Do I need statistical methods?

1. Do I need statistical methods? Samu Mäntyniemi

2. Learning from experience • Which way a bottle cap is going to land? • Think, and then write down your opinion about the probability that in the next toss the cap will end up upside down. • After seeing the result of the first toss, re-evaluate your opinion • Continue this process for 20 times.. • Did your opinion change during the accumulation of evidence?

3. Scientific? • Explain your existing knowledge • What do you know about bottle caps and how this knowledge is brought into this process of learning more? • Explain your experiment • How did you conduct the experiment? • What kind of bottle cap was used? • Reveal your logic • How did you combine your existing knowledge and observations to come up with your conclusion?

4. Problems in explanation • In an earlier study, the cap was found upside down in 6 out of 10 cases, and the cap and the experiment are identical, therefore the initial guess for the first toss is 0.6 • In our first toss the cap was upside down, then for the next toss the probability was changed to 0.63… • After 19 tosses observing the cap upside down did not affect the probability that much anymore because larger number of tosses had already taken place • It is difficult to replicate the logic and conclusions of the study based on the verbal explanation!

5. How will statistical methods help? • Provides mathematical presentation of knowledge • common language for more precise expression of uncertainty • Results of previous analysis can be directly accounted for in a new study • Provides precise and transparent logic for updating and combining knowledge • Conclusions can be replicated and sources of information affecting them can be isolated

6. Subjectivity in science • Subjective : depends on the person • Each scientist has slightly different background: the knowledge about any given question is slightly different • Interpretation of new evidence is slightly different • In this context subjectivity does not include personal opinions affected by fear, hope, political orientation etc.

7. Objectivity • Objective : independent of the person • State of the world for which there is no room for interpretation • For example, the position of the bottle cap: it is upside down or not, regardless of the person assessing the position. • Data: objective set of facts • Can scientific reasoning be objective? • Yes, when reporting the data • No, when drawing conclusions about unobserved quantities: subjective interpretation can not be avoided

8. Role of statistical inference • There is an objective true state of the world • We do not know exactly what it is • If it cannot be simply observed by a measurement, then collect indirect evidence about the unknown state (data) • Use statistical methods to formulate existing knowledge about the unknown state and then combine with interpretation of new evidence • “Given my past knowledge and my interpretation of the observed data set, what can I say about the true state of the world?”

9. Why to use statistical inference? • More precise description of your logic and inference -> your message is more clear • Can be very valuable in case of large and complex problems • Setup your logic in small local pieces, then pull everything together in a consistent way • -> Modern computing power can solve problems you could not • Editor or referee is asking you to • Is this a good reason? • Are you describing or making inference?