# ANOVA Table Data

What data from an ANOVA table contribute to business decision making? Graduate Level: Please give examples.

Thank you.

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Please see response attached, including two supporting examples. I hope this helps and take care

1. What data from an ANOVA table contribute to business decision-making?

The goal of Analysis of Variance is to test the hypothesis that the means of the p-groups are equal. We cannot simply use a t-test because there is no way to "take the difference" of more than two different means. It just doesn't make sense. To get around this problem we need to use a different method. Instead of focusing on means we will focus on variances. In particular we will construct two different variances for our situation: a variance between the groups (due to the treatments) and a variance within the groups (due to random error).

The F statistic tells us whether or not we can reject the null hypothesis e.g., there is a significant difference between group means.

Why divide the variances? Because we know that dividing two variances gives us an F distribution! So what we will do is use groups within variance groups between variance = F, and will reject the null hypothesis when F is large. The goal of the ANOVA table is to calculate this F statistic. The Total Sum of Squares is the uncertainty that would be present if one had to predict individual responses without any other information. The best one could do is predict each observation to be equal to the overall sample mean. The ANOVA table partitions this variability into two parts. One portion is accounted for (some say "explained by") the model. It's the reduction in uncertainty that occurs when the ANOVA model,

Yij = m + ai + eij

is fitted to the data. The remaining portion is the uncertainty that remains even after the model is used. The model is considered to be statistically significant if it can account for a large amount of variability in the response (See http://www.tufts.edu/~gdallal/aov1out.htm).

So, how does this data from the ANOVA e.g. the variances and F statistic contribute to business decisions? It has to do your null hypothesis e.g., what are you predicting. The data from the ANOVA table will lend support for your hypotheses or not (e.g. reject the null hypotheses or not). Business decisions will be inferred from your hypotheses. In other words, the ANOVA table lists all our main effects and interactions.

Example 1: ANOVA TABLE data - to decide that the order of the information presented to auditor impacts the quality of decision-making

For example, Burger (2005) predicted the following two hypotheses, which were both supported. In other words, the data contributed to business decisions by confirming the following two predictions. Briefly, the authors found the F statistic was large enough to reject the null hypotheses in favor of the alternative hypotheses, meaning that data from the ANOVA contributes to the business decisions related to these two predictions:

H1: The order in which client information is reviewed will positively impact auditors' performance of analytical procedures

H2: The presence of a management explanation will impact the auditor's performance in the planning phase of the engagement.

The effectiveness of an audit is impacted by an auditor's ability to accurately perform analytical procedures in the planning phase of the engagement. In the study by Burger (2005), the accuracy of auditor performance when presented with client information in a causal framework is compared to auditor performance when information is presented in an audit-planning framework. In addition, auditors' ability to effectively react to a fraudulent management explanation is examined. The authors found that the order of client information presentation in the audit planning stages impacts the auditor's ability to accurately perform analytical procedures. It affects the auditor's decision-making choices. Specifically, this study examined the impact that the order of client information and the presence of a fraudulent management explanation have on auditors' ability to accurately perform analytical procedures during the planning phase of the audit. Experimental evidence, using a 2 x 2 experimental design and a sample of 42 junior and senior auditors, is used to examine auditors' performance in the completion of analytical procedures. The results of this study indicate that information order impacts ...

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This solution addresses this question: What data from an ANOVA table contribute to business decision making? Examples are provided.