Important Questions for IGNOU MAPC MPC006 Exam with Main Points for Answer - Block 4 Unit 1 Rationale for Nonparametric Statistics

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Block 4 Unit 1 Rationale for Nonparametric Statistics

1) Define Non-parametric statistics.

Non-parametric statistics are statistical methods that do not assume the data follows a specific distribution (such as the normal distribution). This means they are "distribution-free." They are often used when data is nominal or ordinal, or when the assumptions of parametric tests are not met.

2) What are the charateristic featurs of non-parametric statistics

Characteristic features of non-parametric statistics:

Fewer assumptions about the underlying population distribution.
Can be used with small sample sizes.
Appropriate for nominal or ordinal data.
Often easier to understand and apply than parametric tests.

3) What are the major differences between parametric and non-parametric statistics?

Major differences between parametric and non-parametric statistics:

Difference	Parametric	Non-parametric
Distribution	Assumes a specific distribution (e.g., normal).	Does not assume a specific distribution ("distribution-free").
Data type	Typically used for interval or ratio data.	Can be used for nominal, ordinal, interval, or ratio data.
Sample size	Generally requires larger sample sizes.	Can be used with small sample sizes.
Assumptions	More assumptions (normality, homogeneity of variance, etc.).	Fewer assumptions.
Power	More powerful when assumptions are met.	Less powerful when parametric assumptions are met, but can be more powerful when assumptions are violated.
Conclusions	Can make more precise inferences about population parameters.	Inferences are more general, often focusing on ranks or medians.

4) Enumerate the advantages of non-parametric statistics.

Advantages of non-parametric statistics:

Fewer assumptions: Less likely to be violated, making them more robust.
Suitable for small samples: Can be used when parametric tests are not appropriate.
Can handle nominal and ordinal data: Expands the types of data that can be analyzed.
Simplicity: Often easier to understand and apply.
Robustness: Less affected by outliers or violations of assumptions.

5) Are there any assumptions for “Assumption Free tests”? If yes what are the assumptions of non-parametric statistics?

Assumptions of "Assumption-Free" tests: Even though non-parametric tests are often called "assumption-free," they still have some assumptions:

Independence of observations: Except for paired data.
Continuity of the variable: The variable being measured should be continuous.

6) What are the assumptions underlying parametric statistics?

Assumptions underlying parametric statistics:

Normality: Data should be normally distributed.
Homogeneity of variance: Variances across groups should be equal.
Interval or ratio data: Data should be measured on an interval or ratio scale.
Large sample size: Preferably 30 or more observations per group.
Independence of observations: Except for paired data.

7) “Non-parametric Statistics has much wider scope than parametric statistics” support the statement with your arguments.

Wider scope of non-parametric statistics: Non-parametric statistics have a wider scope because:
Fewer assumptions: They can be applied to a broader range of data and situations where parametric assumptions are not met.
Handle different data types: They can analyze nominal and ordinal data, which are common in many fields.
Work with small samples: Useful when limited data is available, expanding research possibilities.
Simple and robust: Their ease of use and resistance to violations make them accessible to a wider audience.

8) What are the major misconceptions regarding non-parametric statistics?

Major misconceptions about non-parametric statistics:

Less powerful: While true when parametric assumptions are met, they can be equally or more powerful when those assumptions are violated.
Limited applications: A misconception; non-parametric methods exist for a wide range of designs, from simple comparisons to complex modeling.
Lack of familiarity: Researchers may be hesitant to use them due to unfamiliarity or perceived resistance from reviewers.

9) What are the aspects to be kept in mind before we decide to apply parametric or non-parametric tests?

Aspects to consider before choosing between parametric and non-parametric tests:

Level of measurement: Nominal, ordinal, interval, or ratio.
Sample size: Small or large.
Distribution of the data: Normal or non-normal.
Research question: Whether you're testing differences, relationships, or making descriptive statements.

10) What is ordinal data? Give suitable examples?

Ordinal data: Data where variables are ranked in a specific order, but the differences between ranks are not necessarily equal. Examples: Likert scales (strongly disagree to strongly agree), educational attainment (high school, college, graduate school), socioeconomic status (low, middle, high).

11) What are interval and ratio data ? Give examples.

Interval data: Data with equal intervals between values, but no true zero point. Example: Temperature in Celsius or Fahrenheit (0 degrees does not mean the absence of temperature).
Ratio data: Data with equal intervals and a true zero point. Examples: Height, weight, age, income (0 indicates the absence of the variable).

12) Why is sample size important to decide about using parametric or non-parametric tests?

Sample size and test choice: Sample size influences the choice between parametric and non-parametric tests because:

Small samples: Parametric tests may not be reliable with small samples as the data may not adequately represent the population distribution. Non-parametric tests are more suitable in this case.
Large samples: The sampling distribution tends towards normality with larger samples, making parametric tests more appropriate, even if the population distribution is not perfectly normal.

13) What is meant by normality of a data? Explain.

Normality of data: Data is considered normally distributed when it follows a bell-shaped curve, with most values clustered around the mean and fewer values at the extremes. Parametric tests assume normality for reliable results. However, in real-world research, data often deviates from perfect normality.

14) When do we use the non-parametric statistics?

When to use non-parametric statistics:

Nominal or ordinal data.
Small sample sizes.
Non-normal data distribution.
Violations of parametric assumptions: Like unequal variances across groups.

15) What is meant by descriptive statistics in the context of non-parametric statistics?

Descriptive statistics in non-parametric context: Non-parametric descriptive statistics summarize data without making assumptions about the underlying distribution. They often focus on ranks and medians, rather than means and standard deviations. Examples: median, mode, quartiles, percentiles.

16) State when to use which test – parametric or non-parametric?

Choosing the right test (parametric or non-parametric):

Situation	Parametric Test	Non-parametric Test
Comparing two independent groups (normal data, large samples)	Independent samples t-test	Mann-Whitney U test
Comparing two related groups (normal data, large samples)	Paired samples t-test	Wilcoxon signed-ranks test
Comparing more than two independent groups (normal data, large samples)	One-way ANOVA	Kruskal-Wallis test
Testing correlation (normally distributed variables, interval or ratio data)	Pearson correlation (r)	Spearman's rho (ρ) or Kendall's tau (τ)
Testing association between categorical variables (independent observations)	Chi-square test (χ2)	-

17) What are the four problems for which non-parametric statistics is used?

Four problems for which non-parametric statistics are used:

Differences between independent groups: Comparing two or more groups when assumptions of parametric tests are not met.
Differences between dependent groups: Comparing two related variables (e.g., pre-test and post-test) when parametric assumptions are violated.
Relationships between variables: Assessing the correlation between variables when data is ordinal or assumptions of Pearson's r are not met.
Descriptive statistics: Summarizing data when it is not normally distributed or measured on an interval or ratio scale.

18) What are the disadvantages of non-parametric statistics?

Disadvantages of non-parametric statistics:

Less powerful when parametric assumptions are met: May fail to detect a significant effect that a parametric test could have found.
Less precise conclusions: Often focus on ranks or medians, rather than providing specific estimates of population parameters.
Information loss: Ranking data can discard some information contained in the original values.

Important Points

Parametric tests have more assumptions than non-parametric tests.
Non-parametric tests are particularly suitable for ranked data.
Small sample sizes can be analyzed with parametric tests, but their reliability may be questionable. Non-parametric tests are generally preferred for small samples.
Both parametric and non-parametric tests have strong statistical foundations, and the choice depends on the data and research question.
Non-parametric methods can be used with complex designs, including those with multiple factors or repeated measures.

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