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The arithmetic mean of the age determinations is ¯ = =, but this value can be misleading, unless each determination of the age is of equal significance. When each measured value can be assumed to have the same weighting, or significance, the biased and unbiased (or "sample" and "population" respectively) estimators of the variance are computed ...
The plot is usually drawn by evaluating the values of Y for high and low values of both X and Z, and creating two lines to represent the effect of X on Y at the two values of Z. Sometimes this is supplemented by simple slope analysis, which determines whether the effect of X on Y is statistically significant at particular values of Z.
The result of the F test can be determined by comparing calculated F value and critical F value with specific significance level (e.g. 5%). The F table serves as a reference guide containing critical F values for the distribution of the F-statistic under the assumption of a true null hypothesis.
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr or 3 σ, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean ...
Statistical hypothesis testing is based on rejecting the null hypothesis when the likelihood of the observed data would be low if the null hypothesis were true. If multiple hypotheses are tested, the probability of observing a rare event increases, and therefore, the likelihood of incorrectly rejecting a null hypothesis (i.e., making a Type I ...
The value q s is the sample's test statistic. (The notation | x | means the absolute value of x; the magnitude of x with the sign set to +, regardless of the original sign of x.) This q s test statistic can then be compared to a q value for the chosen significance level α from a table of the studentized range distribution.
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Instead, students in classes with better teachers have especially high test scores (regardless of whether they receive the experimental treatment) while students in classes with worse teachers have especially low test scores. The researcher can cluster her standard errors at the level of a classroom to account for this aspect of her experiment. [7]