1. Inductive and deductive reasoning: relation to quantitative analysis
A workshop of two halves Ways of reasoning Quantitative analysis

2. Components of Research Design
A study’s questions
It’s propositions (if any)
It’s units of analysis
The logic linking the data to the propositions
The criteria for interpreting the findings

3. (Oxford Concise Dictionary)
Induction
To prove general statement: inferring of general law from particular instances
(Oxford Concise Dictionary)

4. (Collins Dictionary, slightly abbreviated)
Induction
General conclusion from a set of premises, based mainly on experience or experimental evidence.
Conclusion goes beyond information contained in the premises and does not necessarily follow from them.
(Collins Dictionary, slightly abbreviated)

5. Deduction Inference from general to particular, a-priori reasoning
(Reasoning from cause to effect)
(Oxford Concise Dictionary)

6. Deduction
The process of reasoning, typical of mathematics and logic, whose conclusions follow necessarily from their premises.
(Collins Dictionary)

7. Three main ways to reason
Calculation : Routine application of a procedure
Deduction: Less systematic process in which goal is to draw a valid conclusion from premises
Induction: Sacrifices validity for plausibility
(Deduction: Johnson-Laird and Byrne)

8. Aristotle said:
He “viewed scientific inquiry as a progression from observations to general principles and back to observation”. He maintained that the scientist should induce explanatory principles from the phenomena to be explained, and then deduce statements about the phenomena from premises which include those principles.

9. And Sherlock Holmes said:
“when you have eliminated the impossible then whatever remains, however improbable, must be the case”.
Is this true?

10. So what did Sherlock Holmes do?
At their first meeting, the great detective surprised Dr. Watson by remarking:
“you have been in Afghanistan”.

11. His logic (quote from Conan Doyle A. “A study in scarlet” p28)
The train of reasoning ran, “Here is a gentleman of a medical type, but with the air of a military man.
Clearly an army doctor, then.
He has just come from the tropics, for his face is dark, and that is not the natural tint of his skin for his wrists are fair.
He has undergone hardship and sickness, as his haggard face says clearly. His left arm has been injured. He holds it in a stiff and unnatural manner.
Where in the tropics could an English doctor have seen much hardship and got his arm wounded?
Clearly Afghanistan.

12. Is this deduction? Clearly Holmes was reasoning But:
Do his conclusions necessarily follow?
A possible alternative put forward for Watson, by Johnson-Laird and Byrne is
“I am an army doctor but I have been in a Swiss Sanatorium recovering from TB. The sun is responsible for my tan and my arm was injured in a climbing accident.”

13. A set of premises All A are B All B are C Therefore all A are C
No matter what A,B and C are, the result is a valid deduction.

14. Quantitative Methods
Mathematics
Operational Research
Statistics

15. So what is quantitative analysis?
Analysing data to create meaningful information.