State and explain seven (7) assumptions that are made when using the parametric statistics to test a hypothesis
Parametric statistics rely on certain assumptions to ensure the validity and accuracy of the results. Here are seven common assumptions made when using parametric statistics to test a hypothesis:
1. Normality of Data: The assumption is that the data follows a normal distribution. This means that the data should be symmetrically distributed around the mean, with the majority of observations falling close to the mean and fewer in the tails. Violations of normality can affect the accuracy of results.
2. Independence: Observations should be independent of each other. This means that the value of one observation should not be influenced by the value of another. Violations of independence, such as repeated measurements on the same subjects, can lead to biased results.
3. Homogeneity of Variance: Homogeneity of variance assumes that the variances of the different groups being compared are roughly equal. Unequal variances can affect the validity of statistical tests like ANOVA or t-tests, leading to incorrect conclusions.
4. Interval or Ratio Scale: Parametric tests require data to be on an interval or ratio scale. This means that the differences between values are meaningful and consistent across the entire range of values. Categorical or ordinal data may not meet this assumption.
5. Linearity: When examining relationships between variables, parametric tests assume that the relationship is linear. This assumption may not hold if the relationship is non-linear or if outliers are present.
6. Absence of Outliers: Outliers can heavily influence the results of parametric tests. The assumption is that outliers do not significantly impact the results. If outliers are present, they can distort means, variances, and relationships.
7. Adequate Sample Size: Parametric tests assume a sufficiently large sample size. This helps ensure that the central limit theorem holds, allowing the distribution of sample means to be approximately normal even if the underlying population is not normal.
Explanation of Assumptions:
- Normality of Data: Normality is crucial because many parametric tests rely on the assumption of normal distribution. When data is normally distributed, it’s easier to make inferences about population parameters from sample statistics.
- Independence: The assumption of independence ensures that the observations are not influenced by one another. If observations are dependent, it can lead to pseudoreplication and undermine the validity of results.
- Homogeneity of Variance: Equal variances are necessary for valid comparisons across groups. If variances differ significantly, the results of tests like ANOVA and t-tests can be compromised.
- Interval or Ratio Scale: Parametric tests involve calculations based on the differences between data points. This requires that the measurement scale provides meaningful intervals between values.
- Linearity: Linear relationships are easier to analyze statistically. If the relationship between variables is non-linear, parametric tests might not provide accurate results.
- Absence of Outliers: Outliers can distort the distribution of data and affect summary statistics like means and standard deviations. Their presence should be carefully examined before applying parametric tests.
- Adequate Sample Size: A larger sample size helps approximate the normal distribution of sample means, even if the population distribution is not normal. This allows parametric tests to be more robust.
It’s important to remember that violating these assumptions can lead to incorrect conclusions. If assumptions are not met, alternative non-parametric tests might be more appropriate. Always verify assumptions before applying parametric tests to ensure the reliability of your results.
1. Parametric tests assume that the data follows a ____________ distribution.
2. Violations of the normality assumption can impact the ____________ of results.
c) Precision and accuracy
3. Observations should be ____________ for accurate parametric analysis.
4. The independence assumption prevents ____________ of observations.
5. Homogeneity of variance assumption ensures ____________ variances across groups.
6. Violations of homogeneity of variance can affect tests like ____________.
7. Parametric tests require data on ____________ or ____________ scale.
a) Categorical, ordinal
b) Nominal, ordinal
c) Interval, ratio
8. Interval and ratio scales have ____________ intervals between values.
9. Parametric tests assume a ____________ relationship between variables.
10. Non-linear relationships might lead to ____________ of assumptions.
11. Outliers can ____________ the results of parametric tests.
12. The assumption is that outliers have ____________ impact on results.
13. Adequate sample size helps parametric tests approximate the ____________ distribution.
14. The central limit theorem allows normality of sample means with ____________ sample size.
15. The ____________ assumption ensures accurate results when applying parametric tests.
c) Proper understanding