Analysis Of Variance

Question 1

What is analysis of Variance?

Answer 1

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

Question 2

What is Experiment?

Answer 2

A procedure carried out for analyzing cause and effect.

Question 3

What is Experimental Design?

Answer 3

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

Question 4

Three parts of Experimental Design

Answer 4

1. Write Statistical Hypotheses
2. Collect Data
3. Analyze Data

Question 5

Statistical Hypotheses

Answer 5

An assumption about value of population parameter? Mane?

Question 6

Types of Statistical Hypotheses

Answer 6

1. Null hypothesis
2. Alternative Hypothesis

Question 7

What is null hypothesis

Answer 7

○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.

Question 8

What is alternative hypothesis?

Answer 8

○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.

Question 9

Independent variable

Answer 9

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

Question 10

Dependent Variable

Answer 10

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

Question 11

Extraneous variables

Answer 11

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

Question 12

F Ratio:

Answer 12

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.

Question 13

P-Value:

Answer 13

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.

Question 14

S

Answer 14

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).

Question 15

Significance Level

Answer 15

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

Question 16

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

Answer 16

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.