Introduction-to-Parametric-and-Non-Parametric-Tests.pptx

Introduction-to-Parametric-and-Non-Parametric-Test

1. Introduction to Parametric and Non-Parametric Tests In the realm of statistical analysis, researchers often encounter situations where they need to choose between parametric and non-parametric tests to analyze their data. Parametric tests are a family of statistical methods that make specific assumptions about the underlying distribution of the data, such as normality, equal variances, and independence. On the other hand, non-parametric tests do not rely on these assumptions and are often more robust to violations of these assumptions. Understanding the differences between these two types of tests is crucial for researchers to select the appropriate analysis method for their research questions and data characteristics. Sa by Shriram Kargaonkar

2. Definition of Parametric Tests Defined by Underlying Assumptions Parametric tests are a class of statistical tests that make specific assumptions about the underlying distribution of the data. These assumptions typically include that the data follows a normal distribution, has equal variances across groups, and has independence between observations. Parametric tests are designed to be more powerful and precise when these assumptions are met, as they can leverage information about the shape and parameters of the underlying distribution. Rely on Population Parameters Parametric tests use information about the population parameters, such as the mean and standard deviation, to make inferences about the data. This allows them to provide more detailed and robust conclusions compared to non-parametric tests, which make fewer assumptions about the underlying distribution. Parametric tests are often the preferred choice when the necessary assumptions can be confidently met. Widely Used in Research Parametric tests are widely used across various fields of research, including psychology, biology, and economics. They are a fundamental part of the statistical toolbox and are often the starting point for data analysis. Researchers rely on parametric tests to draw conclusions about populations, test hypotheses, and quantify the strength of relationships between variables.

3. Assumptions of Parametric Tests Parametric tests are a class of statistical tests that make certain assumptions about the underlying distribution of the data being analyzed. These assumptions are crucial for the validity and reliability of the test results. The key assumptions of parametric tests include: Normality: Parametric tests assume that the data is normally distributed, meaning that the distribution of the variable follows a bell-shaped curve. This assumption is important because many statistical methods, such as t-tests and ANOVA, rely on the normal distribution for their validity. Homogeneity of Variance: Parametric tests also assume that the variance (or spread) of the data is the same across the different groups or conditions being compared. This assumption is known as homogeneity of variance or homoscedasticity. Independence: Parametric tests require that the observations in the data set are independent of one another. This means that the value of one observation should not depend on the value of another observation. Interval or Ratio Scale: Parametric tests assume that the data is measured on an interval or ratio scale, meaning that the differences between the values are meaningful and can be interpreted numerically. If these assumptions are not met, the validity of the parametric test results may be compromised, and the conclusions drawn from the analysis may be inaccurate or misleading. In such cases, it may be necessary to use non-parametric tests, which have different assumptions and are more robust to violations of the parametric test assumptions.

4. Understanding Non-Parametric Tests Non-parametric tests are a class of statistical methods that do not rely on specific assumptions about the shape of the data distribution, such as the normal distribution. These tests are used when the data does not meet the requirements of parametric tests, such as when the data is not normally distributed or when the variances are not equal. Non-parametric tests are based on ranking or ordering the data rather than using the actual data values directly. This approach makes them more robust and less affected by outliers or violations of assumptions. Non-parametric tests are often preferred when the sample size is small, the data is ordinal or ranked, or when the distribution of the data is unknown or cannot be assumed to be normal.

5. Assumptions of Non-Parametric Tests No Assumption of Normality Non-parametric tests do not assume that the data is normally distributed. This is a key difference from parametric tests, which rely on the assumption of normality for their statistical inferences. Non-parametric tests are more robust to deviations from normality, making them suitable for analyzing data that does not meet the normality assumption. No Assumption of Homogeneity of Variance Unlike parametric tests, non-parametric tests do not require the assumption of homogeneity of variance. This means that the variances of the populations being compared do not need to be equal. This makes non-parametric tests more appropriate when the assumption of equal variances is violated, as is often the case with real-world data. No Assumption of Interval or Ratio Scales Non-parametric tests can be used with ordinal, ranked, or even categorical data, as they do not require the data to be on an interval or ratio scale. This flexibility allows non-parametric tests to be applied to a wider range of research questions and data types, making them a useful tool for researchers working with data that does not meet the assumptions of parametric tests.

6. Advantages of Parametric Tests Statistical Power Parametric tests generally have higher statistical power compared to non-parametric tests when the data meets the necessary assumptions. This means they are more likely to detect an effect or difference if one truly exists, reducing the risk of a false negative result. Precision and Sensitivity Parametric tests can provide more precise and sensitive measurements because they make use of the full information contained in the data, such as the means and variances. This allows for more nuanced analyses and the detection of smaller effects. Familiarity and Interpretability Parametric tests are widely used and well-understood statistical methods, with a rich body of literature and established conventions. This familiarity makes the results more interpretable and easier to communicate to a broader audience. Parametric Modeling Parametric tests can be used to fit complex statistical models that allow for the exploration of relationships between multiple variables. This flexibility is valuable in many research and applied settings where understanding these relationships is important.

7. Advantages of Non-Parametric Tests Flexibility Non-parametric tests are more flexible than parametric tests because they do not rely on strict assumptions about the underlying distribution of the data. This makes them well-suited for analyzing data that may not follow a normal distribution or have equal variances, which are common assumptions of parametric tests. Robustness Non-parametric tests are more robust to outliers and extreme values in the data. Parametric tests can be heavily influenced by outliers, which can skew the results. Non-parametric tests, on the other hand, are less sensitive to these extreme values, making them more reliable for datasets with unusual distributions. Ordinal Data Non-parametric tests are particularly useful for analyzing ordinal data, which are data that can be ranked but do not have a meaningful numerical scale. Parametric tests, which rely on numerical values, are not well-suited for this type of data, whereas non-parametric tests can effectively analyze ordinal data. Small Sample Sizes Non-parametric tests can be more effective than parametric tests when the sample size is small. Parametric tests often require larger sample sizes to ensure the assumptions are met, whereas non-parametric tests can provide reliable results even with smaller datasets.

8. Situations Requiring Non-Parametric Tests 1 Small Samples When the sample size is small and the distribution of the data is unknown. 2 Non-Normal Distributions When the data does not follow a normal distribution. 3 Ordinal Data For data measured on an ordinal scale, such as ratings or rankings. 4 Heterogeneous Variances When the variances of the populations are not equal. Non-parametric tests are often required when the assumptions of parametric tests are violated. This can occur in a variety of situations, such as when the sample size is small, the data does not follow a normal distribution, the data is measured on an ordinal scale, or the variances of the populations are not equal. In these cases, non-parametric tests can provide more robust and reliable results than their parametric counterparts. For example, if you're comparing the median income of two different neighborhoods, a non-parametric test like the Mann-Whitney U test would be appropriate, as the income data may not follow a normal distribution. Similarly, if you're analyzing survey data where respondents rated their satisfaction on a scale of 1 to 5, a non-parametric test like the Kruskal-Wallis test would be suitable, as the data is ordinal rather than continuous.

9. Examples of Parametric and Non-Parametric Tests Parametric tests are widely used statistical methods that make assumptions about the underlying distribution of the data, such as normality and equal variances. Some common examples of parametric tests include: t-test: Used to compare the means of two groups, such as comparing the average test scores of a control group and an experimental group. ANOVA (Analysis of Variance): Used to compare the means of three or more groups, such as comparing the performance of different treatment groups in a clinical trial. Pearson's correlation: Used to measure the linear relationship between two continuous variables, such as the relationship between income and education level. On the other hand, non-parametric tests are more flexible and do not make assumptions about the underlying data distribution. Some examples of non-parametric tests include: Mann-Whitney U test: Used to compare the medians of two independent groups, such as comparing the pain scores of patients in a treatment group and a control group. Kruskal-Wallis test: Used to compare the medians of three or more independent groups, such as comparing the satisfaction levels of customers across different service channels. Spearman's rank correlation: Used to measure the monotonic relationship between two variables, such as the relationship between customer satisfaction and loyalty.

10. Conclusion and Takeaways In conclusion, the key differences between parametric and non-parametric tests lie in their underlying assumptions and the type of data they can effectively analyze. Parametric tests, such as the t-test and ANOVA, rely on specific assumptions about the distribution of the data, including normality and homogeneity of variance. These tests are powerful when the assumptions are met, providing robust and precise results. In contrast, non-parametric tests, like the Mann-Whitney U test and the Kruskal-Wallis test, make fewer assumptions about the data distribution and are more flexible in their application. They are particularly useful when the data is ordinal, skewed, or does not follow a normal distribution. The choice between parametric and non-parametric tests ultimately depends on the characteristics of the data and the research question at hand. Parametric tests are generally preferred when the assumptions are met, as they offer greater statistical power and the ability to make more precise inferences. However, when the assumptions are violated, non-parametric tests become the more appropriate choice, as they can provide reliable and valid results without the need for strict distributional assumptions. Researchers should carefully evaluate the assumptions of their data and select the most appropriate statistical test to ensure accurate and meaningful conclusions. In summary, understanding the differences between parametric and non-parametric tests, their assumptions, and their respective strengths and weaknesses is crucial for researchers to select the most suitable analytical approach for their specific research questions and data characteristics. By considering these factors, researchers can ensure the validity and reliability of their findings and draw meaningful insights from their data.