# Can i get some help with an Analysis of variance table ANOVA?

• scot72001
In summary, the conversation discusses a questionnaire completed by 155 hospital patients, examining the variables of Satisfaction and Stay. A partial analysis of variance table is given for the means model, and a partial analysis of variance table for the regression of Satisfaction on Stay is also provided. The conversation also mentions performing a lack-of-fit F-test to determine the null hypothesis and R2. The conclusions drawn are that the means of the different levels of Stay are not significantly different, there is a significant linear relationship between Satisfaction and Stay, and the predicted values are significantly different from the observed values. R2 is equal to 0.069 in both cases.
scot72001
having a little trouble with the question below. its on a sample exam paper I'm doing. any help would be appreciated

155 hospital patients completed a questionnaire about their hospital stay. We examine the variables
Satisfaction and Stay (length of stay). Stay is measured in days and takes values 1,2,3,4,5,6,7, while
Satisfaction is compiled from the completed questionnaire.
(a) A partial analysis of variance table for the means model is given below.
Analysis of Variance on Stay
Source DF SS MS F p
Stay * 25.23 * * *
Error * * * * *
Total * 364.51
Fill in the entries marked *'. State the hypothesis being tested and give your conclusions.
What is R2? What is the estimate of ?
(b) A partial analysis of variance table for the regression of Satisfaction on Stay is given below.
Analysis of Variance
SOURCE DF SS MS F p
Regression * * * * *
Error * 345.57 *
Total * *
Fill in the entries marked *'. State the hypothesis being tested and give your conclusions.
(c) Perform the lack-of- t F-test. What is the null hypothesis? Do you reject the null hypothesis?

What is R2?(a)MS = 25.23/7 = 3.61F = MS/ErrorError = SS/(n-1)Error = 364.51/154 = 2.364F = 3.61/2.364 = 1.52p = 0.22The hypothesis being tested is whether the means of the different levels of Stay are equal. Since p>0.05, we do not reject the null hypothesis and conclude that the means of the different levels of Stay are not significantly different. R2 = SSregression/SStotal = 25.23/364.51 = 0.069(b)MS = SSregression/1 = 25.23F = MS/ErrorError = SSerror/154 = 345.57/154 = 2.25F = 25.23/2.25 = 11.2p<0.05The hypothesis being tested is whether there is a significant linear relationship between Satisfaction and Stay. Since p<0.05, we reject the null hypothesis and conclude that there is a significant linear relationship between Satisfaction and Stay. (c)The null hypothesis for the F-test is that there is no difference between the predicted values and the observed values. We compare the SSE with the SST to determine if there is a significant difference. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that the predicted values are significantly different from the observed values. R2 = SSregression/SStotal = 25.23/364.51 = 0.069

## 1. What is an Analysis of Variance (ANOVA) table?

An ANOVA table is a statistical tool used to analyze the differences between multiple groups or treatments, by comparing the variability within each group to the variability between groups. It provides a summary of the data, including the mean, sum of squares, degrees of freedom, F-statistic, and p-value.

## 2. How does ANOVA differ from t-test?

While both ANOVA and t-test are used to compare means between groups, t-test is used when there are only two groups, while ANOVA can be used for more than two groups. ANOVA also takes into account the variability within each group, whereas t-test only looks at the differences between the means of two groups.

## 3. When should ANOVA be used?

ANOVA should be used when there are three or more groups being compared. It is commonly used in experimental studies to determine if there is a significant difference between groups, for example, to test the effectiveness of different treatments.

## 4. How do you interpret the results of an ANOVA table?

The F-statistic in the ANOVA table measures the ratio of the between-group variability to the within-group variability. A large F-statistic means that there is a significant difference between the groups. The p-value indicates the probability of obtaining the observed results by chance. A p-value less than 0.05 is typically considered statistically significant.

## 5. Can ANOVA be used for non-parametric data?

No, ANOVA is a parametric test, which means it assumes that the data follows a normal distribution. If the data does not meet this assumption, a non-parametric test such as the Kruskal-Wallis test should be used instead.

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