chance variation

(noun)

the presence of chance in determining the variation in experimental results

Examples of chance variation in the following topics:

  • The Sum of Draws

    • Your sum of draws is, therefore, subject to a force known as chance variation.
    • To better see the affects of chance variation, let us take 25 draws from the box.

  • Avoiding Repetitiveness

    • Introducing variation benefits not only your reader, but also yourself, the writer.
    • Repeating ideas or revisiting concepts in different ways gives you the chance to say convey the importance of your argument by approaching it from varied angles and fleshing out the ideas thoroughly; each variation is a chance to think through your argument and introduce nuance into your writing while driving your point home.

  • Chance Error and Bias

    • Chance error and bias are two different forms of error associated with sampling.
    • The variations in the possible sample values of a statistic can theoretically be expressed as sampling errors, although in practice the exact sampling error is typically unknown.
    • In sampling, there are two main types of error: systematic errors (or biases) and random errors (or chance errors).
    • Of course, this is not possible, and the error that is associated with the unpredictable variation in the sample is called random, or chance, error.

  • The F-Distribution and the F Ratio

    • The variance is also called variation due to treatment or explained variation.
    • The variance is also called the variation due to error or unexplained variation.
    • SSwithin = the sum of squares that represents the variation within samples that is due to chance.
    • Unexplained variation- sum of squares representing variation within samples due to chance: SSwithin = SStotal−SSbetween
    • Mean square (variance estimate) that is due to chance (unexplained): MSwithin = SSwithin /dfwithin

  • Mean Squares and the F-Ratio

    • The variance is also called variation due to treatment or explained variation.
    • The variance is also called the variation due to error or unexplained variation.
    • $SS_{\text{within}}$ is the sum of squares that represents the variation within samples that is due to chance.
    • Unexplained variation: sum of squares representing variation within samples due to chance: $SS_{\text{within}} = SS_{\text{total}} = SS_{\text{between}}$
    • Mean square (variance estimate) that is due to chance (unexplained): $\displaystyle{ MS }_{ \text{within} }=\frac { { SS }_{ \text{within} } }{ { df }_{ \text{within} } }$

  • Varying Your Sentence Structure and Vocabulary

    • Perhaps the biggest secret to creating captivating writing is variation.
    • If variation is key, what can we vary?
    • The same will be true of all variation.
    • Syntax variation cultivates interest.
    • Each variation is a chance to introduce nuance into your writing while driving your point home.

  • Chance Models

    • A stochastic model is used to estimate probability distributions of potential outcomes by allowing for random variation in one or more inputs over time.
    • Therefore, accurately determining the standard error of the mean depends on the presence of chance.
    • A stochastic model is a tool for estimating probability distributions of potential outcomes by allowing for random variation in one or more inputs over time.
    • The random variation is usually based on fluctuations observed in historical data for a selected period using standard time-series techniques.
    • Distributions of potential outcomes are derived from a large number of simulations (stochastic projections) which reflect the random variation in the input(s).

  • Advantages and Disadvantages of Sexual Reproduction

    • The genetic diversity of sexual reproduction, observed in most eukaryotes, is thought to give species better chances of survival.
    • The genetic diversity of sexually-produced offspring is thought to give species a better chance of surviving in an unpredictable or changing environment.
    • The only source of variation in asexual organisms is mutation.
    • Variation is the outcome of sexual reproduction, but why are ongoing variations necessary?
    • Each tiny advantage gained by favorable variation gives a species an edge over close competitors, predators, parasites, or even prey.

  • Variations in Accuracy

    • In the age of fact-checking, it's especially important to make sure that you have done your homework and fully researched your topic and supporting evidence because chances are, your audience already has.

  • Coefficient of Determination

    • $r^2$, when expressed as a percent, represents the percent of variation in the dependent variable $y$ that can be explained by variation in the independent variable $x$ using the regression (best fit) line.
    • $1-r^2$ when expressed as a percent, represents the percent of variation in $y$ that is NOT explained by variation in $x$ using the regression line.
    • For example, if one is trying to predict the sales of a car model from the car's gas mileage, price, and engine power, one can include such irrelevant factors as the first letter of the model's name or the height of the lead engineer designing the car because the $r^2$ will never decrease as variables are added and will probably experience an increase due to chance alone.
    • Approximately 44% of the variation (0.4397 is approximately 0.44) in the final exam grades can be explained by the variation in the grades on the third exam.
    • Therefore approximately 56% of the variation ($1-0.44=0.56$) in the final exam grades can NOT be explained by the variation in the grades on the third exam.