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Questions and Answers
In a one-factor ANOVA, what conclusion can be drawn if the calculated F-statistic exceeds the critical F-value?
In a one-factor ANOVA, what conclusion can be drawn if the calculated F-statistic exceeds the critical F-value?
- Fail to reject the null hypothesis due to a mistake in the calculation.
- Reject the null hypothesis because there is evidence that all variances are equal.
- Fail to reject the null hypothesis because there is no evidence of a difference in the means.
- Reject the null hypothesis because there is evidence that at least one of the means is different. (correct)
What is the primary purpose of the analysis of variance (ANOVA) procedure?
What is the primary purpose of the analysis of variance (ANOVA) procedure?
- To determine if the variances of two or more samples are equal.
- To determine if the means of two or more populations are equal. (correct)
- To determine if the means of two samples are equal.
- To determine if the means of two or more samples are equal.
Which of the following assumptions is crucial for the validity of an ANOVA test?
Which of the following assumptions is crucial for the validity of an ANOVA test?
- The means associated with the dependent variable must be equal for each population.
- The dependent variable of interest for each population has a normal distribution. (correct)
- The variance associated with the dependent variable of interest must be independent for each population.
- All of the above assumptions are required.
An engineer measures the strength of plywood boards made with three different types of glue, with 20 boards per glue type. Given the following summary data, what is the grand mean of the plywood strength? Glue 1: Average = 37.8, Glue 2: Average = 41.05, Glue 3: Average = 41.95
An engineer measures the strength of plywood boards made with three different types of glue, with 20 boards per glue type. Given the following summary data, what is the grand mean of the plywood strength? Glue 1: Average = 37.8, Glue 2: Average = 41.05, Glue 3: Average = 41.95
An engineer tests the strength of plywood boards using three types of glue, measuring 20 boards per type. In a one-way ANOVA, what are the error degrees of freedom?
An engineer tests the strength of plywood boards using three types of glue, measuring 20 boards per type. In a one-way ANOVA, what are the error degrees of freedom?
An engineer investigates plywood board strength using three glue types, with 20 boards each. In a one-way ANOVA, what are the degrees of freedom between treatments?
An engineer investigates plywood board strength using three glue types, with 20 boards each. In a one-way ANOVA, what are the degrees of freedom between treatments?
An engineer analyzes plywood strength with three glue types, testing 20 boards per glue. Based on the summary data, determine the error sum of squares (SSE). Glue 1 Variance = 31.74737, Glue 2 Variance = 24.26053, Glue 3 Variance = 12.47105
An engineer analyzes plywood strength with three glue types, testing 20 boards per glue. Based on the summary data, determine the error sum of squares (SSE). Glue 1 Variance = 31.74737, Glue 2 Variance = 24.26053, Glue 3 Variance = 12.47105
An engineer tests plywood strength with three glue types (20 boards each) and conducts a One-Way ANOVA. Given the between groups SS is 190.6333, what is the MSTR (Mean Square Treatment)?
An engineer tests plywood strength with three glue types (20 boards each) and conducts a One-Way ANOVA. Given the between groups SS is 190.6333, what is the MSTR (Mean Square Treatment)?
An engineer investigates plywood strength using three glue types and ANOVA. With a total sample size of 60 and 3 groups, what is the MSE (Mean Square Error) given the within groups SS is 1301.1?
An engineer investigates plywood strength using three glue types and ANOVA. With a total sample size of 60 and 3 groups, what is the MSE (Mean Square Error) given the within groups SS is 1301.1?
Using the ANOVA table, what is the F-statistic?
Using the ANOVA table, what is the F-statistic?
Using the ANOVA output, what is the critical value at the 5% significance level?
Using the ANOVA output, what is the critical value at the 5% significance level?
Using the ANOVA output from question 11, what is the estimated p-value at the 5% significance level?
Using the ANOVA output from question 11, what is the estimated p-value at the 5% significance level?
According to the F-table above using an alpha of 5%, what is the result of our hypothesis test?
According to the F-table above using an alpha of 5%, what is the result of our hypothesis test?
A company is testing at the 5% significance level with the F-Stat at 23.34 and the critical value at 3.35, what is the conclusion to the hypothesis test?
A company is testing at the 5% significance level with the F-Stat at 23.34 and the critical value at 3.35, what is the conclusion to the hypothesis test?
When running a Tukey-Kramer test procedure with an alpha of 0.05, the null hypothesis was rejected for regional sales. What is the critical range?
When running a Tukey-Kramer test procedure with an alpha of 0.05, the null hypothesis was rejected for regional sales. What is the critical range?
Flashcards
Analysis of Variance (ANOVA)
Analysis of Variance (ANOVA)
A statistical approach for determining if the means of two or more populations are equal.
F Statistic vs. Critical F Value
F Statistic vs. Critical F Value
In ANOVA, if the F statistic exceeds the critical F value, you reject the null hypothesis, indicating that at least one of the means is different.
Required ANOVA Assumption
Required ANOVA Assumption
A required assumption is that the dependent variable of interest for each population has a normal distribution
Error Sum of Squares (SSE)
Error Sum of Squares (SSE)
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Degrees of freedom between treatments(c)
Degrees of freedom between treatments(c)
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MSTR (Mean Square Treatment)
MSTR (Mean Square Treatment)
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MSE (Mean Square Error)
MSE (Mean Square Error)
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F-Statistic in ANOVA
F-Statistic in ANOVA
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Tukey-Kramer Procedure
Tukey-Kramer Procedure
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Factor B in Two-Way ANOVA
Factor B in Two-Way ANOVA
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Finding MSA
Finding MSA
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F-Stat for Factor A
F-Stat for Factor A
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Critical Value for Factor A
Critical Value for Factor A
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Study Notes
- These notes pertain to a sample exam for ISDS 2001, covering topics in analysis of variance(ANOVA).
One-Factor ANOVA
- If the computed F statistic exceeds the critical F value, the null hypothesis (Hâ‚€) should be rejected
- Rejecting Hâ‚€ indicates evidence that at least one of the means are different
- The analysis of variance procedure is a statistical approach to determine whether means of two or more populations are equal
Assumptions for ANOVA
- The dependent variable of interest for each population has a normal distribution
Plywood Strength Experiment
- An engineer measures the strength of 20 plywood boards for each of three types of glue used.
- The data is used in a One-Way ANOVA.
Grand Mean Calculation
- To calculate the grand mean (average) of all values, you would consider all the groups count, sum and averages in excel to determine of grand mean of 40.27
Error Degrees of Freedom
- The error degrees of freedom for the plywood experiment is 57
- Calculated as the total number of observations (20 boards x 3 glues = 60) minus the number of groups (3 glues)
- Degrees of freedom between treatments(c) for the experiment is 2
Error Sum of Squares (SSE)
- The error sum of squares (SSE) for the plywood experiment is 1301.10.
Mean Square Treatment (MSTR)
- MSTR is 95.32
Mean Square Error (MSE)
- MSE for the plywood experiment is 22.83
F-Statistic Calculation
- The F-Stat is found to be 4.18, this is found dividing the MS for Between Groups by the MS for Within Groups.
- F = 95.31667/22.82632 = 4.18
Critical Value at 5% Significance
- The critical value at the 5% significance level is 3.35
Estimated P-Value
- P-value at the 5% significance level is greater than 0.10
Conclusion at 5% Significance Level
- The population means are not all equal
- The p-value is less than the alpha level
Hypothesis Test Conclusion
- With a statistical value of with the F-Stat at 23.34 and a critical value of 3.35, the null hypothesis is rejected
- The conclusion states the population means are not all equal
Tukey-Kramer Procedure
- The Tukey-Kramer procedure is used to test the difference in regional sales between Region 1 and Region 2
- The critical range is 2.06, with a 0.05 level of significance
Q Critical Value
- With error degrees of freedom of 23 and 3 treatment groups, the Q critical value at the 5% significance level is 3.56
Interpretation of Tukey-Kramer Results
- Do not reject the null, the sample mean difference is less than the critical range.
Two-Way ANOVA Components
- Factor B represents the rows in a two-way ANOVA test without interaction
Critical F-Value
- The critical F-value for the two-way ANOVA without interaction for Factor A with F(2,4) = 5.45 and alpha = 0.01 is 18.00
Degrees of Freedom
- For a two-way ANOVA without interaction, the degrees of freedom for Factor B, where there are 4 rows and 5 columns is 3
Excel Output Analysis
- Using the Excel output from a work shift using 4 different machines, the Mean Sum of Squares for Factor A (MSA) is 1916.58
- The F-stat for Factor A is 0.57 (Columns)
- the F-stat for Factor B (rows) is 8.71
- The critical value for Factor A at the 5% significance level is 5.14
- The critical value for Factor B is 4.76
- Factor B means differ, the null hypothesis is rejected at the 5% significance level
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