Question

A building contractor wants to compare the bids of three DS1120 construction engineers, \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C},\) to determine whether one tends to be a more conservative (or liberal) estimator than the others. The contractor selects four projected construction jobs and has each estimator independently estimate the cost (in dollars per square meter) of each job. The data are shown in the table: Analyze the experiment using the appropriate methods. Identify the blocks and treatments, and investigate any possible differences in treatment means. If any differences exist, use an appropriate method to specifically identify where the differences lie. Has blocking been effective in this experiment? What are the practical implications of the experiment? Present your results in the form of a report.

Short answer

How might this affect the building contractor's decision-making process in selecting an estimator for future projects? Answer: As we do not have the actual data for the estimates, we cannot provide a specific conclusion regarding which estimator appears to be more conservative or liberal in their estimates. However, from the results of the ANOVA test and Tukey's HSD test (if necessary), one can determine if there is a significant difference in the estimators' mean estimate costs. The building contractor can use this information to identify which estimator(s) may be more conservative or liberal in their estimates, and consider the practical importance of these differences when selecting an estimator for future projects.

Step-by-step solution

Identify Blocks and Treatments

The blocks in this experiment are the four projected construction jobs. The treatments are the three different estimators, A, B, and C.

Set Up Null and Alternative Hypotheses

Let's set up our null and alternative hypotheses for the ANOVA analysis. - Null hypothesis (H0): All three estimators have the same mean estimate cost. - Alternative hypothesis (H1): At least one estimator has a different mean estimate cost.

Perform the ANOVA Test

Using the data provided, perform an ANOVA test to compare the means of the three estimators. If the resulting p-value is less than the predetermined significance level (usually 0.05), then we can reject the null hypothesis (H0) and conclude that at least one estimator has a different mean estimate cost.

Perform Tukey's HSD Test (if necessary)

If the ANOVA test results in a significant difference in the means, perform the Tukey's HSD test to specifically identify where the differences lie between the estimators. This test will provide a set of pairwise comparisons between the estimators, highlighting the differences in their mean estimate costs.

Evaluate Blocking Effectiveness

Blocking is the arrangement of experimental units in groups (blocks) that are similar to one another. In this case, the experimental designs can be analyzed to see if blocking has been effective. To do so, compare the variation between the blocks (jobs) to the total variation in the data. If blocking has been effective, the variation between the blocks will be relatively small compared to the total variation.

Discuss Practical Implications

Based on the results of the ANOVA test and Tukey's HSD test (if necessary), discuss the practical implications of the experiment. Which estimator(s) appear to be more conservative or liberal in their estimates? How might this affect the building contractor's decision-making process in selecting an estimator for future projects? Consider the practical importance of the differences found, not only the statistical significance.

Present Your Results in a Report

Summarize your findings in a clear and concise report, discussing the analysis process, the conclusions drawn from the performed tests, the effectiveness of blocking, and the practical implications of the experiment. Make sure to present your results in a manner that is easily understandable for the building contractor.

Key concepts

Blocking in Experimental Design

In the realm of experimental design, blocking is a method used to minimize the effects of variables that the experimenter is not interested in studying. By grouping experimental units into blocks, researchers can control the influence of these extraneous variables. For instance, in our building contractor's experiment, the four projected construction jobs serve as blocks.

Think of each block as a 'bucket' that holds conditions constant. In this case, each bucket is a construction job, which means the job-specific factors like location, materials, and design complexities are held constant within each block. The estimators (A, B, C) then represent the treatments that are compared within these controlled conditions.

Effectively utilizing blocking in an experiment can lead to more accurate results. It's akin to comparing apples to apples in each bucket while ignoring the differences between buckets. The goal is to assess whether the treatment effects (estimator differences) are consistent across these similar conditions. If blocking is effective, it reduces the noise caused by block-related variations, leading to a more precise estimate of the treatment effects.

Cost Estimation Comparison

Comparing cost estimations can be quite challenging due to the inherent variability in each job. In the case of our building contractor, the aim is to discern whether there are consistent differences in the cost estimates provided by the three engineers. An ANOVA (Analysis of Variance) is the statistical tool used for this purpose.

ANOVA assesses the mean differences across multiple groups. Here, the null hypothesis posits that all three estimators give the same average cost, implying no difference in estimating style. If our ANOVA indicates a significant difference in means, then we may reject the null hypothesis, confirming that at least one estimator's average differs from the others.

What does this mean for our contractor? If the estimators indeed provide significantly different bids, it could suggest a more conservative or liberal estimation approach, which is central to project planning and budgeting. The outcome of this cost estimation comparison aids the contractor in understanding estimator tendencies, which is critical for future project estimations and financial planning.

Tukey's HSD Test

When we find that there's a statistical difference in the estimators' bids from the ANOVA, we can't immediately tell which estimator(s) differ from the others. We need a follow-up test to drill down into these differences. Enter Tukey's Honestly Significant Difference (HSD) Test, a post-hoc test directly comparing each pair of means to find where the differences lie.

This test lets us confidently make multiple comparisons without the typical increase in the chance of a Type I error—that is, incorrectly concluding there is a difference when there isn't one. After conducting Tukey's HSD test, we'll get a clear picture of which pairs of estimators' cost estimates are genuinely different from one another.

Working through Tukey's HSD test, our contractor can pinpoint specific estimator pairs that have significantly different estimation habits. This information is highly practical, as it sheds light on estimator behaviors and provides guidance for future engagements with construction engineers for project cost estimations.