Business

The data on the performance of the corporations has been tabulated below

Large CapPForecastMedium CapPForecastShadow StocksPForecastU.S. Healthcare16.7Vencor Inc20.4Ashworth Inc23.4Cisco Systems24.8Westcott Communicns22.3Homecare Mgmt Inc30.8Parametric Technology25.4CML Group10.4Methode Elec B20.6United Healthcare25.2Snyder Oil33.1Marten Transport10.5EMC Corp.18.6Owens  Minor22.1GatesF.A. Distrib15.6Amer. Power Conversion29.7Xilinx Inc24.1Rotech Medical Corp20.2Cabletron Systems19.4Invacare Corp.15.3Cosmetic Center B16.5CUC International30.0Tech Data Corp.17.0Volunteer Capital26.1Intel Corp10.3Brigggs  Stratton13.5BGS Systems8.1BMC Software15.0KCS Energy Inc10.1Microsoft Corp23.6Applebees International35.8Blcokbuster Entertain20.1Bowne  Co.10.6Linear Technology31.9Horizon Healthcare26.0Sysco Corp21.5Oakwood Homes14.7Home Depot31.8Progress Software18.5

To understand whether the growth potentials of stocks differ across classification of market capitalization we will carry out an ANOVA (analysis of variance) study on MS Excel to see if there is a significant difference between the three sets of values given. Before that we check if all the data sets are normal or not.

All the p-values in the Anderson-Darling test are  0.05 and hence they are all normal. The following are the p-values, Large Cap  0.851, Mid Cap  0.466  Shadow Stocks  0.965. Now, for the ANOVA test, the following are the null and alternate hypothesis

Null hypothesis
H0 There is no significant difference between the three sets of corporations

Alternate hypothesis
H1 There exists a significant difference between the sets of values

The following is the result from the Anova exercise

As can be seen from the analysis, the p value is  0.05 and hence the null hypothesis has to be accepted. It means that there is no statistically significant difference between the three sets of values. Hence, the growth potential of the stocks does not vary with the market classification of the stocks.
Also, the classification of corporations does not cause differences in ratios of 1994 market price to 1995 forecasted earnings per share because the growth in the corporations is not dependant on the market capitalization level of the firms. This is proved by the analysis done above. The merits of ANOVA over normal Hypothesis testing are as follows

Hypothesis testing can be successfully applied to only two samples or populations
If we are interested in testing a hypothesis on more than two populations, then hypothesis testing loses its accuracy (0.950.95  0.95)

ANOVA helps analyze multiple populations without increasing the probability of error
If we look at the p-values of three independent hypothesis tests, we can clearly see the difference, for Large Cap  Mid Cap, there is no significant statistical difference but there is a significant statistical difference of each of the above with Shadow Stocks. Hence it is difficult to ascertain if there is statistical difference between all three samples together