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Discriminant test

Discriminant analysis is a statistical technique used to compare effectiveness, understand the profits and losses, and set the best practices and recommendations. The target of this analysis is to determine the detectable difference between products. The Discriminant command in SPSS performs the canonical linear Discriminant analysis. It is based on linear combinations of the predictor variables. The Discriminant function analysis, linear function analysis are all generalised terms of Fisher's linear Discriminant. LDA is very closely related to ANOVA and regression analysis. In ANOVA there is the use of categorical independent variables and a continuous dependent variable, whereas Discriminant analysis has continuous independent variables and a categorical dependent variable. The analysis is done by creating one or more linear combinations of predictors. The purpose of Discriminant analysis is to maximally separate the groups and predict a classification based on the independent variables.

A Discriminant score can be calculated based on the weighted combination of the independent variables Di = a + b1x1 + b2x2 +…+ bnxn

Here, Di is the predicted score (Discriminant score)

x is predictor and b is the Discriminant coefficient

Assumptions

The assumptions of Discriminant analysis are very same as those for MANOVA.

    1. Cases should be Independent
    2. Linear Discriminant analysis is used when covariances are equal, and that quadratic Discriminant analysis may be used when covariances analysis are not equal.
    3. Predictive power can decrease with an increased correlation between predictor variables.
    4. The sampling of participants is done randomly and the score of the participant on one variable is assumed as the independent score for all other participants too.

Steps of conducting Discriminant analysis (DA)

Discriminant analysis is to predict group membership from a set of predictors. Thus, DA is MANOVA turned around.

Research question: Do PERF, INFO, VERBEXP permit the classification of students by types of learning disabilities?

    1. DV: Types of learning disabilities (3 groups)
    2. Memory: Children whose major difficulty seems to be with tasks related to memory;
    3. Perception: Children who show difficulty in visual perception;
    4. Communication: Children with language difficulty. IVs (predictors):
    5. PERF: Performance Scale IQ of the WISC;
    6. INFO: Information subtest of the WISC;
    7. VERBEXP: Verbal Expression subtest of the ITPA;

Open SPSS then:

    1. From the menu, click on Analyze -> Classify -> Discrimiant…
    2. In the appearance window, move DV (grouping variable) into Grouping Variable: -> hit Define Range… -> specify lowest and highest values of grouping -> Continue
    1. Move all IVs to Independents: Hit Statistics… -> Check Box’s M, Fisher’s -> Continue
    1. Hit Classify… -> check Combined-groups -> Continue
    1. Hit Save… -> check predicted group membership, Discriminant scores, probabilities of group membership -> Continue
    1. Hit Continue and then hit Paste.

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