comparison

Examples of comparison in the following topics:

• A Comparison

• [PF content: State Government Comparisons]

• Comparison Tests

  • Comparison test may mean either limit comparison test or direct comparison test, both of which can be used to test convergence of a series.
  • Comparison tests may mean either limit comparison tests or direct comparison tests.
  • The limit comparison test is a method of testing for the convergence of an infinite series, while the direct comparison test is a way of deducing the convergence or divergence of an infinite series or an improper integral by comparison with other series or integral whose convergence properties are already known.
  • The direct comparison test provides a way of deducing the convergence or divergence of an infinite series or an improper integral.

• Pairwise Comparisons (Correlated Observations)

  • In the section on all pairwise comparisons among independent groups, the Tukey HSD test was the recommended procedure.
  • The standard practice for pairwise comparisons with correlated observations is to compare each pair of means using the method outlined in the section "Difference Between Two Means (Correlated Pairs)" with the addition of the Bonferroni correction described in the section "Specific Comparisons. " For example, suppose you were going to do all pairwise comparisons among four means and hold the familywise error rate at 0.05.
  • Since there are six possible pairwise comparisons among four means, you would use 0.05/6 = 0.0083 for the per-comparison error rate.
  • In order to compute all pairwise comparisons, the difference in times for each pair of conditions for each subject is calculated.
  • Using the Bonferroni correction for three comparisons, the p value has to be below 0.05/3 = 0.0167 for an effect to be significant at the 0.05 level.

• Specific Comparisons (Correlated Observations)

  • Determine whether to use the formula for correlated comparisons or independent-groups comparisons
  • The comparison is the difference:
  • Issues associated with doing multiple comparisons are the same for related observations as they are for multiple comparisons among independent groups.
  • For the weapons and aggression data, the comparisons L1 and L2 are correlated 0.24.
  • Although mathematically possible, orthogonal comparisons with correlated observations are very rare.

• Specific Comparisons (Independent Groups)

  • Therefore these comparisons are called planned comparisons.
  • The per-comparison error rate is the probability of a Type I error for a particular comparison.
  • If we use the 0.05 level for each comparison, then the per-comparison rate is simply 0.05.
  • Independent comparisons are often called orthogonal comparisons.
  • Therefore, the two comparisons are orthogonal.

• Elements of a Designed Study

  • If we do not assume that the comparisons are independent, then we can still say:
  • $\bar { \alpha } \le n\cdot { \alpha }_ {\text{per comparison}}$.
  • A more sensitive correction can be obtained by solving the equation for the familywise error rate of independent comparisons for ${\alpha }_ {\text{per comparison}}$.
  • In order to retain a prescribed familywise error rate $\alpha$ in an analysis involving more than one comparison, the error rate for each comparison must be more stringent than $\alpha$.
  • Multiple comparison procedures are then used to determine which means differ.

• Multiple Comparisons of Means

  • ANOVA is useful in the multiple comparisons of means due to its reduction in the Type I error rate.
  • Several statistical techniques have been developed to prevent this, allowing direct comparison of means significance levels for single and multiple comparisons.
  • "Multiple comparisons" arise when a statistical analysis encompasses a number of formal comparisons, with the presumption that attention will focus on the strongest differences among all comparisons that are made.
  • Failure to compensate for multiple comparisons can have important real-world consequences
  • Our confidence that a result will generalize to independent data should generally be weaker if it is observed as part of an analysis that involves multiple comparisons, rather than an analysis that involves only a single comparison.

• Formation and Comparison of Adverbs

  • There are three degrees of Comparison,—the Positive, the Comparative, and the Superlative.
  • Many adjectives do not admit terminational comparison, but form the Comparative and Superlative degrees by prefixing magis (more) and maximē (most).
  • Many adjectives, which, from the nature of their signification, do not admit of comparison; as, hodiernus, of to-day; annuus, annual; mortālis, mortal.
  • Adverbs are for the most part derived from adjectives, and depend upon them for their comparison.

• Simile and Metaphor

  • Simile and metaphor are creative ways of making comparisons in your speech.
  • Similes and metaphors are forms of descriptive language that make comparisons.
  • Similes make their comparisons by using the words "like" or "as" while metaphors directly state what something is.
  • Simile and metaphor are artful ways of speaking to make a comparison.
  • The vehicle is the comparison or description used to describe the subject.