Degrees of freedom (df) is a statistical concept representing the number of independent values that are "free to vary" in a data set when estimating a population parameter from a sample. In simpler terms, it's about how many pieces of information in a dataset can be chosen independently, given that some constraints or calculations are already in place.
An example from psychology
Imagine a psychologist is conducting a study to see if a new therapeutic intervention improves self-esteem. They recruit a sample of 10 participants and measure their self-esteem before the intervention and after the intervention.
To analyze the data, the researcher might use a statistical test like a dependent samples t-test (also called a paired samples t-test), which compares the means of two related groups (in this case, the same participants before and after the intervention).
In a dependent samples t-test, the degrees of freedom are calculated as the number of pairs of observations (or the number of participants in this case) minus 1. So, for a study with 10 participants, the degrees of freedom would be:
df = n - 1 = 10 - 1 = 9
This means that out of the 10 data points (representing the change in self-esteem for each participant), 9 of them are free to vary independently to estimate the mean difference in self-esteem. The last data point, however, is determined by the previous 9 and the calculated mean difference.
Why are degrees of freedom important?
Determining Critical Values: Degrees of freedom are crucial for finding the correct critical values for statistical tests, which are used to determine if a result is statistically significant.
Shape of Distributions: Degrees of freedom influence the shape of probability distributions like the t-distribution and chi-square distribution, affecting the likelihood of obtaining certain test statistics.
Validity and Reliability: Appropriately calculating degrees of freedom helps ensure the validity and reliability of research findings by providing a more accurate assessment of the precision of parameter estimates.
Reference for using scales in research:
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Reference for clinicians and students on understanding assessment
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