Chebyshev’s and Markov’s Inequality Theorems Chebyshev’s Inequality Theorem — named after Russian mathematician Pafnuty Chebyshev (1821-1894) — states that for a population (or sample) at most 1/k2 of the distribution’s values can be more than k standard deviations away from the mean. The beauty of the theorem is that although we may not know the exact distribution of the data — e.g. if it’s normally distributed — we may still say with certitude (since the...

Read More »## How to prove things

How to prove things .[embedded content] Great lecture series. Yours truly got Solow’s book when he was studying mathematics back in the 80s. Now in its 6th edition, it’s better than ever.

Read More »## The dangers of using unproved assumptions

The dangers of using unproved assumptions The unpopularity of the principle of organic unities shows very clearly how great is the danger of the assumption of unproved additive formulas. The fallacy, of which ignorance of organic unity is a particular instance, may perhaps be mathematically represented thus: suppose f(x) is the goodness of x and f(y) is the goodness of y. It is then assumed that the goodness of x and y together is f(x) + f(y) when it is...

Read More »## Diskret matematik

.[embedded content] Bra föreläsningsserie från Chalmers! När jag själv läste matematik i Lund på 80-talet tyckte jag bäst om kurserna i diskret matematik. Mycket logik och problem av ‘tankenötskaraktär’. Och kul hjärngympa att lägga några timmar på när man vill pausa lite från schackspel och korsord …

Read More »## The Binomial and Poisson distributions (student stuff)

The Binomial and Poisson distributions (student stuff) .[embedded content]

Read More »## On the validity of econometric inferences

On the validity of econometric inferences The impossibility of proper specification is true generally in regression analyses across the social sciences, whether we are looking at the factors affecting occupational status, voting behavior, etc. The problem is that as implied by the three conditions for regression analyses to yield accurate, unbiased estimates, you need to investigate a phenomenon that has underlying mathematical regularities – and, moreover,...

Read More »## A different way to solve quadratic equations

A different way to solve quadratic equations .[embedded content] This one is for Linnea, my youngest daughter, who has now begun studying mathematics at my university 🙂

Read More »## Statistical models and the assumptions on which they build

Statistical models and the assumptions on which they build Every method of statistical inference depends on a complex web of assumptions about how data were collected and analyzed, and how the analysis results were selected for presentation. The full set of assumptions is embodied in a statistical model that underpins the method … Many problems arise however because this statistical model often incorporates unrealistic or at best unjustified assumptions …...

Read More »## Support Vector Machines (student stuff)

Support Vector Machines (student stuff) .[embedded content]

Read More »## Avoiding statistical ‘dichotomania’

We are calling for a stop to the use of P values in the conventional, dichotomous way — to decide whether a result refutes or supports a scientific hypothesis … The rigid focus on statistical significance encourages researchers to choose data and methods that yield statistical significance for some desired (or simply publishable) result, or that yield statistical non-significance for an undesired result, such as potential side effects of drugs — thereby invalidating...

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