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Expected values

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Intro to Statistics

Definition

Expected values are the theoretical frequencies of outcomes in a distribution, calculated based on a specified model. They are used to determine how well observed data fits an expected distribution.

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5 Must Know Facts For Your Next Test

  1. Expected values are calculated using the formula $E_i = N \times p_i$, where $N$ is the total number of observations and $p_i$ is the probability of each outcome.
  2. They play a crucial role in the Chi-Square Goodness-of-Fit test, which compares observed frequencies to expected frequencies.
  3. The Chi-Square statistic is computed as $$\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$$ where $O_i$ and $E_i$ are observed and expected frequencies, respectively.
  4. A significant difference between observed and expected values indicates that the observed data does not fit the expected distribution well.
  5. Expected values must be greater than or equal to 5 for each category to ensure the validity of the Chi-Square test.

Review Questions

  • What formula is used to calculate expected values?
  • How do expected values relate to the Chi-Square Goodness-of-Fit test?
  • Why must each expected value be at least 5 for a valid Chi-Square test?
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