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The Statistical methodology

The overall estimates are derived from two different components. Based on a sample of roughly 5,500 enterprises, the program provides detailed financial data on incorporated businesses in Canada in both the financial and non-financial sectors. The sample portion of the survey includes a take-all stratum of the largest corporations based on revenue and assets, along with a sampling of medium sized corporations. Sample results for the medium sized corporations are multiplied by a weighting factor to represent the universe from which the sample was drawn. Data for smaller corporations are estimated by applying a statistical model to predict the value of the take-none portion of the population using the estimates from the surveyed population and other sources. The fact that the data for small businesses are model based results in the estimates being preliminary. The results are subsequently benchmarked to the Annual Financial and Taxation data, when the data becomes available. The proportion of each of the two components of the final estimate (survey and take-none model) varies significantly between industry aggregations. The proportion represented by the survey component ranges from 5% to 100% of the population for both revenue and assets at the Level III (67 categories) aggregation.

(See Text tables 1  and 2  showing the percentage of assets and operating revenue represented by the take-none component for each of the Level 1 ( 22 industry) groups.)

Sample design for the survey component

The frame used for sampling purposes is the Statistics Canada Business Register (BR). A stratified random sample is used. There are two size strata for each of the Level III (67 categories) aggregations (take-all and take-some). All units in the first stratum (take-all) are selected. For the lower stratum (take-some), sampling rates vary by aggregation, but average to about one unit selected in seven. The total sample size is approximately 5,500 enterprises.

Stratum boundaries

The stratum boundaries for the take-all, take-some and take-none strata vary by industry aggregation. The boundaries are available upon request.

Sample weights and imputation for incomplete responses or non-response

Although significant effort and resources are used to maximize response rates, there is always an element of non-response in a statistical survey. Units which do not respond in the current period are imputed (their characteristics are estimated). Units are imputed by applying a growth factor to previously reported data when available. The growth factor is estimated using the survey responses for the units that are most similar to the unit being imputed.

When partial survey data covering three key variables (total assets, operating revenue, operating profit) are received, the imputation factors are calculated at the unit level using these partial data. For records without historical information, a donor imputation system is used. Information on the size of the non-respondent is obtained and a similar sized respondent is found. The size information consists of the three key variables. If this information is not available, the Business Register revenue and asset values are used. In the former situation, the donor record is used to calculate the distribution of the detailed values around the three key variables. In the latter case the donor’s values are directly copied over to the non-respondent. In the case where donor imputation is required for two or more consecutive quarters, a new donor is not reselected. Rather, the imputation factor is applied to the previously imputed data.

The response values for sampled units are multiplied by a sampling weight in order to estimate for the entire surveyed population. The sampling weight is calculated using a number of factors, including the probability of the unit being selected in the sample.

Seasonal adjustment

The seasonal component of a time series reflects sub-annual movements caused by characteristic weather changes, holidays or other factors which tend to recur every year at approximately the same time. The seasonal adjustment process attempts to quantify the seasonal component in a time series and to remove its effect from observed data.

The seasonal adjustment method used is a computerized ratio-to-moving-average method in widespread use at Statistics Canada. It is based on the U.S. Bureau of the Census Method II, but has some additional features. Beginning with the first quarter of 1999, the Quarterly Financial Statistics series uses "end-point" seasonal adjustment, which recalculates seasonal factors each quarter as more recent data becomes available. For a more complete description of these features, refer to "X11ARIMA v. 2000 – Seasonal Adjustment Method Foundations and User’s Manual."

Series containing no significant seasonality have not been seasonally adjusted. In these cases, the unadjusted series are used in the place of seasonally adjusted data.

Data quality

There are two categories of errors in statistical information – sampling errors and non-sampling errors. Sampling errors are errors that arise because estimates are being prepared based on a sample of the universe rather than collecting information from all units in the universe. These errors can be measured.

Non-sampling errors can arise from a variety of sources and are much more difficult to measure. Non-sampling errors include errors in the information provided by respondents, data capture errors and other processing errors.

Sampling errors

Sample surveys are designed to provide the highest sampling efficiency (the smallest sample that will produce a sampling error of a given size). This optimization is usually performed for only a few variables, limited by the data items that are available at the time of sample design and selection, the resources available, and the complexity introduced by trying to optimize for many variables at one time. The sample used for these statistics was designed to produce a reasonable level of accuracy for assets and revenue. Consequently, other items may be less accurately estimated.

A measure of the sampling error is the standard error. This measurement is based upon the idea of selecting several samples, although in reality only one sample is drawn. Sampling variability can also be expressed relative to the estimate itself. The standard error as a percentage of the estimate is called the coefficient of variation (CV), or the relative standard error. Small CVs are desirable, since the smaller the CV, the smaller the sampling variability relative to the estimate.

The sample for the Quarterly Survey of Financial Statistics for Enterprises was drawn such that the CV at the Level III (67 categories) aggregation, should be no more than 10% for operating revenue or total assets. The CV indicators are shown next to these variables in the tables according to the scale presented on page 2.

Estimation errors in the non-sampled strata

Data for smaller corporations are estimated by applying a statistical model to predict the value of the take-none portion of the population using the estimates from the surveyed population and other sources. The error introduced by this method depends on several factors, including the contribution of these strata to the overall estimate and the error in estimating the movement of the stratausing sampled units and other external factors. It is difficult to calculate a coefficient of variation for the non-sampled strata, as the estimates are calculated at the Level III aggregation level only. Therefore, the CV indicator displayed in the publication reflects only the survey portion of the estimate. When the estimate reflects only the take-none portion, there is no CV indicator shown.

Other non-sampling errors

There are no objective measures of other non-sampling errors applied to these statistics. However, most reporting and data entry errors are corrected as a result of the intricate computer capture and edit procedures applied to the data. This is particularly effective for financial data where accounting relationships are established and balancing is required. However, most financial data collected are derived from audited financial statements resulting in minimal errors and inconsistencies. As well, the Quarterly Survey of Financial Statistics for Enterprises utilizes trained accounting staff to capture and analyze reported data to minimize the frequency of non-sampling errors.

One source of non-sampling error is the non-response error. There are several measures that can help the user evaluate this type of error, including the response rate and the data response rate.

The response rate (see Text table 3 ) is a measure of the proportion of those sample units which have responded in time for inclusion in the estimate. To calculate the response rate, one should simply divide the number of actual responses by the total number of sampled units. For example, a sample with 20 active units for which 10 respond for a particular quarter would have a response rate of 50%.

Response rate is:

Figure 1

The data response rate is the proportion of the estimate which is based upon actual reported data. The data response rate can be calculated by dividing the design assets or revenue (or whatever variable is being analyzed) represented by the responding units by the corresponding value for the entire sample. In the previous example, if the 10 responding units have a design asset value totaling $15 billion out of a total sample asset value of $20 billion, the data response rate for assets would be 75%.

(Where the design value is a frame value for the record which is derived from administrative sources and is available for the entire population.)

Data response rate for assets is:

Figure 2

(Where asset values are the design values.)

Weighted data response rates consider that units in sample represent more than themselves through weighting factors. Some units contribute more to the estimates than other units when weights are applied. The weighted data response rate can be calculated by dividing the respondents’ weighted frame value by the weighted sample for assets or revenue (or whatever variable is being analyzed).

In the previous example, if the weighted asset value of the responding 10 units is $40 billion out of a total sample weighted asset value of $50 billion, the weighted asset response rate would be 80%.

Weighted data response rate for assets is:

Figure 3

(Where the weighted assets for a respondent is defined as the design weight multiplied by the design assets value.)

Limitations of the data

To be valid for either time-series or cross-sectional analysis, the definitions of data must be consistent within time periods or across time periods. In other words, the differences and similarities in data must reflect only real differences and not differences in the concepts or definitions used in preparing the data. The ability to use the data for analysis depends on the conceptual framework in which the data are being used.

These data are consistent with the Generally Accepted Accounting Principles (GAAP) of the Canadian Institute of Chartered Accountants. As such, they do not necessarily agree with the concepts used within the Canadian System of National Accounts.

While the GAAP concepts are appropriate for the application of the data, there may still be some problems of consistency (between units or over time) for items where GAAP does not prescribe a particular treatment or allows some latitude. One of the general problems with GAAP for some uses is that it prescribes a historical cost treatment of assets (i.e., their cost at the time of acquisition). As a result, caution should be used when comparing balance sheet data and ratios over time and across industries.

Confidentiality

The confidentiality of the reported statistics to the quarterly survey is protected under the provisions of the Statistics Act. Accordingly, statistics are released in aggregate only, with no potential identification of individually reported information. The confidentiality provisions of the Statistics Act override the provisions of the Access to Information Act to guarantee the confidentiality of reported data of individual respondents.