Inferential Statistics
- Inferential Statistics – Definition, Types, Examples, Formulas
- Observational Studies and Experiments
- Sample and Population
- Sampling Bias
- Sampling Methods
- Research Study Design
- Population Distribution, Sample Distribution and Sampling Distribution
- Central Limit Theorem
- Point Estimates
- Confidence Intervals
- Introduction to Bootstrapping
- Bootstrap Confidence Interval
- Paired Samples
- Impact of Sample Size on Confidence Intervals
- Introduction to Hypothesis Testing
- Writing Hypotheses
- Hypotheses Test Examples
- Randomization Procedures
- p-values
- Type I and Type II Errors
- P-value Significance Level
- Issues with Multiple Testing
- Confidence Intervals and Hypothesis Testing
- Inference for One Sample
- Inference for Two Samples
- One-Way ANOVA
- Two-Way ANOVA
- Chi-Square Tests
Observational Studies and Experiments
Observational vs. Experimental Studies
Observational studies and experiments are two common types of research designs used in many fields, including medicine, psychology, and social sciences.
Observational studies are research designs where the researcher observes and records data without intervening or manipulating any variables. The goal of an observational study is to describe and understand relationships between variables or to identify possible causes and effects. Examples of observational studies include case-control studies, cohort studies, and cross-sectional studies.
Experiments, on the other hand, are research designs where the researcher manipulates one or more variables to observe the effect on another variable. The goal of an experiment is to establish cause-and-effect relationships between variables. Examples of experiments include randomized controlled trials, quasi-experiments, and natural experiments.
Content Overview
Observational Studies
In an observational study investigators observe subjects and measure variables of interest without assigning treatments to the subjects. The treatment that each subject receives is determined beyond the control of the investigator.
- In observational study researchers collect data in a way that does not directly interfere how the data arise. It is merely observed.
- From observation study, we can only establish correlation or association between explanatory and response variable.
Different Types of Observational Studies
There are several types of observational studies, including:
Cross-Sectional studies
These studies involve collecting data on a population or group of people at a single point in time. This type of study is useful for understanding the prevalence of a disease or condition in a population.
Cohort Studies
In cohort studies, a group of individuals is followed over time to observe changes in health outcomes. This type of study is useful for investigating the causes of diseases or conditions.
Case-control Studies
These studies compare individuals with a certain health outcome (the cases) to individuals without the health outcome (the controls) to identify potential risk factors for the disease or condition.
Ecological Studies
In ecological studies, data is collected at the population level rather than the individual level. This type of study is useful for investigating environmental or social factors that may impact health outcomes.
Longitudinal Studies
In longitudinal studies, individuals are followed over a period of time to observe changes in health outcomes. This type of study is useful for investigating the natural history of a disease or condition.
Cross-sequential Studies
These studies combine elements of cross-sectional and longitudinal studies by comparing different cohorts at different points in time. This type of study is useful for investigating how factors change over time and how they affect different generations.
Example of Observational Studies
For example, suppose we want to study the effect of smoking on lung capacity in women.
- Find 100 women age 30 of which 50 have been smoking a pack a day for 10 years while the other 50 have been smoke free for 10 years.
- Measure lung capacity for each of the 100 women.
- Analyze, interpret, and draw conclusions from data.
Retrospective Study
If an observational study uses it data from past then it is called retrospective study.
Prospective Study
If data is collected throughout the study then it is called prospective study.
Confounding Variable
A confounding variable is related both to group membership and to the outcome of interest. It is extraneous variable that affect both the explanatory and response variable and that make it seem like there is a relationship between them. Its presence makes it hard to establish the outcome as being a direct consequence of group membership.
Example of Confounding Variable
Let’s think eating breakfast makes people slim. It means people who eat breakfast regularly are slim. For this case, there might be three explanations.
1. Eating breakfast make people slim.
2. Being slim cause people to eat breakfast.
3. There might be some third variable that might be responsible for both being slim and eating breakfast. Generally, people who are really health conscious they are slim and starts their day with breakfast.
This third variable is called confounding variable.
Experiments
In an experiment investigators apply treatments to experimental units (people, animals, plots of land, etc.) and then proceed to observe the effect of the treatments on the experimental units.
In a randomized experiment investigators control the assignment of treatments to experimental units using a chance mechanism.
Different Types Experimental Studies
Experimental studies can be classified into different types based on the design and the way the participants are assigned to the groups.
Randomized controlled trials (RCTs)
In RCTs, participants are randomly assigned to either a treatment group or a control group. The treatment group receives the intervention being tested, while the control group does not. RCTs are considered the gold standard for evaluating the effectiveness of treatments and interventions.
Quasi-experimental studies
Quasi-experimental studies are similar to RCTs but do not involve randomization. Participants are assigned to groups based on existing characteristics or criteria. Quasi-experimental studies are useful when randomization is not possible or ethical.
Single-blind studies
In single-blind studies, participants are unaware of whether they are in the treatment group or the control group. This helps to reduce bias and ensure that the results are not influenced by participants’ expectations.
Double-blind studies
In double-blind studies, both the participants and the researchers are unaware of which group the participants are assigned to. This helps to further reduce bias and ensure that the results are not influenced by the expectations of either the participants or the researchers.
Crossover studies
In crossover studies, participants receive both the treatment and the control intervention in a random order, with a washout period in between. This type of study is useful for evaluating the immediate effects of an intervention.
Factorial studies
Factorial studies involve testing the effects of multiple interventions at the same time. This type of study is useful for investigating how different interventions interact with each other.
Example of Experimental Studies
In an experiment as researchers randomly assign subjects to various treatments and therefore it establishes causal connection between explanatory and response variable.
- Find 100 women age 20 who do not currently smoke
- Randomly assign 50 of the 100 women to the smoking treatment and the other 50 to the no smoking treatment
- Those in the smoking group smoke a pack a day for 10 years while those in the control group remain smoke free for 10 years.
- Measure lung capacity for each of the 100 women.
- Analyze, interpret, and draw conclusions from data
Principle of Experimental Design
In the design of experiments, treatments are applied to experimental units in the treatment group(s).In comparative experiments, members of the complementary group, the control group, receive either no treatment or a standard treatment.
From a statistician’s perspective, an experiment is performed to decide
1. whether the observed differences among the treatments (or sets of experimental conditions) included in the experiment are due only to change, and
2. whether the size of these differences is of practical importance.
Three Principles of Experimental Design
Statistical inference reaches above decisions by comparing the variation in response among those experimental units exposed to the same treatment (experimental error) with that variation among experimental units exposed to different treatments (treatment effect).
Thus, the three principles of experimental design are:
Control
Compare the treatment of interest to a control group to reduce experimental error by making the experiment more efficient.
Randomize
Randomly assign subject to treatments to ensure that this estimate is statistically valid.
Replicate
Collect a sufficiently large sample or replicate the entire study to provide an estimate of experimental error.
Summary
In summary, observational studies are used to observe and measure variables of interest without manipulating them, while experiments are used to manipulate one or more variables to observe the effect on another variable.
The type of study design chosen should be appropriate for the research question being investigated. Observational studies are useful when it’s not ethical or practical to carry out a randomized controlled trial. However, the results of observational studies can be open to bias and confounding factors. Cohort studies are useful for investigating how a problem develops over time, while case-control studies are efficient when dealing with rare conditions. The randomized controlled trial is still the gold standard for reliable evidence, but there are limitations, including cost, time, and participant restrictions. It’s important to consider the strengths and weaknesses of each study design and choose the most appropriate one to answer the research question.