I have two categorical variables, 1. Type of BO- sole proprietorship, partnership, private, and public, coded as 1,2,3, and 4; 2. Type of training- Technical and behavioural, coded as 1 and 2.
Null hypothesis: There is no significant difference in delivery of training at different types of organisation.
What test can be applied through SPSS?
It seems interesting how one interpets the mean of categorical variables! I think of an example calculating the mean, say, automobile brands: what might be the mean of a Porsche, a Mercendes and two Fords? Possibly a Fiat? Not sure...
Sums, and, hence, means are simply not defined for categorical variables. It is nonsensical to think this ways. And it does not matter how the values are coded (e.g. numerically by 1,2,... as you mentioned). The coding is arbitrary and remains arbitrary, and so are all statistics like sums and means and variances calculated from such arbitrarily numerical-coded categories.
What is possible is to compare frequency distributions. You can analyze the difference in the freuency distribution of "technical" and "behavioural"and the type of BO. One can calulate odds ratios for this. And if one wants mindlessly to test hypotheses, one could go for a Chi² test or Fischers exact test.
Where do the means come in?
IF there is a continuous response (ie. there is another variable measuring say the perceived quality of training) , you have a two-way ANOVA which of course makes asssumptions which need to be at least approximately fulfilled
For SPSS
https://www.youtube.com/watch?v=cOmbrK-TOqo
and
https://statistics.laerd.com/spss.../two-way-anova-using-spss-statistics.php
Two-Way ANOVA - Using SPSS to Test Assumptions
https://www.youtube.com/watch?v=Y8f0DbNp6-c
Means of categorical variable? Or means of categorized continuous variable?
It seems interesting how one interpets the mean of categorical variables! I think of an example calculating the mean, say, automobile brands: what might be the mean of a Porsche, a Mercendes and two Fords? Possibly a Fiat? Not sure...
Sums, and, hence, means are simply not defined for categorical variables. It is nonsensical to think this ways. And it does not matter how the values are coded (e.g. numerically by 1,2,... as you mentioned). The coding is arbitrary and remains arbitrary, and so are all statistics like sums and means and variances calculated from such arbitrarily numerical-coded categories.
What is possible is to compare frequency distributions. You can analyze the difference in the freuency distribution of "technical" and "behavioural"and the type of BO. One can calulate odds ratios for this. And if one wants mindlessly to test hypotheses, one could go for a Chi² test or Fischers exact test.
You should compare the proportions (not means) of two categorical variables using chi-square test.
When determining what analyses to use, I find it helps to start with the outcome.
In your example, you have defined your outcome as "Delivery of training". How is this outcome measured? I would recommend different analysis methods (e.g. linear regression, logistic regression, Chi-sq for homgeneity, etc) based on the form of the outcome (continuous, ordinal, nominal, rate?).
If the "delivery of training" is synonymous with "type of training" (that you defined as a dichotomous variable with levels 1 & 2), I would recommend logistic regression (for models with more than 1 predictor) or Chi-Sq for independence (For models with only a single predictor) to estimate measures of association between the predictor and the outcome. Both of these methods are available in SPSS.
NOTE: there may be more complex issues that require more complex analytic methods due to study design issues that you have not mentioned, e.g. matching, clustering, etc.
Excellent comments...
Thank you all... It was very helpful to me...
I have met the similar problem and I think comparing the proportions of two categorical variables using Minitab. It may help to look at this tutorial https://onlinecourses.science.psu.edu/stat500/node/55
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