#One way anova examples with solutions how to

1 2 k First observation, first sample Second observation, second sample The variablesвЂ™ value are called вЂњresponsesвЂќ. X nk,k Sample size Sample mean X is the вЂњresponse variableвЂќ. Notation Independent samples are drawn from k populations (treatment groups). We hypothesize that the three population means are equal One Way Analysis of VarianceДefining the Hypotheses H 0 : пЃ 1 = пЃ 2 = пЃ 3 H 1 : At least two means differ To build the statistic needed to test the hypotheses use the following notation: Solution Solution The data are interval The problem objective is to compare sales in three cities. One Way Analysis of Variance Weekly sales Weekly sales Weekly sales The weekly sales were recorded for twenty weeks following the beginning of the campaigns. In each city only one of the three characteristics (convenience, quality, and price) was emphasized. One Way Analysis of Variance: ExampleД®xample 12.1 - continued An experiment was conducted as follows: In three cities an advertisement campaign was launched. Three strategies are considered Emphasize convenience of using the product.

#One way anova examples with solutions how to

The marketing manager has to decide how to market the new product. Д®xample 12.1 An apple juice manufacturer is planning to develop a new product -a liquid concentrate. If the within-group variation is small, the same variation between groups produces a larger statistic and a more significant result.

Idea behind ANOVA: recall the two-sample t-statistic Difference between 2 means, pooled variances, sample sizes both equal to n Numerator of t 2 : measures variation between the groups in terms of the difference between their sample means Denominator: measures variation within groups by the pooled estimator of the common variance. 20 25 30 1 7 Treatment 1 Treatment 2 Treatment 3 10 12 19 9 A small variability within the samples makes it easier to draw a conclusion about the population means. Treatment 1 Treatment 2 Treatment 3 20 16 15 14 11 10 9 The sample means are the same as before, but the larger within-sample variability makes it harder to draw a conclusion about the population means. Idea Behind ANOVA Graphical demonstration: Employing two types of variability One variable of interest is the customerвЂ™s age. One Way Analysis of Variance: Example How do five bookstores in the same city differ in the demographics of their customers? A market researcher asks 50 customers of each store to respond to a questionnaire. She assigns 60 stores at random to the three styles of covers and records the number of magazines that are sold in a one-week period. One Way Analysis of Variance: Example A magazine publisher wants to compare three different styles of covers for a magazine that will be offered for sale at supermarket checkout lines. To do this, the technique analyzes the sample variances 12.1 One Way Analysis of Variance The analysis of variance is a procedure that tests to determine whether differences exits between two or more population means. The procedure works by analyzing the sample variance.

Specifically, we are interested in determining whether differences exist between the population means.

Introduction Analysis of variance compares two or more populations of interval data.