Skip to main content

Analysis of Variance

Analysis of Variance (ANOVA)

 is a statistical method used to test differences between two or more means. It may seem odd that the technique is called “Analysis of Variance” rather than “Analysis of Means.” As you will see, the name is appropriate because inferences about means are made by analyzing variance.

ANOVA is used to test general rather than specific differences among means. This can be seen best by example. In the case study “Smiles and Leniency,” the effect of different types of smiles on the leniency shown to a person was investigated. Four different types of smiles (neutral, false, felt, miserable) were investigated. The chapter “All Pairwise Comparisons among Means” showed how to test differences among means. The results from the Tukey HSD test are shown in Table 1.

Table 1. Six Pairwise Comparisons.
Comparison
Mi-Mj
Q
p
False – Felt
0.46
1.65
0.649
False – Miserable
0.46
1.65
0.649
False – Neutral
1.25
4.48
0.010
Felt – Miserable
0.00
0.00
1.000
Felt – Neutral
0.79
2.83
0.193
Miserable – Neutral
0.79
2.83
0.193
Notice that the only significant difference is between the False and Neutral conditions.

ANOVA tests the non-specific null hypothesis that all four population means are equal. That is,

μfalse = μfelt = μmiserable = μneutral.

This non-specific null hypothesis is sometimes called the omnibus null hypothesis. When the omnibus null hypothesis is rejected, the conclusion is that at least one population mean is different from at least one other mean. However, since the ANOVA does not reveal which means are different from which, it offers less specific information than the Tukey HSD test. The Tukey HSD is therefore preferable to ANOVA in this situation. Some textbooks introduce the Tukey test only as a follow-up to an ANOVA. However, there is no logical or statistical reason why you should not use the Tukey test even if you do not compute an ANOVA.

You might be wondering why you should learn about ANOVA when the Tukey test is better. One reason is that there are complex types of analyses that can be done with ANOVA and not with the Tukey test. A second is that ANOVA is by far the most commonly-used technique for comparing means, and it is important to understand ANOVA in order to understand research reports.

Comments

Post a Comment

Popular posts from this blog

Frequency Distribution and Data Presentation

A  frequency distribution is a table that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of values in the sample. Organizing Data. 1.Arrange data into an array 2. Decide on the number of classes( k) 3. Calculate the class interval 4. Prepare a tally sheet There are two types of Frequency:  Categorical frequency distribution. Grouped frequency distribution. Categorical Frequency Distributions The categorical frequency distribution is used for data that can be placed in specific categories or represent values of a qualitative variable. Grouped Frequency Distributions: When the data are numerical and their range is large, the data must be grouped into classes that are more than one unit in length. Histogram The histogram is an accurate graphical representati...
Post a Comment
Read more

Hypothesis Testing

Hypothesis refers means an educated guess or an assumption that can be tested. Forms of hypothesis: 1.       HA- Research hypothesis 2.       HO- Null hypothesis HA: Research hypothesis: The research hypothesis is also known as an alternate hypothesis. HA is a statement on which a statistical hypothesis test is set up. HO- Null hypothesis: Null hypothesis is also known as no difference or no relationship, this is used to facilitate testing of research hypothesis Types of hypothesis: ·         One-tailed- Directional HA: p>0 HO: p<0 ·         Two-tailed- non-directional HA: p not equal to zero Types of Error: Type 1 Error – Rejection of a true Null hypothesis. Type 2 Error – It may have a false negative finding. Type 1 error is donated by Alpha. Level of significant can reduce...
Post a Comment
Read more

Population and Sample

A Population comprises of all elements showing the parameters of an individual or objects. Whereas, a Sample is a sub-set of a population showing statistics.
Post a Comment
Read more