^{ANOVA and Test of Independence}

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^{Md. Ershadul Haque, PhD}

^{Associate Professor}

^{Dept. of Statistics, University of Dhaka}

^{23-24 February, 2024�}

• When we are interested in comparing the mean scores of more than two groups. In this situation we would use analysis of variance. Analysis of variance is so called because it compares the variance.

Assumptions

• Before conducting the ANOVA the necessary assumptions must be met. The assumptions for ANOVA are the same as those for the t-test.
• Population normality- populations from which the samples have been drawn should be normal.
• Homogeneity of variance- the scores in each group should have homogeneous variances between the different groups

One-way Analysis of Variance (ANOVA)

ANOVA (Cont…)

ANOVA (Cont…)

ANOVA (Cont…)

ANOVA (Cont…)

Problems on ANOVA

Problem-2: The manager of a computer software company wishes to study the number of hours senior executives spend at their desktop computers by type of industry. The manager selected a sample of the executives from each of three industries. At the 0.05 significance level, can she conclude there is a difference in the mean number of hours spent per week by industry?

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Problems on ANOVA (Cont…)

Problems on ANOVA (Cont…)

• The use of cellular phones in automobiles has increased dramatically in the last few years. Of concern to traffic experts, as well as manufacturers of cellular phones, is the effect on accident rates. Is someone who is using a cellular phone more likely to be involved in a traffic accident? What is your conclusion from the following sample information? Use the .05 significance level.

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• The quality control department at Food Town Inc., a grocery chain in upstate New York, conducts a monthly check on the comparison of scanned prices to posted prices. The chart below summarizes the results of a sample of 500 items last month. Company management would like to know whether there is any relationship between error rates on regularly priced items and specially priced items. Use the .01 significance level.

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Thank you for your attention!