2uData ⮞Single Factor Experiments ⮞Overview of analysis of variance

Overview of analysis of variance

In order to better understanding the principle of analysis of variance (ANOVA), let's consider the example follows.

Example 2

To study the effect of preferred colour on intelligence of human being, an experiment was conducted with 3 colours A, B and C. For each colour, 10 persons are tested and their `IQ` are measured. The result is shown in Table 1.

Table 1 `IQ` and preferred colour.

	Colour A	Colour B	Colour C
	102	89	51
	88	100	76
	106	92	90
	93	76	117
	98	64	103
	104	104	64
	90	66	64
	103	98	50
	99	90	89
	92	82	67
Mean	97,5	86,1	77,1

The means of three groups are different clearly. But before to conclude about the effect of preferred colour on `IQ`, we consider the variation of `IQ` in these groups. This variation is shown in Fig. 1

Fig. 1 Variation of `IQ` in three groups

From Fig. 1, we recognize that the variation of `IQ` in each group is rather large due to random sampling. So, there is a question: The differences of `IQ` of three groups are really due to effect of colour or due to randomness only?

To answer this question, we compare two types of variations of `IQ`:

• variation between groups (also known as between treatments)
• variation within group (also known as within treatment)

If the variation between groups is greater significantly, there are real differences between groups. On the contrary, those difference is insignificant statistically.

Therefore, the method to realize this type of comparison is named as analysis of variance or briefly ANOVA. It is a form of hypothesis testing with pair of hypotheses:

• Ho : All the means of populations are equal
• Ha : At least two populations whose means are unequal

The details of ANOVA will be investigated in next page.