the complete population being or potentially being studied
• A study population is a manageable subset of the reference population that will be studied
• A sampling frame is a list of all members in the study population.

Sampling

• An element is a single member of a population being studied.
• Sampling frame is a list of all elements in the population.
• Example: list of all medical students at the University of Jordan for the years 2014-2016.

Sampling Methods

• Sampling relies heavily on the sampling frame.
• The sampling frame is a list of every unit that belongs to the study population.

Types of Sampling Methods

• Probability sampling methods uses random selection to sample. Subtypes include simple random sampling, systematic sampling, stratified sampling, cluster sampling, and multistage sampling.
• Non-probability sampling methods do not employ random selection. This could cause bias. Subtypes include convenience sampling, snowball sampling, quota sampling, and purposive sampling.

Probability Sampling Methods

• Random selection is used to ensure that every unit in the study population has an equal or known chance of being included in a sample.
• All units in the study population must have an equal or a known chance of being included in the sample.
• A sampling frame is required.

Simple Random Sampling

• This is the simplest probability sampling method.
• Create a numbered list of all units in the population.
• Decide on the sample size.
• Select the required number of units via the lottery method or random numbers.

Systematic Sampling

• Choose individuals at regular intervals from the sampling frame.
• A starting point is randomly selected.
• Individuals are selected at specified intervals.
• Example: Every 5th household, every 10th woman attending an ANC, etc.

Stratified Sampling

• Divide units into categories (strata) based on characteristics
• Ensures strata proportions in the sample mirror the larger population.
• Example: Samples are divided into strata based on socioeconomic class or race to ensure the representation of the sample mirrors that of the complete population.

Cluster Sampling

• Select study units (clusters) instead of individuals.
• All units in the cluster meet the criteria and are included.
• Useful for geographic units (schools, villages).
• It is helpful when the sampling frame isn't readily available or studying a population that is scattered over a large area.

Multistage Sampling

• More than one sampling method is used, often in phases.
• Sampling frame for entire population isn't necessary but individual clusters need a sampling frame.
• Helpful for studying a population spread over a huge area

Nonprobability Sampling Methods

• Sample elements aren't randomly selected.
• It is more likely to occur or lead to biased samples.
• Often used for convenience and to utilize available subjects. This could lead to bias.

Convenience Sampling

• Selects people who are easily available.
• People may or may not be typical of the population.
• A convenient way in health research.
• An advantage of this technique is that it is quick and cost-effective.

Snowball Sampling

• Study subjects refer to others who fit the sample criteria.
• Useful for populations that are hard to reach.
• Example: Drug users, AIDS patients.

Quota Sampling

• Ensures specific groups (strata) are represented in sample based on their proportions in the population.
• The sample is selected by convenience - e.g. the first 50% of males and 50% of females.

Purposive Sampling

• The subjects are handpicked because they represent the accessible population or they are experts in the field who can add value to the research.

Variables

• A variable is an object, characteristic, or property that can take on different values.
• A quantitative variable can be measured; a qualitative variable can be categorized.

Types of Variables

• Independent variable: presumed cause.
• Dependent variable: presumed effect.
  • example: Smoking (IV) Lung cancer (DV)

Levels of Measurement

• Nominal: categories with no particular order (gender, blood type).
• Ordinal: categories with an order (pain severity).
• Interval: equal intervals, but no true zero (temperature).
• Ratio: equal intervals and a true zero (weight, height).

What Type of Data To Collect?

• The goal of the researcher is to collect data using the highest possible level of measurement (ratio).
• Using a lower level would restrict the analyses that can be performed.

Parameter and Statistic

• A parameter is a numerical value measured from a complete population.
• A statistic is a numerical value computed from a sample.

Statistics

• Statistics is the science of collecting, organizing, and interpreting data.
• Descriptive statistics: organizes, summarizes, and displays data.
• Inferential statistics: makes predictions from samples about a larger population.

Descriptive Statistics

• Measures of location: Mean, median, mode.
• Measures of dispersion: Interquartile range, variance, standard deviation, coefficient of variation.
• Measures of shape: Skewness

Statistical Inference

• Making conclusions about a population using sample data.

Inferential Statistics

• Used to test hypotheses about relationships between variables in a population.
• Techniques involve prediction of population characteristics based on sample data.
• Reports the likely accuracy (confidence) of samples.

Inferential Statistics

• Bivariate parametric tests: one-sample t-test, two-sample t-test, ANOVA, Pearson's correlation.
• Nonparametric tests: Chi-square, Mann-Whitney U test, Kruskal-Wallis test for nominal or ordinal data.

Research Hypotheses

• A tentative prediction or explanation of the relationship between two or more variables.
• Translates a research question into a precise prediction.

Hypotheses Criteria

• Written in a declarative form.
• Written in present tense.
• Contains the population.
• Contains the variables.
• Reflects a problem statement or purpose statement.
• Empirically testable

Hypothesis Testing

• Making decisions based on sample data.
• Null hypothesis (H0) is a statement of no effect or no difference.
• Alternative hypothesis (H1) states the proposed effect or difference.

Types of Errors

• Type I error: Rejecting a true null hypothesis.
• Type II error: Accepting a false null hypothesis.

Steps in Hypothesis Testing

• Formulate H0 and H1.
• Specify the significance level (α).
• Select the test statistic.
• Establish the critical value(s).
• Determine the actual value.
• Draw a conclusion (Reject H0 or Do not reject H0).