6: Measures of Variability
- Page ID
- 50308
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- Understand how to determine variance
- Differentiate between error variance and true variance
- Explain the statistical measures used to determine the location of scores
Key Terms:
- Variance
- Standard Deviation
- Range
- 6.1: What is Variance?
- This page explains the concept of mean as a measure of central tendency, indicating expected performance while not showing individual variations. It introduces variance as a measure of score dispersion around the mean, essential for result analysis and significance interpretation. Variance includes terms such as standard deviation and range, which detail the distances of scores from the mean, emphasizing its importance in distinguishing significant outcomes from non-significant ones.
- 6.2: How Do You Determine Variance?
- This page explains how to calculate variance by evaluating deviation scores, which must be squared to prevent cancellation during summation. Squaring is crucial for understanding the normal distribution's area, aiding in identifying significant results (occurring less than 5% of the time). It emphasizes that accurate variance calculation relies on a normal distribution, and deviations from this may require other statistical methods.
- 6.3: Partitioning of the Variance
- This page discusses "partitioning of the variance," which divides variance into true variance, representing actual differences in the studied phenomenon, and error variance, resulting from unrelated external factors. This differentiation is crucial for establishing statistical significance and assessing the accuracy of study results, typically expressed as a ratio of true variance to error variance.
- 6.4: Standardized Values of Reporting Scores
- This page covers standardized values such as z-scores, t-scores, and percentiles, crucial for converting raw scores, especially for exams like the EPPP. It explains the significance of standard deviation (SD) in evaluating data variability, with low SD indicating homogeneity and high SD implying heterogeneity. Z-scores allow comparison across distributions, while t-scores provide a standardized way to interpret scores without negatives.
- 6.5: Discussion Questions
- This page explains the concept of variance, highlighting its importance in understanding data spread. It differentiates between sample and population variance and discusses various statistical methods to measure variance, including mean differences. Additionally, it emphasizes the significance of standard deviation, which offers a clearer and more intuitive grasp of variability by being expressed in the same units as the data, thereby aiding in comparisons and interpretations.