Kashif Latif

A statistical method for making

simultaneous comparisons between three or

more means.

If we are only comparing two means,

ANOVA will produce the same results as

the t test for independent & dependent

Samples.

The t-test can only be used to test differencesbetween two means. When there are more than twomeans, it is possible to compare each mean witheach other mean using many t-tests.

But conducting such multiple t-tests can lead tosevere complications and in such circumstanceswe use ANOVA. Thus, this technique is usedwhenever an alternative procedure is needed fortesting hypotheses concerning means when thereare several populations.

When you choose to analyses your data using aone-way ANOVA, part of the process involveschecking to make sure that the data you want toanalyses can actually be analyses using a one-wayANOVA.

You need to do this because it is only appropriateto use a one-way ANOVA if your data "passes“following assumptions that are required for a oneway ANOVA to give you a valid result.

Dependent variable should be measured at the interval

or ratio level.

Independent variable should consist of two or more

categorical, independent groups.

Should have independence of observations.

There should be no significant outliers.

Dependent variable should be approximately normally

distributed.

There needs to be homogeneity of variances.

One of the principle advantages of this

technique is that the number of

observations need not be the same in each

group.

Additionally, layout of the design and

statistical analysis is simple.

A manager wants to raise the productivity at his company byincreasing the speed at which his employees can use aparticular spreadsheet program. As he does not have the skillsin-house, he employs an external agency which providestraining in this spreadsheet program.

They offer 3 courses: a beginner, intermediate and advanced course.He is unsure which course is needed for the type of work they do athis company, so he sends 10 employees on the beginner course, 10on the intermediate and 10 on the advanced course.

When they all return from the training, he gives them a problem tosolve using the spreadsheet program, and times how long it takesthem to complete the problem. He then compares the three courses(beginner, intermediate, advanced) to see if there are anydifferences in the average time it took to complete the problem.

SPSS generates following quite a few

tables in its one-way ANOVA analysis.

Descriptives Table

ANOVA Table

Multiple Comparisons Table

The descriptives table (see below) provides some very useful

descriptive statistics, including the mean, standard deviation and

95% confidence intervals for the dependent variable (Time) for each

separate group (Beginners, Intermediate and Advanced), as well as

when all groups are combined (Total). These figures are useful when

you need to describe your data.

This is the table that shows the output of the ANOVA analysis and

whether we have a statistically significant difference between our

group means. We can see that the significance level is 0.007 (p =

.007), which is below 0.05. and, therefore, there is a statistically

significant difference in the mean length of time to complete the

spreadsheet problem between the different courses taken. This is

great to know, but we do not know which of the specific groups

differed. Luckily, we can find this out in the Multiple Comparisons

Table which contains the results of post-hoc tests.

From the results so far, we know that there are significant differences between the groups

as a whole. The table below, Multiple Comparisons, shows which groups differed from

each other. The Tukey post-hoc test is generally the preferred test for conducting post-

hoc tests on a one-way ANOVA, but there are many others. We can see from the table

below that there is a significant difference in time to complete the problem between the

group that took the beginner course and the intermediate course (p = 0.021), as well as

between the beginner course and advanced course (p = 0.011). However, there were no

differences between the groups that took the intermediate and advanced course (p =

0.960).

There was a statistically significant difference betweengroups as determined by one-way ANOVA(F(2,27) = 6.087, p = .007).

A Tukey post hoc test revealed that the time tocomplete the problem was statistically significantlylower after taking the intermediate(23.0 ± 2.8 min, p = .021) and advanced(22.6 ± 3.8 min, p = .011) course compared to the beginnerscourse (27.2 ± 3.0 min).

There were no statistically significant differences between theintermediate and advanced groups (p = .960).