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Statistical testing is essential in research for validating findings. This overview covers parametric and non-parametric tests, focusing on the Wilcoxon signed-rank test used for non-normally distributed paired data. It explains the test's procedure, from ranking differences to interpreting outcomes, and notes the importance of choosing the correct test based on data assumptions.
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Statistical testing evaluates the validity of research findings by determining if observed effects or differences are statistically significant or due to random variation
Null Hypothesis
Statistical tests are used to make informed decisions about the validity of the null hypothesis, which suggests no effect or difference, versus the alternative hypothesis, which suggests an effect or difference exists
P-value
A p-value of less than 0.05 is commonly accepted as the threshold for statistical significance, indicating a less than 5% chance that the results are due to random chance alone
Parametric tests assume normal distribution and other statistical properties, while non-parametric tests offer a robust alternative for data that do not meet these assumptions
The Wilcoxon signed-rank test is a non-parametric alternative to the paired t-test, suitable for analyzing matched-pair data or repeated measurements on a single sample
Calculation of Test Statistic
The test statistic, denoted as W, is calculated by ranking the absolute differences between paired observations, ignoring the sign, and then summing the positive and negative ranks
Interpretation of Test Statistic
The test statistic is compared to a critical value to determine statistical significance, with a smaller W indicating a rejection of the null hypothesis
Non-parametric tests like the Wilcoxon signed-rank test are useful for data that violate parametric assumptions, but may have less statistical power than parametric tests
The Wilcoxon signed-rank test is particularly adept at handling non-normally distributed differences in paired data
Calculation of Differences
Researchers first calculate the differences between each pair of observations
Ranking and Assigning Signs
The differences are then ranked based on their absolute values and assigned signs, with zero differences excluded from the analysis
Comparison to Critical Value
The test statistic is compared to a critical value to determine if the null hypothesis should be rejected
The Wilcoxon signed-rank test provides a necessary option for analyzing data that do not fit the assumptions of parametric tests
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A commonly accepted threshold for statistical significance is a p-value of less than ______, indicating a low probability that results are random.
0.05
01
Assumptions of Parametric Tests
Require normal distribution, homogeneity of variances.
02
Examples of Non-Parametric Tests
Mann-Whitney U test, Wilcoxon signed-rank test.
