Do I need statistical methods? Samu Mäntyniemi

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?

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?

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!

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

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.

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

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?”

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?