Impact Study on the RCABC RoofStar Guarantee on Roofing Issues & Claims

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TO EMAIL

REGARDING

Mr. Judy Slutsky judy@rcabc.org RCABC Guarantee Corp. 9734 - 201st Street Langley, BC, V1M 3E8

8985.000 RCABC Claim Research Phase 1 Research DATE

September 8, 2015

Study of the Impact of the RCABC RoofStar Guarantee on Roofing Issues & Potential Warranty Claims Dear Mr. Slutsky, As requested by RCABC Guarantee Corp., RDH Building Engineering Ltd. (RDH) has performed an analysis to assess the impact of the RCABC RoofStar Guarantee on roofing issues and potential warranty claims for flat roofs in the Lower Mainland of BC. This analysis was performed utilizing RDH’s building asset management database in conjunction with information provided for matching buildings from RCABC. This letter provides a summary of the key findings of the study, with more detailed information within the attached appendix. Recommendations for next steps and further analysis are also provided.

Introduction The service life of a roof is dependent on a number of factors including but not limited to: climate and environmental conditions, materials selection, detailing, traffic & use, workmanship, and maintenance. These factors are well understood and documented within the roofing industry. In addition to these factors, risk management through third party roof warranty or guarantee programs such as the RCABC RoofStar Guarantee program can also be considered, as participation in these programs drives many decisions related to quality of workmanship, materials selection, and maintenance. In order to study the impact of the RCABC program on the frequency of roofing issues and potential claims, independent research was performed by RDH Building Engineering Ltd. (RDH) to evaluate the in-service performance of comparable roofs with and without an RCABC guarantee. This analysis was performed for several hundred flat roofs in the Lower Mainland of BC over their first 10 years of life - both with and without an RCABC guarantee. The population of roofs for analysis were taken from RDH’s internal building asset database, which contains observations for over eight-hundred buildings. The statistical approach was also compared to the claims history of another 3rd party building enclosure warranty program in place in BC during the same period. The primary focus of Phase 1 of the research study was to analyze the relationship between the presence of the risk managed RCABC guarantee and the risk of roofing problems or potential claims during the active guarantee period (5 to 10 years). A later phase of the study will evaluate the financial implications of these roofing issues and review the claims plus roofing maintenance, repair, and replacement costs for this population of RCABC and

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non-RCABC roofs. This information helps to quantify the benefits of the RCABC guarantee to other 3rd party warranty providers, developers, and owners.

Methodology RDH is an engineering firm with six offices across the Pacific Northwest specializing in the evaluation, design, repair, construction, and research of building enclosures including roofs. Through the

course

of

condition

assessments, warranty reviews, claims

investigations, depreciation reports, and new construction projects RDH’s engineers, technologists, and roof inspectors actively review and input observations on the performance of various building enclosure assets into our proprietary database. This database contains hundreds of thousands of unique asset observations for hundreds of buildings. Specific to roofs, this database includes visual observations and photos for each roof asset along with service life estimates and recommendations including cost estimates for necessary maintenance, repairs, or renewals. The buildings and roofs within the database are geographically based in the Lower Mainland and range in size, type and age. The majority of buildings within the database are multi-unit residential buildings (both noncombustible and wood-frame) largely due to the majority of RDH’s reviews being performed for strata corporations during 3rd party warranty reviews, condition assessments, or depreciation reports. The RCABC Roofstar guarantee program was initiated in 1960 and therefore a large number of buildings within the Lower Mainland of various ages and roof types have been covered by the program. Many of these roofs also happen to be contained at random within the RDH database. By combining the pertinent roofing related information from the RCABC and RDH databases, analysis of the performance of RCABC and non-RCABC roofs can be performed. To determine which of the roofs within RDH’s database were constructed under the RCABC guarantee program, a list of addresses for buildings with flat roofs from the RDH database was provided to RCABC to determine which of those roofs were covered by the RCABC guarantee program database. No confidential building information was exchanged. The list of matches was then provided to RDH for the analysis creating a database of RCABC and non-RCABC covered roofs. Phase 1 of this study focuses on the population of flat roofs (low-slope of less than 2:12) with predominantly 2-ply SBS membranes, but also some with liquid applied and single ply (i.e. PVC, TPO, and EPDM) roof membranes. All of the roofs were 10 years of age or less at the time of review by RDH staff or RCABC inspectors. Reviews were performed at various times over the life of the roofs, typically before milestone warranty expiry dates or during other reviews.

Analysis & Results As of June 2015, there are a total of 2024 buildings within the RDH database. For 838 of these buildings, detailed observations and photos have been entered into the database during various building enclosure assessments and reviews. Of these buildings, 267 have flat roofs which was less than 10 years of age at the time of our review. Addresses for these 267 flat roofs were flagged and provided to RCABC for cross reference. Based on the review of these buildings it was determined that 139 of these 267 flat roofs (52%) had an RCABC

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guarantee in place and 128 (48%) did not (Figure 1). This alone is a useful statistic that demonstrates the prevalence of the RCABC program within the local marketplace. Distribution of Buildings in Database covered by RCABC Guarantee (267 Total)

To determine if the roofs within these two databases had observed issues or potential claims we then analyzed the observation data entered by various trained RDH staff into the database

and

sorted

between

potentially

warrantable issues and non-warrantable. When

NonRCABC 128 48%

RCABC 139 52%

roofing observations are entered into the database a condition criticality is also assessed for each observation ranging from normal maintenance tasks like drain cleaning and minor flashing repairs to more critical items such as roof

leaks/staining,

failed

or

damaged

Figure 1: Distribution of Buildings in Database covered by RCABC Guarantee (267 Buildings Total)

membranes, or severe ponding. To perform our analysis, only critical items were then flagged as “warrantable issues” and other non-critical roofing maintenance or repairs were considered as “maintenance issues” and not counted in the analysis here. The observations for each building were then counted and the number of buildings with roofing issues were totalled in each dataset. If there are multiple roofing issues reported at one building it is only counted once to avoid skewing the data. The items recorded by RDH as roofing issues may or may not result in a warranty claim and the translation of these issues into claims made can only be performed with more information and this analysis is recommended as part of Phase 2 of this research. Anecdotal evidence suggests that many roofing problems, even critical ones that shorten the service life of the roof, may go unrepaired for years. Many more may be addressed by the contractor or owner directly without even involving the warranty provider. The results of this data analysis (Figure 2), demonstrate that non-RCABC roofs have a 36% chance of having at least one roofing issue in the first ten years of life, whereas the RCABC Guarantee roofs have only a 21% chance of a roofing issue in the same time frame. This indicates that on a statistical basis, the presence of the RCABC Guarantee reduces the chance of warrantable roofing issues by approximately 42%. It is expected that the number of warrantable claims made as a result of these issues would be proportional to this figure: however, further analysis is required to estimate cost impacts and review the claims history for these RCABC roofs. To confirm that the available sample of roof information provides a statistically significant result, a chi-squared test was conducted. This test determined at a 95% confidence level that the presence of an RCABC warranty does impact the frequency of roofing issues.

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Number of Buildings with Roofing Issues RCABC Roofs

Number of Buildings with Roofing Issues Non-RCABC Roofs

21%

36% 64% 79%

Buildings With Observed Warrantable Roofing Issues (<10 yrs)

Buildings With Observed Warrantable Roofing Issues (<10 yrs)

Buildings With No Observed Roofing Issues (<10 yrs)

Buildings With No Observed Roofing Issues (<10 yrs)

Figure 2: Comparison of observed warrantable issues with flat roofs on Non-RCABC and RCACB

Program buildings in the RDH database. Population of 267 buildings, 52% having RCABC Roofstar Guarantee (139 buildings) and 48% without (128 buildings).

Comparison of Approach with Other Risk Managed Programs Building enclosure and roofing warranties are common for many buildings. Residential buildings in BC are required to have 3rd party warranty coverage (i.e. HPO mandated 2-5-10 coverage). Non-residential buildings may or may not have warranty coverage. There are several types of roofing warranties available including: 3rd party risk managed programs like the RCABC Guarantee, indemnity based warranty programs, and manufacturer’s material warranties, contractor warranties. In addition, buildings may be covered against roof issues for up to 2 years using traditional bond products. As part of this study, a similar assessment was performed on observed building enclosure and roofing issues for another risk managed 3rd party building enclosure warranty program. RDH was primarily involved with the building enclosure risk management portion of this warranty program by performing independent peer reviews of designs and additional field reviews during the course of construction. The purpose of this assessment was to validate the statistical approach and assess the impact of upfront design and construction risk management performed as part of warranty/guarantee programs to reduce the number of building enclosure and roofing issues and potential for future claims. Based on RDH’s experience with both parties, it can be stated that RCABC takes a similar risk management approach to this 3rd party warranty provider, therefore like the RCABC data, less frequent building enclosure issues and claims should be seen in their warrantied buildings than in the larger population as a whole. During this review, all building enclosure (wall, below-grade, window, skylight, roofing etc.) issues were assessed separate from roofing issues to better understand the proportion of roofing issues on a typical building. The first part of the assessment looked at a population of 304 buildings in the Lower Mainland of BC contained within a separate database for the 3 rd party warranty provider. Within this database we have a detailed history of the building enclosure claims information for this population of buildings. In a review of claims history for these 304 buildings, warrantable building enclosure claims of various sizes were made at 21% of the buildings.

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Roofing claims including waterproofing and planters represented 5% of the total (16% other building enclosure). Interestingly because of RDH’s involvement in the risk management, the warranty provider required the roofing to conform to the technical requirements of the RCABC 10 year warranty requirements - even though these buildings did not utilize a RCABC Guarantee.

What this database cannot show is how the number of observed building

enclosure or roofing issues (as observed from the RCABC analysis) translates into actual claims made. The second part of the assessment looked at the relationship between total building enclosure and separate roofing related observations within the population of 267 buildings with flat roofs (both RCABC and non-RCABC). Previously it was determined that warrantable roofing issues were found on 21% of the RCABC roofs versus 36% for the non-RCABC roofs. The interesting finding from the analysis here is that the percent of buildings with any warrantable building enclosure issue (walls, windows, below-grade etc.) was 54% for buildings with an RCABC roof and 55% for buildings with a non-RCABC roof, demonstrating that on the whole the buildings in both population sets are similar. This further reinforces the impact that the RCABC Guarantee has made on the roofs of many buildings

Conclusions & Next Steps The results of our analysis within Phase 1 of our study shows that the risk managed RCABC Roofstar Guarantee program has greatly reduced the number of roofing issues and potential warranty claims on projects when it has been used. Since 1960, the RCABC Roofstar Guarantee program has influenced the performance of tens of thousands of roofs across British Columbia. In our analysis of a random population of 267 flat roofs that were under 10 years of age when reviewed by RDH, 52% of these roofs were covered under the RCABC Roofstar Guarantee, which highlights the great uptake of the program. An in-depth comparison of physical reviews and observations performed by RDH for these 139 RCABC and 128 non-RCABC roofs found that 37% of the non-RCABC roofs had at least one observed warrantable roofing issue whereas 21% of the RCABC roofs had at least one warrantable roofing issue. This indicates that the presence of the RCABC Guarantee program reduced the warrantable roofing issues by up to 42%. The analysis demonstrates that the RCABC Guarantee program appears to have reduced the number of roofing issues and likelihood of claims on flat roofs in the Lower Mainland of BC as compared to roofs built without the guarantee. Further analysis as part of Phase 2 of this study is recommended to evaluate the financial implications of these roofing issues and review the claims history for these roofs. Yours truly,

Graham Finch | MASc, P.Eng Principal, Building Science Research Specialist gfinch@rdh.com RDH Building Engineering Ltd.

Brian Hubbs | P.Eng Managing Principal, Senior Building Science Specialist bch@rdh.com RDH Building Engineering Ltd.

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Appendix: RCABC Guarantee Program Assessment Methodology & Data Analysis

Contents 1

Background

1

1.1

Purpose

1

1.2

Methodology

1

2

Datasets

2

2.1

BAMS (Building Asset Management Software)

2

2.2

Warranty Program

4

2.3

RCABC Program

5

2.4

Determination of the Datasets

5

3

Analysis

8

3.1

3rd Party Building Envelope Warranty Program Dataset 1

8

3.2

RCABC Program Buildings in BAMS Dataset2

8

3.3

NON - RCABC Program Buildings in BAMS Dataset 3

10

3.4

Chi-Squared Analysis

11

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1

Background

1.1

Purpose

RDH Building Engineering Ltd. (RDH) was engaged by Roofing Contractors Association of British Columbia (RCABC) to provide an independent review of their roofing guarantee program (RCABC Program). Ideally RCABC wished to have the following answered: 

Provide information regarding other similar warranty / Guarantee programs and evaluate the success rates of these programs.

Provide an independent review of buildings within the RCABC Program to evaluate their performance and success rates.

Provide a review of buildings not contained within the RCABC Program to evaluate their performance and success rates.

Compare the programs to validate if the RCABC Program has an impact on the performance and success rates of the buildings roofing systems.

1.2

Methodology

RDH is an engineering firm specialising in the construction and science behind building enclosures. RDH has participated in numerous building reviews evaluating the performance of buildings. In order to accomplish these tasks RDH has developed an internal documentation system called Building Asset Management Software (BAMS). Our proposed methodology for evaluating the RCABC Program is to compare the buildings contained within BAMS against the dataset of RCABC Program buildings. The first dataset would be buildings evaluated in the RCABC Program that are contained within BAMS. The second dataset would be buildings that were not evaluated in the RCABC program that are contained within BAMS. The data within BAMS is collected for numerous purposes, some are consistent with the information that we are looking for within this review. While others buildings within BAMS are primarily financially driven with no observed issues. The BAMS dataset will have to be refined in order to isolate for information pertaining to the RCABC Program. Prior to the development of BAMS RDH was a participant in a 3rd Party Warranty Program in which RDH reviewed, documented and assessed risk for a warranty provider. The information was collected and retained in a database in order to be consistently evaluated and so that follow up information could be noted and recorded. One of the follow ups was to record any issues with the buildings enclosures during the warranty program that resulted in a claim. This Warranty Program information will be utilised as validation of the RCABC Program. This Warranty Program will establish our baseline for the program.

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2

Datasets

BAMS is the database that we will use to evaluate the RCABC Program. In order to accomplish this task we will separate the BAMS information into two distinct datasets. Not only do we need the information from the two BAMS datasets but we also require a third baseline dataset. The third baseline dataset was collected independent from the RCABC program and BAMS to determine what other comparable programs are achieving. In order to accomplish the validation requested we require three distinct datasets 1)

3rd Party Building Envelope Warranty Program Information is pulled from 3rd Party Building Envelope Warranty Program database, in order to evaluate a baseline.

2)

RCABC Program Buildings in BAMS Information is pulled from BAMS in order to evaluate buildings that are contained within the RCABC Program.

3)

Non - RCABC Program Buildings in BAMS Information is pulled from BAMS in order to evaluate buildings that are outside and not contained within the RCABC Program.

Overlap of the datasets may exist between dataset 1 and the other two. Dataset 2 and 3 are distinct.

2.1

BAMS (Building Asset Management Software)

BAMS is an integrated online asset management software. RDH has developed BAMS in order to collect information and perform services. The software is an online platform system used to record, track and monitor building information pertaining to RDH’s projects.

2.1.1

Data Organization

Within BAMS the data is organized in a normalized database. The information used to review the RCABC Program is as follows 

Portfolio Portfolios are groups of buildings. Each portfolio can contain many buildings, and each building can be assigned to many portfolios.

Building Information Building information is stored in the building entity. The building entity contains the size, location, occupancy type, replacement cost and numerous other variables.

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Figure 2.1 Sample of Building Information ďƒ

Building Component Information Building Component information is stored in the asset entity. An Asset (Building Component) is a distinct construction type, product, installation and location (eg. On one building we could have 2 roof assets, 1) Two ply SBS roof and, 2) Sloped metal roofing). Assets are linked directly to one specific building. The information stored in the Asset entity consists of size, cost, type, image, age and numerous other variables.

Figure 2.2 Sample of Asset, 2 Ply SBS Roof ďƒ

Observation Information (Deficiency) Observation information is stored in the deficiency entity. Observations are linked directly to one specific asset. Observations are deficient conditions or activities that are not being performed. These observations are always negative, as in missing, broken or not performing adequately. We at RDH do not collect positive information such as the roof is performing adequately, the lack of observations would indicate that the asset (building component) is performing adequately.

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Figure 2.3 Sample of Roof Observation, Ridging

Figure 2.4 Sample of Roof Observation, Drain damage Data Collection The data collection for BAMS was performed during routine work for RDH services. This information was typically collected on behalf of the owners, or property managers for the facility.

2.2

Warranty Program

RDH was involved with a warranty provider and collected information pertaining to a Warranty Program that was performed between 1999 and 2013. RDH was providing independent reviews of the construction of the facilities to advise and address any risk issues with the project on behalf of the warranty provider. RDH provided reviews prior, during and post construction. RDH was notified of information pertaining to claims that were assigned on each building within the program. This information was collected and evaluated for the purposes of the RCABC Roofing Claim Research. The following table is a sample of the information contained within the Warranty program. The information outlines the types of reviews and when each review was performed for each project. The name of the facilities have been removed.

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Figure 2.5 Sample of Warranty Program information

2.3

RCABC Program

RDH has not been provided with a full list of the RCABC program buildings. RDH provided the buildings list for both BAMS and for the warranty program buildings (including Name and Address), in order for RCABC to match the buildings to their RCABC Program Building list. RCABC provided this information to RDH in order to proceed with the evaluation process.

2.4

Determination of the Datasets

In order to provide information accurately and independent from the RCABC Program, RDH determined to only use the information that was contained within the RDH software both Warranty Program Database and the BAMS Database.

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Figure 2.6 Data integration graphic

2.4.1

Warranty Program Database, Data Isolation Dataset 1

The Warranty program database was evaluated and reviewed to ensure that the dataset was acceptable the following issues were found 

Claim information was only collected in regards to the Building Enclosure reviews. 

Elimination of the structural reviews was performed

Removed buildings that the claim was either cancelled or put on hold, since no claim information was provided for these buildings.

Claims information was collected separately from the database, and was added to the information.

The counts provided pertained to the building and did not distinguish the level of the claim. If a building had a singular (or multiple) claim this was recorded as a single positive result.

After the isolation was performed the warranty program information was considered as the independent industry accepted program for evaluation (Dataset 1).

Figure 2.7 Warranty Program Graphic

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2.4.2

BAMS Database, Data Isolation Dataset 2 and 3

The BAMS database was evaluated and reviewed. The BAMS information was separated into two distinct datasets, those that are linked to an RCABC program and those that are not. The information in BAMS was also isolated in order to perform a review on buildings that would contain the information that RCABC Program would have had an impact. The following is the isolation that was performed, (once the isolation was performed we placed all of these buildings into portfolios so that the building count would not change, since BAMS is a live system). 

Isolated buildings to only include buildings that contained observations. The observations could be on any enclosure asset, 

If there was an observation this would indicate that a building review was performed as a portion of the RDH service.

Isolated building to only include buildings with at least one flat roof.

Isolated building to only include buildings with at least one flat roof that was less than ten years old.

Figure 2.8 BAMS Data Graphic Once we had the isolation for buildings that were acceptable. We isolated the information between those buildings that were contained in the RCABC program and those that weren’t, providing us with Dataset 2 and 3.

Figure 2.9 Dataset 2 and 3 Graphic representation 8985.000

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3

Analysis

3.1

3rd Party Building Envelope Warranty Program Dataset 1

We isolate the warranty information and analysed the dataset. The following was our findings. TABLE 3.1 WARRANTY PROGRAM ANALYSIS DATASET 1 Total number of buildings in warranty program

304

Total number of buildings with a claim in the warranty program

64

Percentage of buildings with a building envelope claim

21.0%

Total number of buildings with a roofing claim in the warranty program

15

Percentage of buildings with a roofing claim

4.9%

The process for reviewing in both the RCABC program and warranty program are similar and comparable.

3.2

RCABC Program Buildings in BAMS Dataset2

The BAMS information was compiled and isolated in order to provide the most accurate list of buildings possible to the team. We have isolated the information such that it is only valuating buildings with either new or existing flat roof installations performed within the last 10 years. We have also only declared an issues if it meets the following criteria. 

Priority had to be defined as high importance, requiring the activity to be performed within the next 3 years. The following is the standard RDH priority levels, as an example

“1 – Currently Critical”

Would be considered an issue.

“2 – Potentially Critical” Would be considered an issue.

“3 – Necessary”

Would NOT be considered an issue.

“4 – Recommended”

Would NOT be considered an issue.

“5 – Grandfathered”

Would NOT be considered an issue.

The review type would have to be considered either 

WR – Warranty

CA - Condition Assessment

Some examples of issues that would be considered issues are,

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Figure 3.1 Sample of Observations, Blistering

Figure 3.2 Sample of Observations, Lack of slope

Figure 3.3 Sample of Observations, Unprotected memberane terminations

Figure 3.4 Sample of Observations, Water ingress below roofing Some of the standard failure mechanisms that were noted in the review of the roofs were; 

Exposed membrane; cracking of membrane due to exposure.

Staining below the roof in drywall and exterior wall elements.

Failed, missing or deteriorated sealant.

Ridging of the membrane.

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Unadhered or debonded membrane.

Missing roof jacks.

Ponding water.

Discontinuous membrane.

These were the typical issues that were found within both datasets of roofs (RCABC program buildings in BAMS and Non-RCABC program buildings in BAMS). The counts provided are for RCABC program buildings in BAMS dataset. TABLE 3.2 RCABC PROGRAM BUILDINGS IN BAMS DATASET 2 Total number of buildings in Dataset

139

Total number of buildings with a roofing issue

29

Percentage of buildings with a roofing issue

20.9%

Total number of buildings with a building enclosure issue

75

Percentage of buildings with a building enclosure issue

54.0%

This would indicate that the buildings within the RCABC program will have an issue approximately 21 % of the time. This also matches our findings for the Warranty Program. RCABC requested that we remove 3rd Party Warranty Program items from the dataset. TABLE 3.3 RCABC PROGRAM BUILDINGS IN BAMS WITHOUT 3RD PARTY WARRANTY PROGRAM SUBSET OF DATASET 2 Total number of buildings in Dataset

134

Total number of buildings with a roofing issue

29

Therefore percentage of buildings with a roofing issue is

21.6%

Total number of buildings with a building enclosure issue

74

Percentage of buildings with a building enclosure issue

55.2%

If we remove the warranty program from the RCABC Program Buildings in BAMS our value increases to 22%.

3.3

NON - RCABC Program Buildings in BAMS Dataset 3

The final dataset that we analysed is BAMS information that is not associated to the RCABC Program. This dataset has been developed exactly the same way as the previous section “RCABC Program Buildings in BAMS”, with the exception that these are the values that are not associated with the RCABC Program. The counts provided, are for buildings and does not delineate the severity or replacement cost implications. TABLE 3.4 NON - RCABC PROGRAM BUILDINGS IN BAMS DATASET 2 Total number of buildings in Dataset

128

Total number of buildings with a roofing issue

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TABLE 3.4 NON - RCABC PROGRAM BUILDINGS IN BAMS DATASET 2 Therefore percentage of buildings with a roofing issue is

35.9%

Total number of buildings with a building enclosure issue Percentage of buildings with a building enclosure issue

70 54.7%

This would indicate that the buildings that were not in the RCABC program would have an issue 36% of the time. The warranty program information was also removed from the third dataset. TABLE 3.5 NON - RCABC PROGRAM BUILDINGS IN BAMS WITHOUT 3 RD PARTY WARRANTY PROGRAM SUBSET OF DATASET 2 Total number of buildings in Dataset

115

Total number of buildings with a roofing issue Therefore percentage of buildings with a roofing issue is

43 37.4%

Total number of buildings with a building enclosure issue Percentage of buildings with a building enclosure issue

63 54.8%

When the warranty dataset was removed from the previous non-RCABC program roofs the issue rate increased to 37%. From the analysis the difference between providing the RCABC program and not providing the RCABC program is an absolute difference of 15% (or 42% reduction in issues with RCABC). If the 3rd Party Warranty Programs were removed from the subsets, the difference increases to 16%. The RCABC Guarantee program has significantly impacted the performance and reduced the number of roofing issues on buildings. When we compare the building enclosure issue, we note that the percentages of issues match between both datasets. The issue rate is 55% of the buildings, within both the RCABC program buildings in BAMS and non-RCABC program buildings in BAMS.

3.4

Chi-Squared Analysis

To evaluate whether there is statistically significant dependence between the presence of an RCABC warranty and the frequency of roof issues, a Chi-Squared (Χ²) test was performed on the sample data. To perform this analysis first it is stated that the null hypothesis is: ďƒ

The presence of an RCABC warranty does not impact the frequency of roof issues.

To facilitate analysis of the data it is arranged into a grid with the rows being the presence of roof issues and the columns being the presence of an RCABC warrant. This grid is shown in Table 3.6. A number of analysis steps were then completed to assess the relationship between roof issues and the presence of an RCABC warranty. Step 1: Calculate the Degrees of Freedom (DF) Degrees of freedom is a measure of the possible variation in results based on the number of independent variables.

đ??ˇđ??š = (đ?‘&#x;đ?‘œđ?‘¤đ?‘ − 1) ∙ (đ?‘?đ?‘œđ?‘™đ?‘˘đ?‘šđ?‘›đ?‘ − 1) = (2 − 1) ∙ (2 − 1) = 1

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Step 2: Calculate the Expected Values The expected value for each result is the number of occurrences of a particular result given that the odds of each result are equal. These values are calculated as if the columns and rows are independent.

đ?‘›đ?‘&#x;đ?‘– ∙ đ?‘›đ?‘?đ?‘— đ?‘› Example Calculation for Expected Value of Row 1, Column 1 (Roof Issue, Non-RCABC): đ?‘›đ?‘&#x;1 ∙ đ?‘›đ?‘?1 72 ∙ 128 đ??¸đ?‘&#x;1,đ?‘?1 = = = 34.5 đ?‘› 267 đ??¸đ?‘Ľđ?‘?đ?‘’đ?‘?đ?‘Ąđ?‘’đ?‘‘ đ?‘‰đ?‘Žđ?‘™đ?‘˘đ?‘’ đ?‘“đ?‘œđ?‘&#x; đ?‘&#x;đ?‘œđ?‘¤ đ?‘– đ?‘Žđ?‘›đ?‘‘ đ?‘?đ?‘œđ?‘™đ?‘˘đ?‘šđ?‘› đ?‘— = đ??¸đ?‘&#x;đ?‘–,đ?‘?đ?‘— =

TABLE 3.6 OBSERVERED AND EXPECTED RESULTS Non-RCABC Roof Issue No Roof Issue Total

RCABC

43

(Observed)

29

(Observed)

34.5

(Expected)

37.5

(Expected)

85

(Observed)

110

(Observed)

93.5

(Expected)

101.5 (Expected)

128

139

Total 72 195 267

Step 3: Calculate Chi-Squared The Chi-square value is based on the difference between the observed and expected values, and is used to indicate how much the observed results vary from the expected results if the odds of each outcome are equal.

đ?‘‚đ?‘&#x;đ?‘–,đ?‘?đ?‘— = đ?‘‚đ?‘?đ?‘ đ?‘’đ?‘&#x;đ?‘Łđ?‘’đ?‘‘ đ?‘‰đ?‘Žđ?‘™đ?‘˘đ?‘’ đ?‘“đ?‘œđ?‘&#x; đ?‘&#x;đ?‘œđ?‘¤ đ?‘– đ?‘Žđ?‘›đ?‘‘ đ?‘?đ?‘œđ?‘™đ?‘˘đ?‘šđ?‘› đ?‘— 2

(đ?‘‚đ?‘&#x;đ?‘–,đ?‘?đ?‘— − đ??¸đ?‘&#x;đ?‘–,đ?‘?đ?‘— ) đ?›¸ =∑ đ??¸đ?‘&#x;đ?‘–,đ?‘?đ?‘— 2

�2 =

(43 − 34.5)2 (29 − 37.5)2 (85 − 93.5)2 (110 − 101.5)2 + + + = 5.48 34.5 37.5 93.5 101.5

Step 4: Reject/Accept Null Hypothesis and Determine Significance Using the calculated degrees of freedom (1) and the calculated Chi-Squared value (5.48) we can use tabulated significance levels to determine a significant level of 0.02 for the given analysis. Based on this result, we reject the null hypothesis and find that the presence of an RCABC warranty does impact the frequency of roof issues at a confidence level of at least 95%. In other words, we can be more than 95% certain that the presence of an RCABC warranty impacts the frequency of roof issues.

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