By Hans-Michael Kaltenbach
The textual content provides a concise advent into basic strategies in records. bankruptcy 1: brief exposition of chance conception, utilizing normal examples. bankruptcy 2: Estimation in idea and perform, utilizing biologically encouraged examples. Maximum-likelihood estimation in coated, together with Fisher details and gear computations. equipment for calculating self belief periods and strong possible choices to straightforward estimators are given. bankruptcy three: speculation trying out with emphasis on thoughts, fairly type-I , type-II error, and studying try effects. numerous examples are supplied. T-tests are used all through, vital different exams and robust/nonparametric possible choices. a number of trying out is mentioned in additional intensity, and mix of self sufficient checks is defined. bankruptcy four: Linear regression, with computations completely in line with R. a number of workforce comparisons with ANOVA are lined including linear contrasts, back utilizing R for computations.
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Additional info for A Concise Guide to Statistics
5-quantile). Thus, the middle 50% of the data are contained in that rectangle. 75-quantiles. Sample points outside this range are plotted individually. The previous normal and exponential data are both normalized to mean 2 and standard deviation 1 and the resulting data are shown as a barplot (left) and boxplot (right) in Fig. 11. In the barplot, no difference between the two samples can be noticed, while the different distributions of the data, the skewness of the exponential, and the symmetry of the normal are immediately recognized in the boxplot.
The same argument holds for the two estimators for the variance, which both also have a breakdown point of zero. While this might in practice not be as dramatic as theory suggests, simply because contaminations far away from the sample are often unlikely, it is nevertheless a reason to be uncomfortable, as it means that even a small amount of contamination can potentially yield very misleading results. For a small number of sample points, we might try a visual inspection to see if there are any unusual values in the sample, but this is clearly not a good strategy if we want to investigate large amounts of data.
M n . The main new idea is to consider this probability as a function of the parameter p for given observations. This function is known as the likelihood function n L n ( p) = P(M1 = m 1 , . . , Mn = m n ) = P(Mi = m i ) = p m (1 − p)n−m ; i=1 note that we can only write the joint probability as a product because we assume the positions (and therefore the individual matches) to be independent. We then seek the value pˆ n that maximizes this likelihood and gives the highest probability for the observed outcome.
A Concise Guide to Statistics by Hans-Michael Kaltenbach