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What does researcher want of statistics?

Learn about variability, relationships between variables, statistical tests, correlation analysis, and more in research. Explore how to interpret data and graphs effectively. Discover key statistical concepts and tools for your research journey.

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What does researcher want of statistics?

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  1. What does researcher want of statistics?

  2. What does researcher want of statistics? “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!..” • How variable it is? • Does “my pet thing” work? • Why do the things differ? • Why does it fail from time to time? • Why patients have different fate and where is the hope for them? • What would the outcome of a perturbation? Generally speaking, all the statistics is about finding relations between variables

  3. 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

  4. Deterministic vs. stochastic data

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

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

  7. Two graph concepts: Histograms vs. scatterplots

  8. Normal distribution –––––– +++––– ++++++ +-+–+– …………… ---+++

  9. Not a normal distribution

  10. 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

  11. Kurtosis: positive

  12. Kurtosis: negative

  13. Skewness

  14. Analysis of correlations

  15. Simple linear correlation (Pearson r): r = Mean(CoVar) / (StDev(X) x StDev(Y)) CoVar = (Deviation Xifrom mean X) x (Deviation Yifrom mean Y)

  16. 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

  17. Outliers • Correlations in non-homogeneous groups

  18. Nonlinear relations between variables • Measuring nonlinear relations

  19. Spurious correlations • Multiple comparisons and Bonferroni correction • Coefficient of determination: r2 • How to determine whether two correlation coefficients are significant • Other correlation coefficients

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

  21. Exploratory examination of correlation matrices

  22. When it should not work?

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

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

  25. 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

  26. 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

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