Let me address each in kind.

Problem One: calculating the minimum sample size will require more information about your study. You need to specify a power level (usually 80%) and a false positive rate (usually 5%), as well as minimum expected effect size for the primary outcome of your study, as well as the exact type of model you are running to estimate this effect. All of this information is required to do a real sample size calculation.

An ad hoc approach (not recommended, but sometimes necessary for practical considerations) would be to use the general rule of thumb that you need approximately 15-20 units of measurement for each variable you wish to estimate in order to have a decently powerful model. It isn't clear to me exactly what you mean by "dimensions," but since you mention Likert scales in the figure it seems that you have ordinal predictors and moderators? In which case, the number of variables in your model depends on how you choose to parameterize your ordinal variables. The traditional (but by no means the only) approach is to use m-1 dummy variables, where m is the number of levels to the variable. In your case, that means your model would have seven total variables (including the criterion variable), in which case you should be looking for at least 100+ individuals. Note that this is a rule of thumb, not a strict contingency (and, further, not everyone agrees with this rule of thumb); more exact numbers require a detailed analysis using the information I mentioned above.

Problem Two: Comparing the p-values is not likely to be useful. P-values are more reflective of the model you fit than any strength of effect inherent in the variables in that model. All comparing the p-values would really tell you is the relative false positive rate for each variable given the modeling assumptions.

It depends on what exactly you mean by "stronger" or "better". It helps to review the literature in your field and develop a specific mathematical prediction for what would constitute a "stronger" variable in your context. This would depend on exactly what your moderator and criterion variables are "in the real world", and what you expect to see. If this is purely exploratory (e.g. you have no a priori knowledge of the relationships at hand), then you can just use any standard measure of effect size, which is dependent on exactly what kind of model you are fitting. For example, if you are fitting some sort of regression model, you can look directly at the coefficients of the moderator variables, which tell you how much they effect the criterion in a numerical sense, or use something like Cohen's d.

Let me address each in kind.

Problem One: calculating the minimum sample size will require more information about your study. You need to specify a power level (usually 80%) and a false positive rate (usually 5%), as well as minimum expected effect size for the primary outcome of your study, as well as the exact type of model you are running to estimate this effect. All of this information is required to do a real sample size calculation.

An ad hoc approach (not recommended, but sometimes necessary for practical considerations) would be to use the general rule of thumb that you need approximately 15-20 units of measurement for each variable you wish to estimate in order to have a decently powerful model. It isn't clear to me exactly what you mean by "dimensions," but since you mention Likert scales in the figure it seems that you have ordinal predictors and moderators? In which case, the number of variables in your model depends on how you choose to parameterize your ordinal variables. The traditional (but by no means the only) approach is to use m-1 dummy variables, where m is the number of levels to the variable. In your case, that means your model would have seven total variables (including the criterion variable), in which case you should be looking for at least 100+ individuals. Note that this is a rule of thumb, not a strict contingency (and, further, not everyone agrees with this rule of thumb); more exact numbers require a detailed analysis using the information I mentioned above.

Problem Two: Comparing the p-values is not likely to be useful. P-values are more reflective of the model you fit than any strength of effect inherent in the variables in that model. All comparing the p-values would really tell you is the relative false positive rate for each variable given the modeling assumptions.

It depends on what exactly you mean by "stronger" or "better". It helps to review the literature in your field and develop a specific mathematical prediction for what would constitute a "stronger" variable in your context. This would depend on exactly what your moderator and criterion variables are "in the real world", and what you expect to see. If this is purely exploratory (e.g. you have no a priori knowledge of the relationships at hand), then you can just use any standard measure of effect size, which is dependent on exactly what kind of model you are fitting. For example, if you are fitting some sort of regression model, you can look directly at the coefficients of the moderator variables, which tell you how much they effect the criterion in a numerical sense, or use something like Cohen's d.

HI, as you are going to do prediction, then we can use the G. power software to calculate sample size. Beside the information you provided in your case, one need to determine alpha {.05}, power {.80}, and effect size ES. The effect size can vary {small, moderate, & large}.

For moderate ES in regression (.15) and considering a total of 9 predictors [including the moderators] then the minimum sample size needed is 114.

However, with small ES (.02) minimum sample size is 791

and with large ES (.35) minimum sample size is 54

you can refer to literature to approximate your best ES

For the first question - since you are using SEM, I suggest you follow the sample size requirement proposed by Hair et al. (2010).

For the second question - you can test the moderation using Multi-Group CFA. First of all you need to confirm the existence of moderation. Then you use t-test for testing the two slopes. If both slopes are significant, then the type of moderation is "Partial Moderation". If one is significant and one is not, the the type of moderation is "Full Moderation"

You can download the notes in my RG.

I think Simmons and Prof. Ahmad answered it all.

Dear Ryan Simmons

thank you for the elaborate and comprehensive answer. These are my respond and further question based from your answer. Hope you are still willing to reply. Before you read i just want to inform you that my major in counseling, thus my field is considered as social science or behavioral science. I also found this article:

Green, S. B. (1991). How many subjects does it take to do a regression analysis. Multivariate behavioral research, 26(3), 499-510.

From this article i found a formula to determine sample size using multiple regression. I know that in testing moderation study, multiple regression can still be used. The formula are:

N>50+8k (To test R Square) and N>104+k (To test Individual β)

What do you think about this? Can i use this formula instead? If you not agree i hope you still willing to read my futher question about the sampling.

                                                         ----------------------

1. Regarding the sample size

From the two method that you have describe i prefer more using power analysis method rather than ad hoc methodh since you also wrote that not everyone agrees on ad-hoc method. Furthermore Ive been enriching myself about the term power analysis yesterday and have several question. I understand power and also false positive rate, however i still confuse about how do i determine the effect size. I know now  there are standardized effect size from Cohen (Small, Medium, Large). But I still confuse about this. Which effect size should i choose for my study? Upon my research i know that i have to go to previous studies to choose one of them.

However, i read that a lot of  researches actually do not inform their effect size once they have published their paper. So it will give me some difficulties to actually find one. So my next question is: Do i have to find "effect size" value from the previous researches or i can make use some other value to determining my effect size? 

I am aware that you wrote i can use of coefficient value to choose the effect size. And from an article i found this paragraph:

"Effect size measures either measure the sizes of associations or the sizes of differences. You already know the most common effect-size measure, as the correlation/regression coefficients r and R are actually measures of effect size. Because r covers the whole range of relationship strengths, from no relationship whatsoever (zero) to a perfect relationship (1, or -1), it is telling us exactly how large the relationship really is between the variables we've studied -- and is independent of how many people were tested. Cohen provided rules of thumb for interpreting these effect sizes, suggesting that an r of |.1| represents a 'small' effect size, |.3| represents a 'medium' effect size and |.5| represents a 'large' effect size."

So my question is: Can i use the coefficient r or R value from the previous researches to help me choose the effect size for my current research? Since usually every researches report their r or R value. More over, what kind of research should i look into? i am now doing a moderation study, do i need to find a "effect size value" from another moderation study or simple predictor study with similar variables will do? 

Say there are simple studies about relationship between the moderator variable to both predictor and criterion variable. Both studies shows that the r value is ".3". So basing from that 2 researches, can i choose "medium effect size" for my current study?

                                                                   -------------------

2. Regarding your confusion about dimensions

To make it more clear, i will give you an example. Happiness (or usually called Subjective Well Being) consist of two dimension (or maybe component is the right term) which are cognitive and affect. Diener conceptualize that for someone to be happy, one must satisfy with their life (cognitive) and feel more positive emotion and lack of negative emotion (affect).

That is the example, hope you ger more idea about what i meant by dimension.

                                                                       ----------------------- 

3. Regarding the better or stronger variable

Zainudin Awang has given me some information on how to tackle this. However i just want to inform on what i meant by better and stronger moderator variable. 

What i meant by better or stronger is: Which of this two moderator variable give a better buffering effect? Ill give example:

Let say student perceived stress is usually highly correlated with low level of happiness. But upon reading, is not always like that. Social Support and perceived financial security can affect those relationship. So i test these two variables (Social Support and Perceived Financial Security). Result show that social support is a better/stronger moderator variable compare to perceived financial security.

So, if a student feel high level of stress, having a high level social support would likely preserved their high level of happiness. Perceived financial security however, only buffer a little. So if a student feel high level of stress, having i high level of financial security will only help a little bit in preserving their level of happiness. Student may still feel happy but maybe only in medium level. Can you get an idea from my explanation?

Thank you, sorry for the long question. Cause im completely lost here... Hope you will still reply.

Best Regards

Dear Professor Muayyad Ahmad

Thank you for your answer really appreciate it. I know now about the G Power program. It is nice to know that this program also free to download. However, similar to my respond to Ryan Simmons. I still kind of confuse on how to determine my current choice of effect size. Especially in your final statement you said "you can refer to literature to approximate your best ES".

However, im still novice to this power analysis and dont really know how to analyze previous literature to determine my current choice of ES.

This are my question for your answer. This is the same with my question to Ryan Simmons, im just copy the specific part to make it easier for you to read.

                                                 --------------------------------------------

However, i read that a lot of  researches actually do not inform their effect size once they have published their paper. So it will give me some difficulties to actually find one. So my next question is: Do i have to find "effect size" value from the previous researches or i can make use some other value to determining my effect size? 

I am aware that you wrote i can use of coefficient value to choose the effect size. And from an article i found this paragraph:

"Effect size measures either measure the sizes of associations or the sizes of differences. You already know the most common effect-size measure, as the correlation/regression coefficients r and R are actually measures of effect size. Because r covers the whole range of relationship strengths, from no relationship whatsoever (zero) to a perfect relationship (1, or -1), it is telling us exactly how large the relationship really is between the variables we've studied -- and is independent of how many people were tested. Cohen provided rules of thumb for interpreting these effect sizes, suggesting that an r of |.1| represents a 'small' effect size, |.3| represents a 'medium' effect size and |.5| represents a 'large' effect size."

So my question is: Can i use the coefficient r or R value from the previous researches to help me choose the effect size for my current research? Since usually every researches report their r or R value. More over, what kind of research should i look into? i am now doing a moderation study, do i need to find a "effect size value" from another moderation study or simple predictor study with similar variables will do? 

Say there are simple studies about relationship between the moderator variable to both predictor and criterion variable. Both studies shows that the r value is ".3". So basing from that 2 researches, can i choose "medium effect size" for my current study?

That is my question Professor Muayyad Ahmad hope you will still reply.

Best Regards

Dear Zainudin Awang, thank you for your answer. Really appreciate it. These are my respond and further question from your answer. Hope you are still willing to answer.

1. Regarding the SEM (Structural Equation Modelling)

I am completely new to this SEM. I just read about it yesterday, I know from the book you wrote yesterday that the advantages of using SEM is that these technique examines series of dependence relationship simultaneously instead of single relationship at a time. However, i believe this statistical procedure is way above my level. In my statistic class, i have never encountered SEM. So my question for you is that:

Giving this situation, Can i pursue this research using a simple Multiple Regression technique? Can i still answer my research question (which is to know which one is the better moderator variable)?

                                                        -----------------------------

2. Regarding problem 2

Thank you for the suggestion i know and understand partial and fully moderated. But my question is, let say both moderation variable are significant (partial moderation) which among them has a stronger buffering effect. 

I may confuse you by my term of "stronger" and "better" but i hope this next example will give you a glimpse of idea.  This is the same with my explanation to Ryan Simmons, im just copy the specific part to make it easier for you to read.

                                                     --------------------

What i meant by better or stronger is: Which of this two moderator variable give a better buffering effect? Ill give example:

Let say student perceived stress is usually highly correlated with low level of happiness. But upon reading, is not always like that. Social Support and perceived financial security can affect those relationship. So i test these two variables (Social Support and Perceived Financial Security). Result show that social support is a better/stronger moderator variable compare to perceived financial security.

So, if a student feel high level of stress, having a high level social support would likely preserved their high level of happiness. Perceived financial security however, only buffer a little. So if a student feel high level of stress, having i high level of financial security will only help a little bit in preserving their level of happiness. Student may still feel happy but maybe only in medium level. Can you get an idea from my explanation?

                                                           -----------------------

So giving this explanation, can i still use t test to find out this problem?

Those are my question Zainudin Awang hope you will still reply.

Best Regards

Dear Giuseppe Cotellessa, thank you for the link. But im really sorry, i dont understand the language. 

Anyway you can explain it briefly in english?

Thanks

Dear Pelumi Oguntunde.

Yes i have found several information from their answer. However, if you see i still have several question regarding to their answer. If you dont mind to read and give further information i would appreciate it. 

Thanks

Best regard

You can use Gpower software ( avaliable as free version in the web ) to calculate sample size for many types of tests . 

also, you can get information about sample size calculation from the attachments files

Good Luck

Hi  Wilibrordus,

I apologize this is going to be rather a brief reply, but I'm in a bit of a hurry.

Anyway, let me try to address all of your questions. I apologize if I missed anything.

1) I am not familiar with that paper, but the formulas they provide there seem analogous to the rule of thumb I cited, and seem to give comparable results. I see nothing wrong with using it as a guideline, with all the caveats that must necessarily come with any rule of thumb.

2) As for finding estimated effect sizes, it is more art than science. It is not a mathematical question, anymore, it is a question of what you think you will see. You CAN use previous research (and should), but it isn't NECESSARY. If you have some other method of obtaining an estimate, by all means go ahead. As long as it is a principled estimate that you can justify, there is nothing wrong with it. And yes, you can use the R values from previous papers to determine this.

As for which effect size you should choose, it depends on what you expect. In many cases, people will power their analysis on the WORST CASE SCENARIO. That is, the minimum size of an effect that they think can possibly be important. For example, if the outcome measurement for your study is blood pressure and you are comparing two treatment groups with respect to blood pressure, you may decide that the smallest change in blood pressure that you would consider big enough to construe a treatment difference is, say, 10mmHg. So, you power your study around that hypothesized treatment difference.

In your case, you have to consider, non-statistically but practically, how you expect these moderators to influence the outcome. Is it realistic to expect the moderator to double the effect of the predictor? Or is it more realistic for it to modulate the predictor's effect by, say, 30%? Since you found those papers that seem to imply a value in the  0.3 range, that's a very safe bet.

And no, when looking through the literature for possible effect size ranges it doesn't HAVE to come from another moderation study. Realistically, it can come from any type of study design, so long as it is actually measuring the same thing you are trying to measure (e.g. an association between a moderator and an outcome).

I hope this helps. I apologize if it is a bit rushed or if I missed any questions.

Dear Giuseppe Cotellessa

I see, okay i will take a look into it. Thank you for the article and yes, if i have further questions. I will definitely post another questions in here

Thank you for your suggestion and have a nice day...

Dear Khalid Hassan

Thank you very much for your articles and suggestion. Yes i am now aware of the software and already downloaded it. I will take a look into all the articles that you have given me. 

Thank you very much for the suggestion and have a nice day...

Dear Ryan Simmons ·

Thank you for the follow up explanation. It more than enough. It gave so much information as to i am novice in this moderation study. I will now look into simple relations study between this variables, noted the r value and maybe i will go from there.

Again thank you for the explanation, have a nice day...

If you have data enough to test statistical significance, then you already have data for estimating association statistics. By comparing these association statistics you can figure out what you want: to decide which one is "stronger". ¿Which are your association statistics?.

Question: Giving this situation, Can i pursue this research using a simple Multiple Regression technique? Can i still answer my research question (which is to know which one is the better moderator variable)?

Answer: Solving the inter-relationship among constructs using Regression Methods is no longer acceptable since dealing with latent constructs (a construct measured using multiple items in a questionnaire) is one of the limitations in Ordinary Least Squares (OLS). 

Question: let say both moderation variable are significant (partial moderation) which among them has a stronger buffering effect. 

Answer: Testing moderation - first of all you need to verify the existence of moderation effects using the Multi-Group CFA. Once established and supposed that the type of moderation is partial moderation. The next step is you want to know in which group (low education respondents or high education respondents) the effects is more prominent. To answer this question, you need to compare the standardized path coefficients of Low Education and compare with the High Education respondents. The higher is the more prominent  group.

Hi 

I Use the NCSS PASS soft, that can be help to you.this soft is kind of simple.

this soft can be calculate your sample size for different situation,for example in you know or not your st.deviation of Statistical Society,By filling several blank,simply you calculate your sample size .if you want see the  software image please check attachment. 

Please work on the explanations given, it will assist alot