Statistical errors arise from inaccuracies in data collection, measurement, computation, or interpretation; understanding their types and sources is essential for valid statistical inference and decision-making.
## Core Concept
Statistical errors are deviations between observed values and true values. Unlike mistakes (which are avoidable), errors are inherent to the measurement and estimation process. In CA Foundation, you focus on two main categories:
- Sampling Errors – occur because we study a sample instead of the entire population
- Non-Sampling Errors – occur due to defects in data collection, processing, or analysis regardless of sample size
Both reduce the reliability of statistical conclusions and must be minimized in business data analysis and auditing contexts.
## Types of Statistical Errors
### Sampling Errors - Arise when a sample doesn't perfectly represent the population - Unavoidable when using sampling; can be quantified and estimated - Decrease as sample size increases - Formula for Standard Error of Mean: SE = σ / √n (where σ = population SD, n = sample size) - Example: A survey of 200 customers out of 5,000 to estimate average purchase value will have a sampling error
### Non-Sampling Errors - Occur whether you use a sample or census - Arise from: - Data collection errors: incorrect measuring instruments, bias in data entry, faulty questionnaires - Processing errors: computational mistakes, data entry errors, classification errors - Response errors: false information by respondents, misunderstanding of questions - Non-response errors: missing data from selected units - Coverage errors: wrong population frame, omission of certain units
## Formula / Rule
| Error Type | Cause | Control Method | |---|---|---| | Sampling Error | Sample ≠ Population | Increase sample size; use proper sampling design | | Bias | Systematic deviation in one direction | Randomization; eliminate source of bias | | Measurement Error | Faulty instruments or technique | Calibrate instruments; standardize procedure | | Computational Error | Calculation mistakes | Double-check; use validated software |
Key relationship: Total Error = Sampling Error + Non-Sampling Errors
## Common Exam Applications
- Auditing Context: An auditor sampling 50 invoices out of 1,000 monthly invoices encounters both sampling error (because not all invoices checked) and non-sampling error (if the sample is selected from easily accessible files, introducing bias).
2. Quality Control: A manufacturer testing 100 items per batch of 10,000 will have sampling error reduced by testing more items, but non-sampling errors (faulty testing equipment, recording errors) persist.
3. Survey Data: When estimating employee satisfaction, response bias (employees fear being candid) is a non-sampling error that cannot be eliminated by increasing sample size.
## Worked Example
Question: A company conducts a survey of 400 employees out of 8,000 to estimate average annual leave usage. The population standard deviation is 5 days. Calculate the standard error.
Solution: - SE = σ / √n - SE = 5 / √400 = 5 / 20 = 0.25 days - This means the sample mean may deviate from the true population mean by approximately 0.25 days on average. - To reduce this error, increase n (e.g., at n = 1,600, SE = 0.125 days).
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Note for exam: Non-sampling errors cannot be reduced by increasing sample size—only by improving data collection design, training enumerators, and using validated instruments. Examiners frequently test understanding of this distinction.