n = 24 zones x 20 = 480 according to

Tabachnik and Fidell, who recommend that you take 20 times more cases than IV for multiple or hierarchical regression.

However, they say that a BARE MINIMUM REQUIREMENT IS AT LEAST 5 TIMES MORE CASES THAN IV:s, pp. 128-129, second edition. In your case it means that between 120 to 480 could be OK.

Thanks you Béatrice Marianne Ewalds-Kvist.

You meant in this case if I am using let's say 2 IV I must use at least 40 observations?

At least 5 per IV and at most 20 per IV. You decide.

Did I understand you in a wrong way when I thought that a zone was an IV?

Yes, Béatrice Marianne Ewalds-Kvist, sorry maybe I wasn't clear in my question. The 24 zones mentioned in this post is about the total number of observation that I have and not the total IV.

n = Number of IV * 20 like you said,

Thank you!

As long as your research aimed to explore the driving forces of crimes in a particular city , i think you should take the minimum number of observations( 5 per IV). Then it's up to you .

Thank you Ali Alhayany,

It helps! I appreciate it.

SEE CORRECTION below! [The "Bible" in medical statistics (Altman, 1991), said at least 50 cases just for a start, and the 8 per IV. If you have, let's say 5 IV, you should have at least 90 - 100 cases. This suggestion is sound; you should have a minimum of cases before you even begin thinking about regression. ]

Best

John-Kåre

Dear Jonh, Thank you very much!

It helped a lot!

PS

Actually it was the other way around. It is Tabachnick & Fidell who advice at least 50 cases + 8 per iv for multiple regression (2007, p. 123). Altman said n/10,(1991, p. 349). As Altman said: "There is no rule, but a guidance would be....n/10 where n is the sample size", and _"a model with too low n would be extremely unreliable".

Similarly, Tabachnick & Fidell called their suggestion a rule of thumb.

Then my advice would be: Follow Barbara & Linda's (Tabachnick & Fidell) suggestion. They seemed to describe this as a minimum and also note situations where n has to be considerably higher (e.g., skewed DV, small effect size etc).

Best John-Kåre

You must have at least two observations for each variable to capture crude variation.In order to get consistent results at least 32 observations for each variable.Sampling & response errors are to controlled by apriori information. Quality data will reflect true variability.However, it is suggested that you need to have 24 zones* 32=768 observations for the study.In case you have data on supplementary variables, multi-way stratification procedure is suggested.

your case consists of an exploratory analysis of a territory limited to a single city that is divided into 24 suburban areas. So your data matrix has 24 lines that correspond to the cases to be analyzed. The first point to clarify is that you have data of the entire population (although limited to areas of a single city) and not of a sample: so you do not have to make any sample inference vs population. The second, and most important point, is that you are working with a unit of ecological (territorial) analysis and therefore you can not make inferences on the individual level. In other words, you must avoid falling into the paradox of the fallacy of ecology, known thanks to the contribution of Robinson (1950). The object of your study is the criminal conduct that is obviously individual behavior, even if the socio-territorial context can exert an influence. My advice is to be aware of the explorative and territorial character of your study and, beyond the number of cases, be very careful not to extend the results from the territorial level to the individual level. Last but not the least observation. Having 24 cases, you must contain at most the number of independent variables (say no more than 4 or 5, if less is better).

to deepen the theme of ecological fallacy I suggest you read:

Robinson W S 1950. Ecological correlations and the behavior of individuals. American Sociological Review 15: 351–357.

Thank you Giovanni Di Franco,

You understood my question very well!

I will check the reference.

You helped me a lot!

Thank you Viswanath N S.

There are two answers I think:

1) k+2 where k is the number of predictors. This is the minimum required to derive an error term for the model. It won't generally be a very useful or precise model (but there may be exceptions)

2) it depends on how big the effects are you want to be able to detect relative to the error in the sample. This leads naturally to some kind of power/sample size estimate (or an analogous approach if you don't use significance tests)

Rules such as those suggested by Tabachnick & Fidell (actually Green's rule as they did not originate the formula) assume certain patterns of correlation among the predictors (probably independence) and a certain magnitude of effect relative to error. It is worth looking at Green's original paper to see if those assumptions are appropriate (I suspect generally not).

Green, S.B. How many subjects does it take to do a regression analysis? Multivariate Behavioral Research, 1991, 26, 499-510

Hi

In order to select a suitable sample, the following remarks need to be developed.

1.Research studies are usually carried out on sample of subjects rather than whole populations. The most challenging aspect of fieldwork is drawing a random sample from the target population to which the results of the study would be generalized. The key to a good sample is that it has to be typical of the population from which it is drawn. When the information from a sample is not typical of that in the population in a systematic way, we say that error has occurred. In actual practice, the task is so difficult that several types of errors, i.e. sampling error, non-sampling error, Response error, Processing error,… In addition, the most important error is the Sampling error, which is statistically defined as the error caused by observing a sample instead of the whole population. The underlying principle that must be followed if we are to have any hope of making inferences from a sample to a population is that the sample be representative of that population. A key way of achieving this is through the use of “randomization”.

2. There several types of random samples, Some of which are: Simple Random Sampling, Stratified Random Sampling, Double-stage Random Sampling... Moreover, the most important sample is the simple random sample which is a sample selected in such a way that every possible sample of the same size is equally likely to be chosen. In order to reduce the sampling error, the simple random sample technique and a large sample size have to be developed.

3. Specific remarks:

The following factors are highly affected the sample size and need to be identified:

• Population Size,
• Margin of Error,
• Confidence Level (level of significance) and
• Standard of Deviation.

4. Then, the sample size can be estimated by,

Necessary Sample Size = (z-score or t-value)2 * StdDev*(1-StdDev) / (margin of error)2 .

5. For more details, please refer to

Cochran,W.G. (1977). Sampling techniques, Wiley.

Snedecor, W.G. and Cochran,W.G. (1989). Statistical Methods, Blackwell.

Regards,

Zuhair