What is One-way anova

One-way analysis of variance is similar to t-test, but is used when you have two or more groups and you wish to compare their mean scores on a continuous variable. It is called one-way because you are looking at the impact of only one independent variable on your dependent variable. A one-way analysis of variance (ANOVA) will let you know whether your groups differ, but it won’t tell you where the significant difference is, but you can conduct post-hoc comparisons to find out which groups are significantly different from one another.

Analysis of variance (ANOVA) is a collection of statistical models used to analyze the differences among group means and their associated procedures (such as "variation" among and between groups)

Oneway Anova used to test the hypothesis of equal average of the sample group with the ability to make the mistake of only 5%.

Example

Example: Analysis of the difference between customer attributes (gender, age, occupation, income …) for 1 certain issues (usually chosen as dependent factors, e.g.  Satisfaction or Loyal).

Assumptions

Some assumptions when analyzing One-way Anova:

– The comparison group must be independent and are selected at random.

– The comparison group to have a normal distribution or sample size should be large enough to be seen as asymptotic normal distribution.

– Variance of the comparison group must be equal.

Note: if the overall assumption normally distributed with equal variances does not meet the test, then you can use a non-parametric test Kruskal-Wallis replace ANOVA.

Levene test

Ho: "The variance equal"

Sig <0.05: reject Ho

Sig> = 0:05: accepting Ho -> eligible for further analysis Anova

ANOVA test

Ho: "Average of differece group equal"

Sig> 0.05: reject Ho -> unqualified to confirm no difference…

Sig <= 0:05: accepting Ho -> confirmed eligible to differ…

When there are differences, they may further analysis to find out the difference between the groups how to observe.

How to using anova with spss:

For example, we answer the question: are there any difference of Satisfaction of customer between 3 Age group of them.

Click Analyze menu -> Compare Means -> One-Way ANOVA

Move variable Age to Factor box

Move variable Satisfaction to Dependent list box

Click on the Options, chose “Homegeneity of variance test” to test the homogeneity of variance.

Click OK, SPSS show the result

Two table explain here:

Table Homegeneity:

Ho: "The variance equal"

Sig <0.05: reject Ho

Sig> = 0:05: accepting Ho -> eligible for further analysis Anova

Tables Anova :

Ho: "Average of differece group equal"

Sig> 0.05: reject Ho -> unqualified to confirm no difference…

Sig <= 0:05: accepting Ho -> confirmed eligible to differ…

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