partition

(noun)

a part of something that had been divided, each of its results

Related Terms

Examples of partition in the following topics:

  • Partitioning the Sums of Squares

    • Partition sum of squares Y into sum of squares predicted and sum of squares error
    • We are now in a position to see how the SSY is partitioned.
    • SSY can be partitioned into two parts: the sum of squares predicted (SSY') and the sum of squares error (SSE).
    • It is often convenient to summarize the partitioning of the data in a table such as Table 4.

  • Repeated Measures Design

    • One of the greatest advantages to using the rANOVA, as is the case with repeated measures designs in general, is that you are able to partition out variability due to individual differences.
    • In a repeated measures design it is possible to account for these differences, and partition them out from the treatment and error terms.
    • The within-treatments variability can be further partitioned into between-subjects variability (individual differences) and error (excluding the individual differences).
    • In reference to the general structure of the $F$-statistic, it is clear that by partitioning out the between-subjects variability, the $F$-value will increase because the sum of squares error term will be smaller resulting in a smaller $MS_{\text{error}}$.
    • It is noteworthy that partitioning variability pulls out degrees of freedom from the $F$-test, therefore the between-subjects variability must be significant enough to offset the loss in degrees of freedom.

  • Sex Bias in Graduate Admissions

    • The practical significance of Simpson's paradox surfaces in decision making situations where it poses the following dilemma: Which data should we consult in choosing an action, the aggregated or the partitioned?
    • The answer seems to be that one should sometimes follow the partitioned and sometimes the aggregated data, depending on the story behind the data; with each story dictating its own choice.
    • Once we extract these relationships we can test algorithmically whether a given partition, representing confounding variables, gives the correct answer.

  • Introduction to Multiple Regression

    • Just as in the case of simple linear regression, the sum of squares for the criterion (UGPA in this example) can be partitioned into the sum of squares predicted and the sum of squares error.
    • In multiple regression, it is often informative to partition the sums of squares explained among the predictor variables.
    • Table 3 shows the partitioning of the sums of squares into the sum of squares uniquely explained by each predictor variable, the sum of squares confounded between the two predictor variables, and the sum of squares error.
    • No assumptions are necessary for computing the regression coefficients or for partitioning the sums of squares.

  • Proportion of Variance Explained

    • In the section "Partitioning the Sums of Squares" in the Regression chapter, we saw that the sum of squares for Y (the criterion variable) can be partitioned into the sum of squares explained and the sum of squares error.

  • Influential Observations

    • The final step is to divide this result by 2 times the MSE (see the section on partitioning the variance).

  • One-Factor ANOVA (Between Subjects)

    • One of the important characteristics of ANOVA is that it partitions the variation into its various sources.
    • Therefore, the total sum of squares of 377.19 can be partitioned into SSQcondition (27.53) and SSQerror (349.66).
    • The Analysis of Variance Summary Table shown below is a convenient way to summarize the partitioning of the variance.

  • Controlling for a Variable

    • A common way to achieve this is to partition the groups into subgroups whose members have (nearly) the same value for the controlled variable.

  • Experimental Design

    • Analysis of experiment design is built on the foundation of the analysis of variance, a collection of models that partition the observed variance into components, according to what factors the experiment must estimate or test.

  • ANOVA

    • In ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation.