Math 430: Lecture 2b

Foundations for Statistical Inference Continued

Professor Catalina Medina

Additional study considerations

When is the data collected?

In cross-sectional study design the data is collected at one time point

Example: GPA of CSUCI students that do and don’t exercise regularly

In longitudinal study design the data is collected on the same subjects at multiple time points

Example: A study comparing weight-loss diets with a primary outcome of change in body weight after two years.

We will focus on modeling cross-sectional studies in our class

Who is the data collected on?

The unit of observation is the entity or individual on which data is collected and studied.

Example: Do CSUCI students who exercise regularly have higher GPA?

The units of observation are the students.

Our data should contain one row per student and each column would represent a variable (i.e. one column each for regular exercise, GPA).

Controls in experiments

In experiments the researchers assign the treatment groups, the levels of the explanatory variable.

Often we include a control which serves as a benchmark for comparison.

Example: Treating septic shock

In a study to treat septic shock, Hwang et al. (2020) used two study groups of equal size: one group received an intravenous infusion of vitamin C and thiamine and the other group received intravenous saline.

Explanatory variable: Injection received

Treatment of interest: infusion of vitamin c and thiamine
Control: saline used as a placebo (Fake replacement meant to simulate the experience of receiving treatment)

Standard of care

Example: Reducing heart attack rate

Suppose we want to learn if a new drug, drug A, can lower heart attack rate.

What should be

Our treatment group?
Our control group?

Blinds

If we think a subject knowing what treatment they got will affect their outcome we can do a blinded study, meaning the subjects do not know what treatment they received.

Example: Treating septic shock

Subject are not told what injection they received.

Example: Do pre-workout supplements improve athletic performance?

Subjects are not told if the supplement they receive is pre-workout or a placebo.

It could just be the idea of pre-workout that helps improve performance.

Blinds

If we think people conducting the research knowing what treatment the subject got will affect the outcome we can do a double-blinded study.

Subjects and people conducting the research do not know who received what treatment

Example: Experimental Alzheimer’s drug

Alzheimer’s is currently irreversible. Maybe a doctor will unintentionally put in more effort at check ups for people they know received the drug.

Careful planning is needed to still record who did and did not receive the experimental drug.

Ethics in research

All research must be ethical, and must meet ethical guidelines, to minimize risk of harm to the environment, property and to participants, and to preserve the well-being, dignity, rights and safety of participants (including animals).

Most research studies require an ethics committee to formally grant ethics approval before research begins. Institutional Review Boards (IRB) are in place to review and approve/disapprove studies.

CSUCI IRB policy

CSUCI IRB states

A Classroom project that will be used for teaching and learning the research tools in the classroom or for pedagogy and will not be published, or presented beyond the classroom does not require IRB review and approval.

Ethical considerations: Data

Example: Confidentiality

Data should be kept confidential.
If data is allowed to be shared, personal identifiers should be removed.

Example: Storage of data

Data should be stored securely, kept for the required amount of time, then (if appropriate) securely disposed.

Ethical considerations: Participants

Example: Consent

When appropriate, people should consent to being in the study, and hence should be told what the study involves.
People should also be able to withdraw from the study without penalty.

Example: Economic risks

Financial loss to participants should be avoided.
Reimbursements of reasonable costs for participating may be appropriate.

Ethical considerations: Risks

Example: Harm or discomfort

Physical/psychological/social harm or discomfort (to researchers, participants or bystanders) should be avoided or minimized.

Ethical considerations: Reporting

Example: Methods

Must report methods and any assumptions
Should use literature supported methods, when appropriate

Example: Analysis

Must use appropriate methods.
Should use reproducible methods .

Ethical considerations: Other’s work

Example: Acknowledgements

All those who contributed to the research should be acknowledged, including those who prepare figures, take photographs, or have helped collect data.

Example: Pagiarism

The work of others should be appropriately acknowledged and not claimed to be original.

Reproducible research

Reproducible research enables others to repeat the study and analysis to confirm findings

Methods, data (when appropriate), analysis and relevant computer code must be made available when possible

There are serious medical consequences to errors attributable to the effects of spreadsheet programs and software operated through a graphical user interface […] that could have been avoided through a reproducible research paradigm…

Simons and Holmes (2019), p. 471

Variable types

Numerical / Quantitative variables

Numerical (or quantitative) variables are mathematically numerical: the numbers have numerical meaning, and represent quantities or amounts. Numerical variables generally arise from counting or measuring.

Types of numerical variables

Discrete numerical variables has a countable number of possible values between any two given values

Example: Number of computers in a classroom

Continuous numerical variables have an infinite number of possible values between any two given values

Example: A person’s height

Sometimes, discrete quantitative data with a very large number of possible values may be treated as continuous.

Categorical / Qualitative variables

Categorical (or qualitative) variables are not mathematically numerical data: they comprise mutually exclusive categories or labels.

Types of categorical variables

Nominal categorical variables are categorical variables where the levels do not have a natural order.

Example: Blood types: Type A, Type B, Type AB, Type O

Ordinal categorical variables are categorical variables where the levels do have a natural order.

Example: Likert scale response: Strongly agree, agree, neutral, disagree, strongly disagree

Example: Age groups: 0-18, 19-55, 56+

Types of variables

(Some) Variable Types in R

Categorical types:

character: takes string values (e.g. a person’s name, address)
factor: categorical variables with different levels
logical: TRUE (1), FALSE (0)

Numerical types:

numeric: integer or double
integer: integer (for discrete)
double: floating decimal (for continuous)

Scientific research article

Microbiome of clothing items worn for a single day in a non-healthcare setting