Exact numbers

(noun)

These numbers are either defined numbers or result of a count. They have an infinite number of significant figures.

Examples of Exact numbers in the following topics:

  • Exact Numbers

    • Exact numbers are defined numbers or result from a count, unlike measured numbers.
    • Exact numbers are either defined numbers or the result of a count.
    • An exact number can only be expressed in one way and cannot be simplified any further.
    • Exact numbers have an infinite number of significant figures, but they often appear as integers.
    • Counted numbers are exact: there are two chairs in the photograph.
  • Molecular Formulas

    • Molecular formulas describe the exact number and type of atoms in a single molecule of a compound.
    • The empirical formula is the simplest whole number ratio of all the atoms in a molecule.
    • The molecular formula indicates the exact number of atoms in the molecule.
    • The empirical formula expresses the smallest whole number ratio of the atoms in the element.
    • Because of this, one molecular formula can describe a number of different chemical structures.
  • Round-off Error

    • A round-off error is the difference between the calculated approximation of a number and its exact mathematical value.
    • A round-off error, also called a rounding error, is the difference between the calculated approximation of a number and its exact mathematical value.
    • Calculations rarely lead to whole numbers.
    • However, when doing a series of calculations, numbers are rounded off at each subsequent step.
    • Rounding these numbers off to one decimal place or to the nearest whole number would change the answer to 5.7 and 6, respectively.
  • Generating the exact null distribution and p-value

    • The number of successes in n independent cases can be described using the binomial model, which was introduced in Section 3.4.
    • Compute the exact p-value to check the consultant's claim that her clients' complication rate is below 10%.
    • This exact p-value is very close to the p-value based on the simulations (0.1222), and we come to the same conclusion.
    • If it were plotted, the exact null distribution would look almost identical to the simulated null distribution shown in Figure 6.20 on page 290.
  • Introduction to finding equivalence Sets

    • With even a small graph, there are a very large number of such alternatives, and the computation is extensive.
    • An alternative approach with the same intent ("optimization by tabu search") (Network>Roles & Positions>Exact>Optimization) can much more quickly sort nodes into a user-defined number of partitions in such a way as to maximize automorphic equivalence.
    • There is no guarantee, however, that the number of partitions (equivalence classes) chosen is "correct," or that the automorphisms identified are "exact."
    • When we have measures of the strength, cost, or probability of relations among nodes (i.e. valued data), exact automorphic equivalence is far less likely.
  • Introducing and Formatting Quotations

    • To quote an author, copy the author's exact language and use quotation marks to show you are reproducing language from another source.
    • Quoting is using the exact words of another author.
    • Generally, you will choose a quotation rather than paraphrasing when you want to add an air of authority to the information you're presenting, when the words you're using are offered by a source important to your particular topic, or when the exact words have historical relevance or are particularly eloquent.
    • To quote an author, you should copy the author's exact language and frame the words with quotation marks, which signals that you are reproducing exact language from another source.
    • This graffiti-style quotation cites its source text and page number.
  • Randomization Tests: Contingency Tables: (Fisher's Exact Test

    • Describe how conservative the Fisher exact test is relative to a Chi Square test
    • The significance test we are going to perform is called the Fisher Exact Test.
    • where N is the total sample size (8), n is the sample size for the first group (4), r is the number of successes in the first group (3), and R is the total number of successes (3).
    • Note that in the Fisher Exact Test, the two-tailed probability is not necessarily double the one-tailed probability.
    • The Fisher Exact Test is "exact" in the sense that it is not based on a statistic that is approximately distributed as, for example, Chi Square.
  • How Fisher Used the Chi-Squared Test

    • Fisher's exact test is preferable to a chi-square test when sample sizes are small, or the data are very unequally distributed.
    • Fisher's exact test is a statistical significance test used in the analysis of contingency tables.
    • Fisher's exact test is one of a class of exact tests, so called because the significance of the deviation from a null hypothesis can be calculated exactly, rather than relying on an approximation that becomes exact in the limit as the sample size grows to infinity.
    • Bristol knows the number of cups with each treatment [milk or tea first] and will, therefore, provide guesses with the correct number in each category).
    • As pointed out by Fisher, under a null hypothesis of independence, this leads to a hypergeometric distribution of the numbers in the cells of the table.
  • Basic properties of point estimates

    • We also determined that these point estimates are not exact: they vary from one sample to another.
    • While we could also quantify the standard error for other estimates – such as the median, standard deviation, or any other number of statistics – we will postpone these extensions until later chapters or courses.
  • Calculating the Payback Period

    • To calculate a more exact payback period: Payback Period = Amount to be initially invested / Estimated Annual Net Cash Inflow.
    • Accumulate by year until Cumulative Cash Flow is a positive number: that year is the payback year.
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