Estimation of Missing observation By ANCOVA Lecture - 22

 

Estimation of Missing observation

By

ANCOVA

The following highlights the steps involved in the missing value procedure:

1.   1.  Insert zero for missing observations, i.e.

2.    2.  Introduce a dummy covariate consisting of 1’s for missing observation and 0’s for all other observations.

3.   3.  Carry out analysis of covariance.

4.   4.  Estimate the missing observation by:

 

Example: Estimate the missing value by using ANCOVA.

A	B	C
5	12	15
7	10	14
8	16	?

Solution:

Introduce a dummy covariate consisting of 1’s for missing observation and 0’s for all other observations and   Carry out analysis of covariance.

Computation for Y:

Computation for X:

Computation for XY:

The estimated missing value:

b = 14.505

Pros & Cons of ANCOVA

Pros of ANCOVA

i.                    ANCOVA used to control extraneous variations that can’t by blocking.

ii.                  ANCOVA identify the interaction between a response variable and concomitant variable.

iii.                ANOCOVA is used when there is a non-constant variability in the dependent variable.

iv.                ANCOVA help to identify the relationship between the independent variables and covariate.

v.                  ANCOVA is used, when the assumption of homogeneity of variance is not met.

vi.                ANCOVA is most suitable, when there is moderate correlation between response and confounded variables.

Cons of ANCOVA

i.                    ANCOVA is sensitive to outliers.

ii.                  The restrictive assumptions for data.

iii.                The technique of ANCOVA is not appropriate for small samples,

iv.                ANCOVA is not suitable, when there is no or weak correlation between response and confounded variables.

Similarities between ANCOVA and ANOVA

1.      1. The ANCOVA and ANOVA are used to analyze the effect independent variable(s) on dependent variable and both techniques are used to test the significance difference between treatment means.

2.      2. The ANCOVA and ANOVA are used to one way or multi way designs.

3.      3. The ANCOVA and ANOVA are used to F test.

Difference  between ANCOVA and ANOVA

The concept of ANOVA and ANCOVA are conceptually similar but different applications. ANOVA and ANCOVA are statistical techniques used to analyze the effect of categorical independent variable on the continuous dependent variable and test the significance between treatment effects by using F test. ANCOVA is used to control and study the influence confounded variables called covariates which ANOVA does not.

Let’s say a researcher desires to investigate the effect of three fertilizers onion growth rate. The researcher assigns three fertilizers to the onions with replication and measure the growth rate after several weeks.

In this experiment, the researcher could use ANOVA to determine whether onion growth rates are statistically different. The dependent variable is the onion growth rate, while the independent variable is the fertilizer types.

Let’s now give our earlier situation a twist. In addition to examine the fertilizer types, the researcher observes that the onion growth rate could be affected by quantity of sun light each batch receives. But the researcher’s primary aim is not sunlight.

ANCOVA would be the appropriate method to take in this situation. The amount of sunlight that each batch receives can be handled as a covariate. In this manner, the amount of sunshine may be controlled for, and the researcher can still investigate the impact of different fertilizers (called the independent variable) on onion growth (called the dependent variable).

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