Types of Statistical Studies and Producing Data All text and images in these slides are taken from  https://courses.lumenlearning.com/wm-concepts-statistics/ where it is published under one or more open licenses. Cover Image: "carlos-muza-84523." Authored by: Carlos Muza. Located at: https://unsplash.com/photos/hpjSkU2UYSU. Content Type: CC Licensed Content, Shared Previously. License: CC0: No Rights Reserved. Types of Statistical Studies and Producing Data Concepts in Statistics

The Big Picture

Steps of Statistical Investigation Begin with a research question, then proceed with these steps: Produce Data: Determine what to measure, then collect data. Explore the Data: Analyze and summarize the data (also called exploratory data analysis). Draw a Conclusion: Use the data, probability, and statistical inference to draw a conclusion about the population. Revision and Adaptation. Provided by: Lumen Learning. License: CC BY: Attribution

Research Questions Population/ Cause and Effect Type of Research Question Examples Type of Study Population Make an estimate about the population (often an estimate about an average value or a proportion with a given characteristic) What proportion of all U.S. college students are enrolled at a community college? Observational Study Test a claim about the population (often a claim about an average value or a proportion with a given characteristic) Do the majority of community college students qualify for federal student loans? Compare two populations (often a comparison of population averages or proportions with a given characteristic) Are college athletes more likely than nonathletes to receive academic advising? Investigate a relationship between two variables in the population Is academic counseling associated with quicker completion of a college degree? Test cause and effect Does drinking red wine lower the risk of a heart attack? Experiment Revision and Adaptation. Provided by: Lumen Learning. License: CC BY: Attribution

Producing Data An observational study measures variables of interest to describe a population or to investigate an association between two variables. Researchers do not attempt to manipulate one variable to cause an effect in another variable so an observational study does not provide evidence of a cause-and-effect relationship. An experiment intentionally manipulates one variable in an attempt to cause an effect on another variable. 

Investigating Relationships Between Variables One variable is the explanatory variable, and the other is the response variable. To establish a cause-and-effect relationship, we want to make sure the explanatory variable is the only thing that impacts the response variable in our experiment. In an observational study, researchers may take steps to reduce the influence of confounding variables, factors other than the explanatory variable on the response but ONLY Experiments can prove cause-and- effect!

Sampling We draw a conclusion about the population on the basis of the sample. To draw a valid conclusion, the sample must be representative of the population. A representative sample is a subset of the population that reflects the characteristics of the population. A sample is biased if it systematically favors a certain outcome. Random selection eliminates bias. Revision and Adaptation. Provided by: Lumen Learning. License: CC BY: Attribution

Does Size Matter? For random samples, bigger is better. Larger samples tend to be more accurate than smaller samples if the samples are chosen randomly. However the accuracy of the sample results depends on the size of the sample, not the size of the population.

Experiment Design The goal of an experiment is to provide evidence for a cause-and- effect relationship between two variables. A well-designed experiment controls the effects of confounding variables to isolate the effect of the explanatory variable on the response.

Random Assignment Random assignment uses random chance to assign participants to treatments, which creates similar treatment groups. With random assignment, we can be fairly confident that any differences we observe in the response of treatment groups is due to the explanatory variable. In this way, we have evidence for a cause-and- effect relationship.

Sample Sizes Size and the traits of the samples matter. Larger treatment groups provide more accurate data. Overgeneralization is when results are applied to a large population based on a sample that is too small or results are applied to a different population.

Controlling Confounding Variables Other strategies for controlling confounding variables include use of a control group, use of a placebo group (participants who believe they are getting the treatment), and blinding. Double blind studies reduce bias because both the participants and the researchers do not know which group is the control or placebo group and which is getting the treatment.

Chance Variation When we randomly assign participants to treatments, we produce similar groups most of the time. But there is a small chance that we will end up with treatment groups that are not similar. This is called chance variation and there is no way to eliminate it in a random sample.

Avoid Overgeneralizing What is the broadest group the results of this study could safely apply to? Researcher performed a double blind experiment on 500 male Harvard students assigning them randomly to control and placebo groups. Harvard students College students Ivy league men Male college students People aged 18-25 Male Harvard students People living in Massachusetts Ivy league students

Why We Need to Study Probability A well-designed experiment provides evidence for a cause-and-effect relationship. But even in a well-designed experiment, differences in the response might be due to chance. Studying probability will allow us to evaluate that possibility. Revision and Adaptation. Provided by: Lumen Learning. License: CC BY: Attribution

Quick Review How do you determine the goal of a statistical study from a research question or a description of the study? How do you determine if a study is an experiment or an observational study? Based on the study design, what types of conclusions are appropriate? What should you consider in evaluating the sampling plan for an observational study? What features of experiment design control the effects of confounding variables? How can we avoid overgeneralization of experiment results?