Errors in Statistics: A Comprehensive Guide

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To learn about errors in statistics, we first need to understand the concepts related to true value, accuracy, and precision. Let us start with these basic concepts.

True Value

The true value is the value that would be obtained if no errors were made in any way by obtaining the information or computing the characteristics of the population under study.

The true value of the population is possible obtained only if the exact procedures are used for collecting the correct data, every element of the population has been covered and no mistake or even the slightest negligence has happened during the data collection process and its analysis. It is usually regarded as an unknown constant.

Accuracy

Accuracy refers to the difference between the sample result and the true value. The smaller the difference the greater will be the accuracy. Accuracy can be increased by

  • Elimination of technical errors
  • Increasing the sample size

Precision

Precision refers to how closely we can reproduce, from a sample, the results that would be obtained if a complete count (census) was taken using the same method of measurement.

Errors in Statistics

The difference between an estimated value and the population’s true value is called an error. Since a sample estimate is used to describe a characteristic of a population, a sample being only a part of the population cannot provide a perfect representation of the population (no matter how carefully the sample is selected). Generally, it is seen that an estimate is rarely equal to the true value and we may think about how close will the sample estimate be to the population’s true value. There are two kinds of errors, sampling and non-sampling errors.

  • Sampling error (random error)
  • Non-sampling errors (nonrandom errors)

Sampling Errors

A sampling error is the difference between the value of a statistic obtained from an observed random sample and the value of the corresponding population parameter being estimated. Sampling errors occur due to the natural variability between samples. Let $T$ be the sample statistic and it is used to estimate the population parameter $\theta$. The sampling error may be denoted by $E$,

$$E=T-\theta$$

The value of the sampling error reveals the precision of the estimate. The smaller the sampling error, the greater will be the precision of the estimate. The sampling error may be reduced by some of the following listed:

  • By increasing the sample size
  • By improving the sampling design
  • By using the supplementary information

Usually, sampling error arises when a sample is selected from a larger population to make inferences about the whole population.

Errors in Statistics, Sampling Error

Non-Sampling Errors

The errors that are caused by sampling the wrong population of interest and by response bias as well as those made by an investigator in collecting, analyzing, and reporting data are all classified as non-sampling errors (or non-random errors). These errors are present in a complete census as well as in a sampling survey.

Bias

Bias is the difference between the expected value of a statistic and the true value of the parameter being estimated. Let $T$ be the sample statistic used to estimate the population parameter $\theta$, then the amount of bias is

$$Bias = E(T) – \theta$$

The bias is positive if $E(T)>\theta$, bias is negative if $E(T) <\theta$, and bias is zero if $E(T)=\theta$. The bias is a systematic component of error that refers to the long-run tendency of the sample statistic to differ from the parameter in a particular direction. Bias is cumulative and increases with the increase in size of the sample. If proper methods of selection of units in a sample are not followed, the sample result will not be free from bias.

Note that non-sampling errors can be difficult to identify and quantify, therefore, the presence of non-sampling errors can significantly impact the accuracy of statistical results. By understanding and addressing these errors, researchers can improve the reliability and validity of their statistical findings.

Errors in Statistics: Potential Sources of Error

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Important MCQs Multivariate Quiz 5

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The post is about the MCQs Multivariate Quiz. There are 25 multiple-choice questions about Multivariate Analysis of Variance (MANOVA), its introduction, assumptions, interpretation, and real-life application. Let us start with the MCQs Multivariate Quiz.

Online multivariate statistics and Manova MCQs

1. Which statistical technique is most similar to MANOVA?

 
 
 
 

2. In which of the following conditions can MANOVA be used? Check all possible options.

 
 
 
 

3. In one-way MANOVA, which variable must be continuous?

 
 
 
 

4. What use do multivariate analyses of variance have, if any?

 
 
 
 

5. An educational psychologist studies the influence of a child’s gender and their parent’s job on a number of behavioral outcomes. Based on the MANOVA output, which dependent variables affected the child’s gender?

 
 
 
 

6. In MANOVA, there are:

 
 
 
 

7. What would this be interpreted as if Box’s M had an associated P-value of < 0.05?

 
 
 
 

8. An educational psychologist studies the influence of a child’s gender and their parent’s job on a number of behavioral outcomes. Based on the MANOVA output, for which of the following dependent variables was there an interaction effect?

 
 
 
 

9. MANOVA:

 
 
 
 

10. The problem of multiple comparisons is dealt with in MANOVA by:

 
 
 
 

11. Which F-value is typically reported in a MANOVA?

 
 
 
 

12. Which of the following is true?

 
 
 
 

13. Which of the following is true?

 
 
 
 

14. What problem is associated with correlated DVs?

 
 
 
 

15. Which of the following has the closest relationship with MANOVA?

 
 
 
 

16. An educational psychologist studies the influence of a child’s gender and their parent’s job on a number of behavioral outcomes. Based on the MANOVA output, which of the following is true?

 
 
 
 

17. The Hotelling multivariate $t^2$:

 
 
 
 

18. In MANOVA:

 
 
 
 

19. An educational psychologist studies the influence of a child’s gender and their parent’s job on a number of behavioral outcomes. Based on the MANOVA output, how many dependent variables are used?

 
 
 
 

20. How does MANOVA handle the DVs in the analysis?

 
 
 
 

21. Which of the following statements is true of MANOVA?

 
 
 
 

22. Where would you find the option for repeated measures MANOVA in SPSS?

 
 
 
 

23. What would you use Box’s M test for?

 
 
 
 

24. If MANOVA is statistically significant:

 
 
 
 

25. MANOVA can lose degrees of freedom:

 
 
 
 

Online MCQs Multivariate Quiz with Answers

MCQs Multivariate Quiz with Answers
  • Which statistical technique is most similar to MANOVA?
  • Which of the following has the closest relationship with MANOVA?
  • In MANOVA, there are:
  • In multivariate analysis of variance (MANOVA):
  • The problem of multiple comparisons is dealt with in MANOVA by:
  • MANOVA can lose degrees of freedom:
  • Which of the following is true?
  • The Hotelling multivariate $t^2$:
  • MANOVA:
  • If MANOVA is statistically significant:
  • Which of the following is true?
  • An educational psychologist studies the influence of a child’s gender and their parent’s job on a number of behavioral outcomes. Based on the MANOVA output, how many dependent variables are used?
  • An educational psychologist studies the influence of a child’s gender and their parent’s job on a number of behavioral outcomes. Based on the MANOVA output, which of the following is true?
  • An educational psychologist studies the influence of a child’s gender and their parent’s job on a number of behavioral outcomes. Based on the MANOVA output, which dependent variables affected the child’s gender?
  • An educational psychologist studies the influence of a child’s gender and their parent’s job on a number of behavioral outcomes. Based on the MANOVA output, for which of the following dependent variables was there an interaction effect?
  • How does MANOVA handle the DVs in the analysis?
  • What would this be interpreted as if Box’s M had an associated P-value of < 0.05?
  • What problem is associated with correlated DVs?
  • What use do multivariate analyses of variance have, if any?
  • What would you use Box’s M test for?
  • Where would you find the option for repeated measures MANOVA in SPSS?
  • Which F-value is typically reported in a MANOVA?
  • Which of the following statements is true of MANOVA?
  • In which of the following conditions can MANOVA be used? Check all possible options.
  • In one-way MANOVA, which variable must be continuous?
Statistics Help

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Important MCQs Nonparametric Quiz 1

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The post is about MCQs nonparametric quiz. There are 22 multiple-choice questions covering different nonparametric tests such as Wilcoxon rank sum test, Spearman’s Rank Correlation test, Mann-Whitney U test, Sign test, Runs Test, Kruskal Wallis test, and Chi-Square goodness of fit test. Let us start with the MCQs nonparametric Quiz.

Please go to Important MCQs Nonparametric Quiz 1 to view the test

Online MCQs Nonparametric Quiz with Answers

MCQs nonparametric test
  • The Wilcoxon rank-sum test can be
  • The Wilcoxon rank-sum test compares
  • The Wilcoxon signed rank is used
  • Which of the following test use rank sums?
  • Which of the following tests must be two-sided?
  • In testing for the difference between two populations, it is possible to use
  • In a Wilcoxon rank-sum test
  • The Spearman rank-correlation test requires that the
  • The sign test is
  • The nonparametric equivalent of an unpaired samples t-test is
  • The Mann-Whitney U test is preferred to a t-test when
  • When using the Sign test, if two scores are tied, then we
  • The sign test assumes that the samples are
  • When testing for randomness, we can use
  • The Runs test results in rejecting the null hypothesis of randomness when:
  • To perform a run test for randomness the data must be
  • Three brands of coffee are rated for taste on a scale of 1 to 10. Six persons are asked to rate each brand so that there is a total of 18 observations. The appropriate test to determine if three brands taste equally good is
  • If a Chi-square goodness of fit test has 6 categories and an N=30, then the correct number of degrees of freedom is
  • Comparing the times-to-failure of radar transponders made by firms A, B, and C, based on an airline’s sample experience with the three types of instruments, one may well call for:
  • Which of the following tests is most likely assessing the null hypothesis of “the number of violations per apartment in the population of all city apartments is binomially distributed with a probability of success in any one trial of $P=0.4$
  • In the Kruskal-Wallis test of $k$ samples, the appropriate number of degrees of freedom is
  • Compare to parametric methods, the nonparametric methods are
MCQs nonparametric Statistics Quiz with answers

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