If you collect data from the whole population, you do not need any inferential statistics! Inferential statistics is a method to estimate the population parameters from a sample and estimate the precision of your estimate. When the 24 samples are your population, then any parameter, mean, standard deciation, correlation is that of this specific population, there is no need to claculate any singnificance or anything like that.

The evaluation of these parameters, e.g. correlation is  high vs. low, is up to you and your expertise. You will not find answers to this questions in inferential statistics.

As you may know, to calculate reliable correlations, the sample size should be larger than 30 (than t-distribution becomes similar to Z-distribution). However, if n=24 most likely represents the populations, it is legitimate to use N=24 to calculate correlations.

N=24 is a populations.

Hi Syamsul Nor Azlan Mohamad, correlations are characterized by strength (magnitude), and if a random sample, by significance. Not by reliability.

To calculate the magnitude, 3 samples would be mathematically sufficient. But for a very small sample size, a very strong magnitude would more likely still result to a non-significant relationship.

On the other hand, in a very large sample size, a very low magnitude may still result to a significant relationship.

For a sample size of 24, t-test of r ( which is parametric), is used to determine significance of relationship.

Hi Syamsul, it is statistically accepted or better for your sampling number =30 and above

If you collect data from the whole population, you do not need any inferential statistics! Inferential statistics is a method to estimate the population parameters from a sample and estimate the precision of your estimate. When the 24 samples are your population, then any parameter, mean, standard deciation, correlation is that of this specific population, there is no need to claculate any singnificance or anything like that.

The evaluation of these parameters, e.g. correlation is  high vs. low, is up to you and your expertise. You will not find answers to this questions in inferential statistics.

No the minimu number of observations is 50 for excelent results

Statistically, you can calculate the correlation for data of size 24 or less but the question is how to calculate it as the method of calculation depends on the type of data (quantitative or qualitative). However, if you want to test whether or not the correlation is the significant, you need to worry about the normality of your data and the size. In your situation as you mention that N=24 is population so you do not worry about the size of population and you can calculate any parameter using tools of descriptive statistics not inferential statistics

I suggest doing  a scatterplot first of all. If it shows no pattern, you have your answer. If it does look flattened around what could be a straight line, then you could obtain a correlation coefficient with its confidence interval (whose lower end will hopefully be well away from zero).

Thanks for all advise, I will look forward everyone suggestion and share the result later. 

Yes you can apply  correlation analysis for 24 sample. U can also apply t-test analysis to check whether these features are same or different (significantly).

In sample if you have taken all units of the population, you can go for correlation analysis. 

The question asks about seeing the relation between variables.  The choice of approach depends on the nature of the variables.

For a pair of "continuous" variables, there is no better way to see their relation than by looking at their scatterplot.  If the pattern of the points is reasonably close to linear, you can use the correlation coefficient to summarize the strength of the relation.  Because the usual correlation coefficient is a measure of the strength of linear relation, I insist on seeing the scatterplot before I consider that numerical measure.

For a pair of categorical variables, you can look at their crosstab.  The step from crosstab to numerical summary depends on whether the variables are ordinal or only nominal and on how many categories they have.

For a categorical variable and a "continuous" variable, I would make parallel "dot plots" of the continuous variable by category of the categorical variable.  To show less detail, I would then make parallel boxplots.

Overall, the key idea is to see what is going on in the data.

Yes it is possible to compute correlation for a sample of size 24. A scatter plot give you a rough and fair idea of the the relationship between the variables. this you can see pictorially. Since correlation talks about the relationship between variables, it beholds on you to go a step further to ascertain the predictive power of your independent variable(s) by computing the coefficient of determination. This helps you to know know the extent to which the independent variable can explain or predict your dependent various. You can compute this by squaring the value of your correlation coefficient and expressing it in percentage form to know how much of the dependent variable has been explained by the independent variable. Remember the number of variables you are studying also need to be considered.

Remember:  correlation is measuring LINEAR relashonship only

Something to add. If this is a case of continued data you can use Pearson correlation, if is not, better measure of correlation can be Spearman 

Dear Syamsul

if your study utilized  DDR as a design approach,  24 experts as your panel of FDM or ISM is ok.  But for the survey method you should add more sample.

Pearson correlation is used when your data is normally distributed, moreover it measures linear relationship only!! Best way is to perform a scatter plot at first to see the pattern of the points you have.

I think I need more information.

1) What is the nature of the scale? (nominal,ordinal etc.)

2) Are the 24 in the sample supposed to represent a larger population? Or are you only interested in the 24? If a larger population is of interest, how was the 24 selected?

3) Is there an independent and dependent variable? Or are you only interested in the relationship between variables?

The answers to these questions should lead to a good answer that might be in the above responses to you question.

Dear Paul Raffled,

Nature of scale is Ordinal, Likert scale 1 to 5.

24 is a sample from the whole population, because I am executing a small group evaluation to test the prototype. Participants were selected based on coursework offers at that time.

Only interested in the relationship between variables, in this case I examine the relationship of ARCS Motivational Level consists 4 factors attention, relevance, confidence and satisfaction.

Dear Prof Saedah Siraj,

The research design was DDR, I have implemented FDM to access expert evaluation on designing and developing a model.

After finish on designing and developing a model, 24 participants were joined the survey to get some feedback on the implementation phase, however the number is a population. Reason why to have correlation to see the significance value of ARCS model towards the use of the model.

I am not familiar with your instrument but if it has multiple items and subscales, reliability will have an effect on any correlations.  There is a relationship between reliability and correlations. Don't use published reliability information. It may not hold for your N of 24.

Check the reliability yourself.

Most use parametric correlations such as Pearson when using such a scale 1-5.

However, if you want to know if this would hold for other such samples of 24, this may not be the best approach.

Hope the helps.

Thanks Paul Raffled for your suggestion. It's very helpful.

Get some clear in my mind...

First of all, I would like to know if you measured the whole population or a sample of a population. It seems not clear to me through all of the answers so far. If you measured a sample, I agree with Paul's statement that you should be cautious to transfer your results on to other samples/populations. But, if it is the case that you measured a whole population, I would not expect that you can transfer your results at all, unless you have a hypothesis that these two populations do not differ with regard to the correlation of your parameters. If interested, you could assess if two correlations from two different samples are different from each other, via Fisher's r to z transformation, but I am not sure if this also holds for populations. If two populations have different parameters, than it is simply that way and that difference is it, again, no inferential statistics needed. Up to you to evaluate the ammount of difference.

About Paul's other statement, concerning the reliability: he is right, but there is also a method to estimate the "true" correlation between your parameters, if both were perfectly reliable. You can use the "Correction for attenuation" formula by Spearman rx'y'=rxy/sqrt(rxx*ryy)

Dear Rainer Duesing,

N=24 is a sample from the whole population. My constraint whereas I only can access one group (n=24) to execute the intervention. 

Ok, than everything of inferential statistics applies to your sample, including the Fisher's transformation, significance testing, power analysis etc., but also Spearman's correction for attenuation, I hope this helps, otherwise just ask ;-)

Thanks Rainer Duesing, very appreciate yours and others help...

Dear Syamsul

You can use G*Power software to calculate suitable sample size.

G*Power software is effective tool to calculate sample size for many ranges of experiments. Also, you can determine effect size and power of the test, G*Power is free to download and easy to use after reading the manual, the download link:

http://download.cnet.com/G-Power/3000-2054_4-10647044.html

The link to download G*Power manual:

http://www.gpower.hhu.de/fileadmin/redaktion/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/gpower/GPowerManual.pdf

Good Luck