What does researcher want of statistics?

1.How variable it is? 2.Does “my pet thing” work? 3.Why do the things differ? 4.Why does it fail from time to time? 5.Why patients have different fate and where is the hope for them? 6.What would the outcome of a perturbation? “I had a fun and get it in addition to my cool microscope images!” “I have done a statistical analysis of my results and now give me my PhD, pleeeease!..” Generally speaking, all the statistics is about finding relations between variables

Basic concepts to understand Variability Variable Relation Signal vs. noise Factor vs. response (outcome), independent vs. dependent variables Statistical test Null hypothesis Power Experimental design Distribution

Deterministic vs. stochastic data

Two graph concepts: Histograms: show quantities of objects of particular qualities as variable-height columns

Two graph concepts: Scatterplots: show objects arranged by 2 particular qualities as coordinates

Two graph concepts: Histograms vs. scatterplots

Normal distribution –––––– ––– +-+–+– ……………

Not a normal distribution

Variance: Var = Sum(deviation from mean)2 Standard deviation: SD = Square root from Var Skewness: deviation of the distribution from symmetry Kurtosis: “peakedness” of the distribution Standard error: e.g. SE = SD / square root from N

Kurtosis: positive

Kurtosis: negative

Skewness

Analysis of correlations

Simple linear correlation (Pearson r): r = Mean(CoVar) / (StDev( X ) x StDev( Y )) CoVar = (Deviation X i from mean X ) x (Deviation Y i from mean Y )

How to interpret the values of correlations –Positive: the higher X, the higher Y –Negative: the higher X, the lower Y –~0: no relation Confidence: –|r| > 0.7: strong –0.25 < |r| < 0.7: medium –|r| < 0.25: weak

Outliers Correlations in non-homogeneous groups

Nonlinear relations between variables Measuring nonlinear relations

Spurious correlations Multiple comparisons and Bonferroni correction Coefficient of determination: r 2 How to determine whether two correlation coefficients are significant Other correlation coefficients

When it should not work? Graphs 2D graphs Scatterplots w/Histograms

Exploratory examination of correlation matrices

When it should not work?

Normalize it! E.g. NewX = log(X)

Causality There is no way to establish from a correlation which variable affects which. It is just about a relation.

Casewise vs. pairwise deletion of missing data How to identify biases caused by the bias due to pairwise deletion of missing data Pairwise deletion of missing data vs. mean substitution

Statsoft’s Statistica A perfect, almost universal tool for the researchers in the range for “very beginner” to ”advanced professional”. An old software with intrinsic development history Most of the methods can be found in >1 module Most of the modules contain >1 method No method is perfect No module is complete Most of the special modules are unavailable in the basic “budget” license