Lecture 1: Statistics, Research Papers and Me
Since 2019, I have been teaching Data Analytics and Statistics at DCU Business School. 
Please introduce yourself:
This lecture focuses on a new way to teach statistics:
Understanding the basics
Using open source software/coding language (JAMOVI and R)
Applying these knowledge and skills to research papers writing
In the end, I want you to become a Data Scientist with enough knowledge and skills to:
Challenge bad science and wrong ideas
Apply to Data Science positions
Based on your research topic, I will provide real data in April. Your task is to write a research paper publication-ready with:
If you haven’t done it already, can you look for the quantitative academic journal paper which is the closest to your Ph.D.
You need to download the pdf version of this paper and to send it to my email damien.dupre@dcu.ie .
Warning:
The shape of the contents of the research paper resembles an hourglass:
Starts wide (introduction),then narrows (hypotheses, method and results) and finally opens (discussion and conclusion).
In research outputs, all sections are linked:
flowchart LR A[Introduction] --> B[Literature<br>Review] B --> C[Methods] C --> D[Results] D --> E[Discussion &<br>Conclusion]
To understand the statistics in the results section it is essential to identify the concepts presented in each section:
flowchart LR A[Introduction] -- Variables --> B[Literature<br>Review] B -- Hypotheses --> C[Methods] C -- Model &<br>Equation --> D[Results] D -- Statistical<br>Test--> E[Discussion &<br>Conclusion]
Thus, it is essential to master the concepts of Variable, Hypothesis, Model, and Equation before the actual Statistical Test.
An introduction is a section presenting your variables and why you investigate them.
There is little reference to previous academic research, just a description of actual facts.
How to start an introduction?
It should end with your Research Question, a question that includes all the main variables investigated which wonders about a potential relationship between them.
For example:
A variable itself is a subtle concept, but basically it comes down to finding some way of assigning numbers or characters to labels.
For example:
The bold part is “the thing that varies” and the italicised part is “the value of the variable”.
Let’s collect more data about our classmates on these three variables: height, coffee and gender!
Warning:
Variables can have different types:
Categorical: If the variable’s possibilities are words or sentences (character string)
if the possibilities cannot be ordered: Categorical Nominal (e.g., \(gender\) male, female, other)
if the possibilities can be ordered: Categorical Ordinal (e.g., \(size\) S, M, L)
Continuous: If the variable’s possibilities are numbers (e.g., \(age\), \(temperature\), …)
Jamovi, our first statistical software, illustrates them with recognisable icons:
Warning
Variables can be converted to either Categorical and Continuous but it is always better to keep them in their correct scale.
It’s important to keep the two roles “variable doing the explaining” and “variable being explained” distinct.
Let’s denote the:
Statistics is only about identifying relationship between Predictor and Outcome variables also called effect:
An effect between 2 variables means that the changes in the values of a predictor variable are related to changes in the values of an outcome variable.
Control Variables
Variables not included in the model OR in the hypotheses but they are in the equation. They are used to remove an irrelevant explanation of the variable changes.
The objective is to find the best predictor variable(s) to predict the variability of the Outcome!
One predictor is simple to handle, but using more than one requires more understanding!
Outcome’s variability is a birthday cake
An effect between a predictor variable and an outcome variable corresponds to the following model:
This arrow does not suggest causation but indicate correlation between \(Predictor\) and \(Outcome\), there is no assumption of one causing the other. An “effect” is reciprocal and does not involves causality.
Warning
Causality analysis is an other kind of test that involves:
A significant effect of a \(Predictor\) on an \(Outcome\) variable means that a predictor is explaining enough variance of the outcome variable.
This shows a significant relationship.
Outcome’s variability is a birthday cake
A significant effect means the slice eat by the predictor is large enough.
If there is no effect between the variables, they are not sharing enough of their variability
If there is a significant effect between the variables, they are sharing a big part of their variability
To decide if the part of the shared variability is big enough, a statistical test is required.
In the research paper you have selected, identify the variables that are used to produce statistical results (e.g. \(p\)-values).
Indicate their Type and Role by using the following table:
| variable_name | variable_type | variable_role |
|---|---|---|
| var 1 | type | role |
| … | … | … |
| var n | type | role |
Send me the table by email at damien.dupre@dcu.ie before the next lecture.
Hypotheses are:
“Hypothesis statements contain two or more variables that are measurable or potentially measurable and that specify how the variables are related” (Kerlinger, 1986)
Hypotheses include:
Warning
Hypothesis cannot test equality between groups or modalities, they can only test differences or effects
Every hypothesis has to state a change (between groups or according values) also called \(H_a\) (for alternative hypothesis) or \(H_1\)
Every alternative hypothesis has a null hypothesis counterpart (no difference between groups or according values) also called \(H_0\) (pronounce H naught or H zero)
\(H_a\) is viewed as a “challenger” to the null hypothesis \(H_0\).
Statistics are used to estimate the probability of obtaining the observed results, assuming the null hypothesis is correct. If this probability is low, the null hypothesis is rejected and the alternative hypothesis is considered more plausible.
… is the predicted relationship between one \(Predictor\) and one \(Outcome\) variable
The \(Outcome\) needs to be Continuous (but some models can use a Categorical Outcome)
The \(Predictor\) can be either Continuous or Categorical but the hypothesis formulation will change with its type
Effect representation:
How to use a template?
In the following formulation templates, replace the variable names with yours and select the direction of the effect expected.
The {outcome} {increases/decreases/changes} when {predictor} increases
Job satisfaction increases when salary increases
How to use a template?
In the following formulation templates, replace the variable names with yours and select the direction of the effect expected.
The {outcome} of {predictor category 1} is {higher/lower/different} than the {outcome} of {predictor category 2}
The Job satisfaction of EU employees is higher than the job satisfaction of non EU employees
How to use a template?
In the following formulation templates, replace the variable names with yours and select the direction of the effect expected.
The {outcome} of at least one of the {predictor} is {higher/lower/different} than the {outcome} of the other {predictor}
The Job satisfaction of at least one of the company’s departments is higher than the Job satisfaction of the other company’s departments
Effect representation:
Main Effect Hypothesis:
Effect representation:
Main Effect Hypothesis:
Effect representation:
Main Effect Hypothesis:
It predicts the influence of a second predictor on the relationship between a first predictor and an outcome variable
Warning
Effects representation:
Exactly the same results:
Imagine a first effect where Job Satisfaction increases when Salary increases
This effect can change according to the values of a second predictor
Here, the effect of Salary on Job Satisfaction is higher for Irish employees than it is for French employees because their line is steeper.
How to use a template?
In the following formulation templates, replace the variable names with yours and select the direction of the effect expected.
The effect of {predictor 1} on {outcome} is {higher/lower/different} when {predictor 2} increases
The effect of Salary on Job Satisfaction is higher when Employees’ Age increases
How to use a template?
In the following formulation templates, replace the variable names with yours and select the direction of the effect expected.
The effect of {predictor 1} on {outcome} is {higher/lower/different} for {predictor 2 category 1} than it is for {predictor 2 category 2}
The effect of Salary on Job Satisfaction is higher for Irish employees than it is for French employees
How to use a template?
In the following formulation templates, replace the variable names with yours and select the direction of the effect expected.
The effect of {predictor 1} on {outcome} is {higher/lower/different} for at least one of {predictor 2}
The effect of Salary on Job Satisfaction is higher for at least one of Employees’ Location
Effects representation:
Interaction Effect Hypothesis:
Warning
The main effect hypotheses of the two predictors also have to be formulated
Effects representation:
Interaction Effect Hypothesis:
Warning
The main effect hypotheses of the two predictors also have to be formulated
When formulating an hypothesis:
Note about hypotheses in academic papers
Remember the birthday cake metaphor: it symbolise the variability of the outcome variable to be explained by the predictors.
Now, imagine one guest take a slice, but the birthday person arrives and take the slice from the guest to eat it.
A mediation is when a Predictor called mediator, explains part of the variability of the outcome already explained by a first predictor. It is usually used to highlight the influence of psychological features.
Effect representation:
Formulation structure:
The effect of {predictor 1} on {outcome} is explained by the {predictor 2}
Warning
A mediation effect involves 3 requirements:
Example:
Here, the requirements are:
Mediation Effect Hypothesis:
In the following hypotheses, find the outcome variable and the predictor(s):
Overweight adults who value longevity are more likely than other overweight adults to lose their excess weight
Larger animals of the same species expend more energy than smaller animals of the same type.
Rainbow trout suffer more lice when water levels are low than other trout.
Professors who use a student-centred teaching method will have a greater positive rapport with their graduate students than professors who use a teacher-centred teaching method.
05:00
Hypothesis 1:
Hypothesis 2:
Hypothesis 3:
Hypothesis 3:
| Outcome | Predictor 1 | Predictor 2 | Hypothesis Type |
|---|---|---|---|
| Work motivation | Gender (Female/Male) | Main Effect | |
| Work motivation | Gender (Female/Male) | Origin (French/Irish) | Interaction Effect |
| Work motivation | Gender (Female/Male) | Origin (French/Irish/Italian) | Interaction Effect |
| Job satisfaction | Stress (0 to 10) | Main Effect | |
| Job satisfaction | Stress (0 to 10) | Age (Millennials/Baby Boomers) | Interaction Effect |
| Job satisfaction | Stress (0 to 10) | Age (in years) | Interaction Effect |
05:00
In the research paper that you have selected, formulate the tested hypotheses using the templates seen in the slide of the lecture and the variables that you have previously determined
Send me your hypotheses by email at damien.dupre@dcu.ie before the next lecture.
Thanks for your attention
and don’t hesitate to ask if you have any questions!
