Analyses of variance on Minitab

Analyses of variance on Minitab

Objective

1. Utilize different functions on the Minitab software.
2. Analyze data from experiments to determine optimal settings, significant factors and future design possibilities.

Introduction

Analysis of variance (ANOVA) is a tool used in statistical analysis that splits an observed aggregate variability found in a data set into two parts: random factors and systematic factors. The systematic factors have a statistical influence on the given data set, while the random factors do not have any statistical influence. ANOVA is used by an analyst to test and determine the effect that independent variables have on the dependent variable in a regression study.

The ANOVA test is the initial step in analyzing factors that affect a given data set. Once the test is finished, an analyst performs additional testing on the methodical factors that measurably contribute to the data set’s inconsistency. The analyst utilizes the ANOVA test results in an f-test to generate additional data that aligns with the proposed regression models.

To determine whether a relation is available between two groups, an ANOVA analysis is used for comparison. The F statistic (also called the F-ratio), (a result of the ANOVA formula) allows for the analysis of multiple groups of data to determine the variability between samples and within samples. Null hypothesis(no distinct difference exists between the tested groups), the result of the ANOVA’s F-ratio statistic will be close to 1. Fluctuations in its sampling will likely follow the Fisher F distribution. This is a group of distribution functions, with two characteristic numbers, called the denominator degrees and the numerator degrees of freedom.

Methodology

The research utilized the collection of data from cleaning different type of stains from clothes using different detergents (detergent 1, detergent 2, detergent 3 and detergent 4). Three sets of clothes (same material and same colour) were stained each by a different type of stains each clothe was cleaned using the same detergent. The percentage of stain removal approximated and recorded. The process was repeated 3 more times using a detergent with different cleaning properties in each round. The experiment was done at a constant temperature of 25^O, a relative humidity of 45% and time 5 minutes using a washing machine. After each experiment, the washing machine was cleaned using clean water, and the water flushed out. The data obtained were analyzed using the Minitab software.

Results and discussion

To determine the best detergent to be used in cleaning all stains, the data obtained were analyzed using one-way ANOVA in Minitab 19.2.0. The percentage of stain removal from the clothes was the response factor while the four different types of detergents were the variables.

Summary

Output

Null hypothesis           All means are equal

An alternative hypothesis, not all means are equal

Significance level        α = 0.05

Equal variances were assumed for the analysis.

Analysis of Variance

From the data obtained the P (0.205) value obtained was greater than the significant level (α = 0.05) thus no enough evidence to reject the null hypothesis that the means are equal (have same cleaning properties).

Grouping Information Using the Tukey Method and 95% Confidence

From the data obtained grouping Information Using the Tukey Method and 95% Confidence since the means have the same letter, the difference in the mean is not statistically significant.

Model Summary

S                      R-sq                 R-sq(adj)         R-sq(pred)

4.38748           41.87%            20.07%            0.00%

From the model summary, the factor explains 41.87% of the variation in the response. S indicates that the standard deviation between the data points and the fitted values is approximately 4.38748units. The R-sq(pred) data obtained was found to be 0.0% showing that the model is less fit the data fed to it.

From the data residuals versus fits plot, the points appear randomly scattered on the plot.No outliers were found to be apparent since none of the group had substantial different variability.

Errors and recommendations.

Some errors were observed in the collection of data since it entailed approximation of the per cent of stain removed by the detergent a better method of stain detection should be used to increase the efficiency.

More data should be taken per detergent to increase the efficiency of the experiment.

Conclusion

The analysis of data obtained from the experiment was performed using a different function in the Minitab software.

The study finding did not show any superior  cleaning properties in any of the four detergents  but detergent 3 according to the interval plot of strain vs detergent  showed had better cleaning properties though not very distinctive while detergent 4 was the list effective

REFERENCES

Aalabaf-Sabaghi, M. (2011) ‘Applied Statistics for Business and Economics’, Journal of the Royal Statistical Society: Series A (Statistics in Society), 174(3), p. 848. doi: 10.1111/j.1467-985X.2011.00709_11.x.

Davies, A. (2017). Understanding Statistics : An Introduction, Libertarianism.org Press, Washington, D.C., viewed 6 August 2019, <http://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=1667844&site=ehost-live>.

Hartmann, H. (2016) ‘Statistics for Engineers’, Communications of the ACM, 59(7), pp. 58–66. doi: 10.1145/2890780.

Hochkirchen, T. (2011) ‘Applied Statistics for Engineers and Physical Scientists’, Journal of the Royal Statistical Society: Series A (Statistics in Society),

Lockow, E. (2012) ‘S. J. Morrison: Statistics for Engineers: an introduction’, Statistical Papers, 53(1), pp. 245–246. doi: 10.1007/s00362-010-0358-x.