Analysis Of Variance Flashcards

(16 cards)

1
Q

What is analysis of Variance?

A

Analysis of Variance is a collection of statistical methods that researchers use to determine whether mean score vary significantly accross treatment groups or not.

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2
Q

What is Experiment?

A

A procedure carried out for analyzing cause and effect.

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3
Q

What is Experimental Design?

A

Experimental Design refers to the plan for conducting the experiment in such a way that the results will be valid and easy to interpret.

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4
Q

Three parts of Experimental Design

A
  1. Write Statistical Hypotheses
  2. Collect Data
  3. Analyze Data
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5
Q

Statistical Hypotheses

A

An assumption about value of population parameter? Mane?

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6
Q

Types of Statistical Hypotheses

A
  1. Null hypothesis
  2. Alternative Hypothesis
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7
Q

What is null hypothesis

A

○Mean of population i and mean of population J have no difference.
○It is denoted by Hnaught.
○It is denoted by H0. H

○H0: μi = μj
○Here, μi is the population mean for group i, and μj is the population mean for group j.

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8
Q

What is alternative hypothesis?

A

○The mean of population ‘i’ and population ‘j’ have difference.

○The alternative hypothesis is automatically accepted if the null hypothesis is rejected.

○H1: μi ≠ μj

○This hypothesis makes the assumption that population means in groups i and j are not equal.

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9
Q

Independent variable

A

The varible that is in control of experimentor. It is generally thought to be a possible cause in a cause-and-effect relationship.

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10
Q

Dependent Variable

A

The varible that is not under experimentors control. On dependent variable affect of independent variable or cause is reflected.

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11
Q

Extraneous variables

A

An extraneous variable is any other variable that could affect the dependent variable, but it is not significantly included in the experiment.

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12
Q

F Ratio:

A

A mathematical formula to compare differences between groups.

Test Statistic (F Ratio)*

  • The F Ratio is a mathematical formula that helps us compare the differences between groups (e.g., dance skills with music vs. without music).
  • It’s like a special calculator that gives us a number (F) that tells us how significant the difference is.
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13
Q

P-Value:

A

The probability of getting the results by coincidence.

  • The P-Value is the probability of getting the results we did (or more extreme) if the Null Hypothesis is true.
  • Think of it like a percentage chance that the difference we saw is just a coincidence.
  • If the P-Value is low (usually less than 0.05), it means the difference is unlikely to be a coincidence, so we reject the Null Hypothesis.
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14
Q

S

A

The actual value of the test statistic (F Ratio) from our data.

  • S is the actual value of the test statistic (F Ratio) calculated from our data.
  • It’s like the answer we get from the special calculator (F Ratio).
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15
Q

Significance Level

A

The maximum probability of being wrong when rejecting the Null Hypothesis.

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16
Q

Is F ratio always given in questions or i have to figure it out

A

In statistical problems, the F Ratio might be:

  1. Given directly:
    The question provides the F Ratio value, and you use it to calculate the P-Value and test the hypothesis.
  2. Calculated from data:
    You’re given the data, and you need to calculate the F Ratio using the appropriate formula. This is often the case in more complex problems or when working with raw data.
  3. Implicitly provided: The question gives you the necessary information to calculate the F Ratio, such as the means, standard deviations, and sample sizes of the groups being compared.

If you’re not given the F Ratio directly, you’ll need to calculate it using the relevant formula, which typically involves:

  • Means of the groups (x̄)
  • Standard deviations of the groups (s)
  • Sample sizes of the groups (n)
  • Degrees of freedom (df)

The F Ratio formula varies depending on the specific test, but common ones include:

  • One-way ANOVA: F = (MSbetween / MSwithin)
  • Two-way ANOVA: F = (MSinteraction / MSwithin)

Make sure to check the problem statement or question for the necessary information to calculate the F Ratio or determine if it’s given directly.