Question

1. Explain the similarities and dissimilarities between a t-test of two independent samples and a chi-square test. In your response, be sure to discuss the following: null and alternative hypotheses, distributions, significance levels, test statistics, critical values, p-values, criteria for making an inference, and interpretation of results.

2. What conditions must be met for three or more samples to be evaluated using Analysis of Variance? What needs to occur before you can determine whether one specific group differs significantly from another specific group?

Answer 1

1)

Two Sample t-test	Chi-square test
The two-sample t-test is used to compare the means of two independent populations, denoted µ1 and µ2	Chi-square test use to compare two independent binomial proportion and Binomial proportion typically represents a response rate, cure rate, survival rate, abnormality rate, or some other ‘event’ rate.
Assumption: 1) Samples of n1 and n2 observations are randomly selected from the two populations. 2) Assume that the two populations are normally distributed and have the same variance ()	Assumption: 1) 2x2 contingency tables: Each observation is independent of all the others. 2) All expected counts should be 10 or greater.
Hypothesis: H0:  µ1 µ2 HA: µ1 µ2	Hypothesis: H0: HA:
significance levels Often, we choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used.	significance levels Often, we choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used
Test statistics Pooled variance	Test statistics Observed cell frequencies Expected cell frequencies
Critical values Using t-test table we can find the Critical value	Critical values Using Chi-square table we can find the Critical value

P-Value 1) P-Value help to decide accept or reject H0 2) A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis

P-Value 1) P-Value help to decide accept or reject H0 2) A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis

criteria for making an inference DF= N-1 or P-Value < or > 0.05 or other level of significance	criteria for making an inference DF = (r - 1) * (c - 1) or P-Value < or > 0.05 or other level of significance
interpretation of results if P-Value <0.05 A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.	interpretation of results if P-Value <0.05 A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

2. What conditions must be met for three or more samples to be evaluated using Analysis of Variance?

One Way ANOVA:

1) ANOVA compare three or more group based on independent sample from each group.

2) Assuming samples are from normally distributed population with equal variance.

What needs to occur before you can determine whether one specific group differs significantly from another specific group?

In ANOVA we need check variance homogeneity which means that the within group variance is constant across groups. This can be expressed as