# One Way Analysis of Variance

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21 March 2016

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One-way Analysis of Variance

(Abbreviated one-way ANOVA) is a technique used to compare means of two or more samples (using the F distribution). This technique can be used only for numerical data. It consists of a single factor with several levels and multiple observations at each level. With this kind of layout we can calculate the mean of the observations within each level of our factor. The residuals will tell about the variation within each level. It can also average the means of each level to obtain a grand mean. And then look at the deviation of the mean of each level from the grand mean to understand something about the level effects. Finally, can compare the variation within levels to the variation across levels. Hence the name analysis of variance.

Used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. It tests the null hypothesis that samples in two or more groups are drawn from populations with the same mean values. And compares the means between the groups you are interested in and determines whether any of those means are significantly different from each other.

Formula

F= q MSBMSWWhere: F = Fisher’s Ratio
K = Number of Columns
N = Total Number of items

MSB= SSBK-1

MSW= SSWN-K

Attitudes of the 1st, 2nd, 3rd and 4th year EHS students towards their computer subject

Attitude| Year| Average Weighted Mean| Rank|
| 1st| 2nd| 3rd| 4th| | |

Study regularly| 3.44| 3.37| 3.50| 3.56| 3.47| 9|
Regularly exercise the skills| 3.73| 3.88| 3.65| 3.58| 3.71| 6.5| Listen attentively during class discussion| 3.62| 3.71| 3.67| 3.85| 3.71| 6.5| Always do the assignment without hesitation| 3.63| 3.73| 3.83| 3.75| 3.75| 5| Always work on projects without hesitation| 3.94| 4.10| 4.12| 4.00| 4.04| 2| Enjoy the hands-on activity| 4.13| 4.38| 4.06| 4.25| 4.21| 1| Search and use other computer reference| 3.83| 3.83| 3.54| 3.92| 3.78| 4| Always take down notes during discussion| 3.67| 3.67| 3.77| 4.04| 3.79| 3| Ask questions whenever the topic is unclear| 3.37| 3.38| 3.54| 3.63| 3.48| 8| Likeability of the subject| 2.98| 3.62| 3.12| 3.25| 3.24| 10| | | | | | |

Grand Means| 3.63| 3.77| 3.68| 3.79| 3.72|

The table shows the summary of the attitudes of the EHS students towards their computer subject. Having computed the Average Weighted Means, Rank 1 is indicator f, which is “I enjoy our hands-on activities” with an average mean of 4.21. The Last rank goes to indicator j, which is “I like my computer subject”, with an average mean of 3.24. This indicates that the EHS students do not like their computer subject. Though the third year likes their computer subject, they are only a fraction of the whole which do not like their computer subject. This further indicates that the students manifest positive attitude towards their computer subject because of the grand weighted mean of 3.72. This signifies that even though they do not like their computer subject, they still manifest positive attitude for they have the majority of the indicators.

Reference

Anonymous.August 23,2013.One-way analysis of variance. http://en.wikipedia.org/wiki/One-way_analysis_of_variance Anonymous.August 23,2013.One-way ANOVA. https://statistics.laerd.com/statistical-guides/one-way-anova-statistical-guide.php Anonymous.August 23,2013.One-Way ANOVA. http://www.itl.nist.gov/div898/handbook/ppc/section2/ppc231.htm

"One Way Analysis of Variance" StudyScroll, 21 March 2016, https://studyscroll.com/one-way-analysis-of-variance-essay

StudyScroll. (2016). One Way Analysis of Variance [Online]. Available at: https://studyscroll.com/one-way-analysis-of-variance-essay [Accessed: 4 December, 2023]

"One Way Analysis of Variance" StudyScroll, Mar 21, 2016. Accessed Dec 4, 2023. https://studyscroll.com/one-way-analysis-of-variance-essay

"One Way Analysis of Variance" StudyScroll, Mar 21, 2016. https://studyscroll.com/one-way-analysis-of-variance-essay

"One Way Analysis of Variance" StudyScroll, 21-Mar-2016. [Online]. Available: https://studyscroll.com/one-way-analysis-of-variance-essay. [Accessed: 4-Dec-2023]

StudyScroll. (2016). One Way Analysis of Variance. [Online]. Available at: https://studyscroll.com/one-way-analysis-of-variance-essay [Accessed: 4-Dec-2023]

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