Population data help the businessman considerably in exploring new markets for his product; they serve as guideposts to market demand. The information on the consumer’s preference, buying habits, levels of living and income, together with their competition to be met, and the cost of operating business should be carefully studied.
It should be noted that not all commodities enjoy large sales even in communities that are thickly populated. Hence, a dealer in working clothes should take into account the number of farmers and laborers in the community, not the total population. Dealers in tractors, in farm machineries, and in agricultural implements may use agricultural income as a good index in determining their sales potentials. Dealers in gasoline should consider the number of motor vehicles in the place of business as a good measure of probable volume of sales.
Monday, March 22, 2010
Wednesday, March 17, 2010
Analysis of Variance (ANOVA)
The analysis of variance (ANOVA) is the statistical method used for testing the null hypothesis that the means of several populations are equal. The comparison in means of 3 or more populations which follow normal distributions can be taken simultaneously in just one application of this test. This test, therefore, is a generalization of the z and t tests of two normal population means.
In order to use ANOVA, certain conditions must be met:
1. The sample(s) must be randomly selected from normal populations.
2. The populations should have equal variances.
3. The distance from one value to its group’s mean should be independent of the distances of other values to that mean (independence of error).
ANOVA is reasonably robust, so that minor variations from normality and equal variance are tolerable.
ANOVA uses squared deviations or variances so that computation of distances of individual data points from their own mean or from the grand mean can be summed.
The test statistic for ANOVA is the F ratio. It compares the variance from the two sources:
F = Between – groups variance / Within – groups variance
F = Mean Square between (MSB) / Mean Square within (MSW)
F = MSB / MSW
Where:
MSB = Sum of Squares between / Degrees of Freedom between
MSB = (SSB) / (dfB)
MSW = Sum of Square within / Degrees of Freedom within
MSW = (SSW) / (dfw)
The degree of freedom for SSB = k – 1 and for SSW = k (n – 1)
Where:
k = number of groups or samples
n = no. of items per column (size of each sample)
In order to use ANOVA, certain conditions must be met:
1. The sample(s) must be randomly selected from normal populations.
2. The populations should have equal variances.
3. The distance from one value to its group’s mean should be independent of the distances of other values to that mean (independence of error).
ANOVA is reasonably robust, so that minor variations from normality and equal variance are tolerable.
ANOVA uses squared deviations or variances so that computation of distances of individual data points from their own mean or from the grand mean can be summed.
The test statistic for ANOVA is the F ratio. It compares the variance from the two sources:
F = Between – groups variance / Within – groups variance
F = Mean Square between (MSB) / Mean Square within (MSW)
F = MSB / MSW
Where:
MSB = Sum of Squares between / Degrees of Freedom between
MSB = (SSB) / (dfB)
MSW = Sum of Square within / Degrees of Freedom within
MSW = (SSW) / (dfw)
The degree of freedom for SSB = k – 1 and for SSW = k (n – 1)
Where:
k = number of groups or samples
n = no. of items per column (size of each sample)
Subscribe to:
Posts (Atom)
