1. Describe a scenario where a researcher could use a Goodness of Fit Test to an
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Question
1. Describe a scenario where a researcher could use a Goodness of Fit Test to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
2. Describe a scenario where a researcher could use a Test for Independence to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
3. Describe a scenario where a researcher could use an Analysis of Variance to answer a research question. Fully describe the scenario and the variables involved and explain the rationale for your answer. Why is that test appropriate to use?
4. The Goodness of Fit Test and Test for Independence both use the same formula to calculate chi-square. Why? I.e., explain the logic of the test.
5. ANOVA is based on an F-ratio that is calculated as the ratio of two variance estimates, the variance between groups and the variance within groups, but enables conclusions to be made about the means of the samples involved. What is the logic of that? I.e., explain the rationale that supports the use of variance estimates.
Explanation / Answer
1. Describe a scenario where a researcher could use a Goodness of Fit Test to answer a research question.
Fully describe the scenario and the variables involved and explain the rationale for your answer.
Why is that test appropriate to use?
Answer-
suppose the resrchar want ot test the data is followes the perticular distribution, the best way to testing is goodness of fit
it is a non-parametric test that is used to find out how the observed value of a given
phenomena is significantly different from the expected value. In Chi-Square goodness of fit test, the term goodness
of fit is used to compare the observed sample distribution with the expected probability distribution.
Chi-Square goodness of fit test determines how well theoretical distribution (such as normal, binomial, or Poisson) fits
the empirical distribution. In Chi-Square goodness of fit test, sample data is divided into intervals. Then the numbers of
points that fall into the interval are compared, with the expected numbers of points in each interval.
2. Describe a scenario where a researcher could use a Test for Independence to answer a research question.
Fully describe the scenario and the variables involved and explain the rationale for your answer.
Why is that test appropriate to use?
Answer-The Chi-Square test of Independence is used to determine if there is a significant relationship between two
nominal (categorical) variables from the data. The frequency in the data of one nominal variable is compared with different values of the second
nominal variable. The data can be displayed in an R*C contingency table, where R is the row and C is the column.
For example, a researcher wants to examine the relationship between gender (male vs. female) and empathy (high vs. low).
The chi-square test of independence can be used to examine this relationship. If the null hypothesis is accepted there
would be no relationship between gender and empathy. If the null hypotheses is rejected the implication would be that
there is a relationship between gender and empathy (e.g. females tend to score higher on empathy and males tend to score
lower on empathy).
3. Describe a scenario where a researcher could use an Analysis of Variance to answer a research question.
Fully describe the scenario and the variables involved and explain the rationale for your answer.
Why is that test appropriate to use?
Answer- suppose reserchar want to test the all tratment are eaqually effective or diffreantlly effective, in a such case the
ANOVA came in to the picture. suppose reserchar want to test the A,B,C and D treatment are giving the same or diffreant effect.
4.The Goodness of Fit Test and Test for Independence both use the same formula to calculate chi-square. Why? I.e.,
explain the logic of the test.
Answer_ the basic reson is that, ei-oi , in both cases we have to calculate the square diffreance diffreance between the data.
5) ANOVA is based on an F-ratio that is calculated as the ratio of two variance estimates, the variance between
groups and the variance within groups, but enables conclusions to be made about the means of the samples involved.
What is the logic of that? I.e., explain the rationale that supports the use of variance estimates.
Answer- Analysis of Variance (ANOVA) is a statistical method used to test differences between two or more means.
It may seem odd that the technique is called "Analysis of Variance" rather than "Analysis of Means." As you will see,
the name is appropriate because inferences about means are made by analyzing variance.wwhen we calculate the variation between the groups it is
depends on the all mean values of the data, f is tha ration of two variances.
ANOVA is used to test general rather than specific differences among means
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