New Information New Information Technologies in Learning Technologies in Learning

StatisticsStatisticsM. Mihova, Ž. PopeskaM. Mihova, Ž. Popeska

Institute of InformaticsInstitute of InformaticsFaculty of Natural Sciences and Mathematics, Faculty of Natural Sciences and Mathematics,

MacedoniaMacedoniamarija@ii.edu.mkmarija@ii.edu.mk, , zaneta@ii.edu.mkzaneta@ii.edu.mk

About the courseAbout the course

Course in the sixth semesterCourse in the sixth semester – two hours of lecturetwo hours of lecture – two hours of theoretical exercisestwo hours of theoretical exercises – one hour of laboratory exercises per weekone hour of laboratory exercises per week

Topics:Topics: Descriptive statisticsDescriptive statistics , , Sampling Distributions,Sampling Distributions, Estimation,Estimation, Test of Hypothesis,Test of Hypothesis, Nonparametric Tests and Categorical Nonparametric Tests and Categorical

Data Testing,Data Testing, Linear Regression,Linear Regression, Analyses of variance (ANOVA).Analyses of variance (ANOVA).

Lecture and theoretical Lecture and theoretical exerciseexercise

Theory of mathematical statisticsTheory of mathematical statistics Examples of application of the theory Examples of application of the theory

in the field of informatics and other in the field of informatics and other fieldsfields

LABARATORY EXERCISELABARATORY EXERCISE demonstrations with statistical demonstrations with statistical

applets,applets, exercise using statistical packageexercise using statistical package made programs for some statistical made programs for some statistical

methodsmethods

Applet for demonstration Applet for demonstration central limit theoremcentral limit theorem

Applet for plotting density Applet for plotting density functions for distributionsfunctions for distributions Demonstration that Demonstration that

t-distribution with t-distribution with higher degrees of higher degrees of freedom is closer freedom is closer to the normal to the normal N(0,1).N(0,1).

Statistical packagesStatistical packages SPSSSPSS

– Organizing data setOrganizing data set

Statistical packagesStatistical packages Analyzing data setAnalyzing data set

Programming statistical Programming statistical methodsmethods

Statistical packages are useful only Statistical packages are useful only for well known distributions.for well known distributions.

MathematicaMathematica Programs for estimating parameters Programs for estimating parameters

by method of moments, testing by method of moments, testing parametric and nonparametric parametric and nonparametric hypothesis, finding confidence hypothesis, finding confidence intervals…intervals…

ExampleExamplea0=Input[“Inpit a0=Input[“Inpit 0”];0”];X=Input[“Input Data”];X=Input[“Input Data”];n=Length[X];n=Length[X];z=Input[“Input significant level”];z=Input[“Input significant level”];k1=FindRoot[Integrate[x^(n-1)*E^(-x)/(n-1)!,x]==z, {k,20}]k1=FindRoot[Integrate[x^(n-1)*E^(-x)/(n-1)!,x]==z, {k,20}]

[[1]][[2]];[[1]][[2]];Print[“k1*a0=”, k1*a0];Print[“k1*a0=”, k1*a0];s=Sum[X[[i]],{I,1,n}];s=Sum[X[[i]],{I,1,n}];Print[“s=”, s];Print[“s=”, s];If[s>k1*a0, Print[“hypothesis is accepted”], If[s>k1*a0, Print[“hypothesis is accepted”],

Print[“hypothesis is not accepted”]];Print[“hypothesis is not accepted”]];

For For data set X={0, 1.1, 3. 4.4, 4.9, 5, 5}, data set X={0, 1.1, 3. 4.4, 4.9, 5, 5}, 0=5 and 0=5 and =0.05 the output is:=0.05 the output is:

k1*a0=16.4266, k1*a0=16.4266, s=23.4 s=23.4 ““hypothesis is not accepted”hypothesis is not accepted”

Thanks for your Thanks for your attentionattention