Make economics easyT-test, f-test,Z-test ,chi squaretest.
1.t-testT-test is a small sample test.It was developed by William Gosset in1908It is also called students t test(pen name)t Deviation from population parameterStandard error of 0th sample statistics
Uses of t-test/applicationSize of sample is small (n 30)Degree of freedom is v n-1T-test is used for test of significance of regressioncoefficient in regression model.In multiple regression with 3 individual variablethe regression coefficient are to be tested by- t-test.
To test the hypothesis that correlationcoefficient in population is zero then we usedt-test.We used t-statistics when parameter ofpopulation are normal.Population Variance are unknown.It is also called Welch t-test.
2.Z-testZ-test was given by Fisher.T-test is used when correlation coefficientof population Is zero.But if population coeff. Correlation is notzero then z-test is used.Z Zr-ZpSEz
In z-test sample size is large (n 30)Z-test is used to determine whether twopopulation means are different ,whenPopulation variance is known.Z-test is based on standard normal distribution.Z-test is also called large sample test.
For each significance level the z-test has singlecritical value ie. 1.96 for 5% two tailed.Z-test conduct various tests like., One sample test,Two sample test.Location test,Maximum likelihood estimate.Paired difference test.
F-test (variance ratio test)F-test also given by Fisher.F-test is used to the two independent estimationof population variance.2122Two sample have same variance. (S and S )F-test is small sample test.Larger estimate of population variance.F Smaller estimate Of population variance.
2The variance ratio S12S2Degree of freedom for larger population varianceis V1 and smaller is V2The null hypothesis of two population variance22are equal ie H0 : S1 S2V1(larger) n-1V2(smaller) n-2F-test are design to test if two populationvariance are equal.
F-test is use by comparing the ratio of22the two variance S1 & .S1The samples must be independent.F-test never be –ve because upper value is2greater than lower. S12S2Testing of overall significance of regression by –F-test.Test for the significance of the adjustedcoefficient of multiple determination is –F-Test.
ȣF-test value lies bw 0 to
T-testGiven by Gosset.Z-testFisherSmall sample.Large sample.Population corr.Coeff. Is zero.Population corr.Coeff. Is not zero.Variance unknownIn multiple regressionwith 3 individualVariance knownF-testFisher.Small sample.Two independent estimationof population.Same variance.Testing for overallsignificance.
Chi square test2Χ test is introduced by- Karl Pearson.2Χ test is sampling analysis for testing significanceof population variance.Chi square is non parametric test, it can be used fortest of goodness of fit r2 .Chi square test is use simple random samplingmethod.Chi square test’s value lies bw 0 to 1.
Conditions for using chi square test.1.Total frequency(sample size) is large.(n 50)2.Samples are independent.3.Cell frequency are linear.4.Expected frequency will not small if it small(e 5) then pooling techniques is used.
Analysis ofvariance(anova)Given by fisher.Assumptions1.Independence of sample.2.Normal population.3.Same population variance.4.Based on qualitative data.
Chi square test Χtest is sampling analysis for testing significance of population variance. 2 Chi square is non parametric test, it can be used for test of goodness of fit r . Chi square test is use simple random sampling method. Χtest is introduced by- Karl Pearson. 2