What Are The Requirements To Perform A Goodness Test
Questions1 What Are The Requirements To Perform A Goodness Of Fit Te
Questions1 What Are The Requirements To Perform A Goodness Of Fit Te
Questions: 1. What are the requirements to perform a goodness-of-fit test? [1 sentence or 2 bullets] 2. Why is the chi-square distribution always positive? [1 sentence] 3. How would the goodness-of-fit procedure be modified to check that data follows a continuous distribution? [2 sentences]
Paper For Above instruction
A goodness-of-fit test is a statistical procedure used to determine how well a sample matches a theoretical distribution. Performing a valid goodness-of-fit test requires several specific conditions: the data should be independent and randomly sampled, and the sample size must be sufficiently large to ensure the approximation to the theoretical distribution is accurate—generally, expected frequencies in each category should be at least five. Additionally, the categories or classes used in the test should be mutually exclusive and collectively exhaustive, covering all possible outcomes to accurately reflect the distribution being tested.
The chi-square distribution is always positive because it is derived from the sum of squared standard normal variables, which eliminates negative values and results in a distribution bounded below by zero. This positivity property makes the chi-square distribution suitable for assessing how observed frequencies deviate from expected frequencies, as it inherently measures magnitude alone, not direction.
To adapt the goodness-of-fit procedure for continuous distributions, data can be grouped into intervals or bins, creating a histogram that approximates the distribution's density function. The test then compares the observed frequency within each interval to the expected frequency derived from the hypothesized continuous distribution—such as a normal or exponential distribution—using a chi-square or similar test statistic, thus enabling assessment of the fit despite data's continuous nature.
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