Your first step is to normalize the data: that is, to assign standard scores in lieu of the raw scores you're starting with. The simplest way of doing this with your spreadsheet is as follows:

1. Calculate the mean and standard deviation of the values (raw scores) for the variable in question. For instance, you might obtain a mean of 77.5 and a standard deviation of 12.5

2. Subtract this mean score from each case's obtained score. (For instance, a case with a raw score of 86 would yield 86 - 77.5 = 8.5)

3. Divide this result by the standard deviation. (For instance, 8.5/12.5 = 0.68) This is a z score, and it is the basic form of standard score from which all others are derived. (That includes IQ scores, T scores, stanines, and so forth.) The mean score will be 0. Most of the values will be between -1 and +1; about 95% will be between -2 and +2.

Personally, I would stop there. But if you really want to force this onto a 0 to 1 scale, you could do as follows:

4. Change all values greater than 2 to 2 and all values lower than -2 to -2. You now have a four-point range. You lose a bit of information at the extremes, but not much.

5. Divide all values by 5. You now have a 1-point range. However, the mean is still 0.

6. Add 0.5 to all values. You now have a mean of 0.5 and a range extending from 0 to 1. About 2/3 of your cases will probably fall between 0.25 and 0.75.

Your first step is to normalize the data: that is, to assign standard scores in lieu of the raw scores you're starting with. The simplest way of doing this with your spreadsheet is as follows:

1. Calculate the mean and standard deviation of the values (raw scores) for the variable in question. For instance, you might obtain a mean of 77.5 and a standard deviation of 12.5

2. Subtract this mean score from each case's obtained score. (For instance, a case with a raw score of 86 would yield 86 - 77.5 = 8.5)

3. Divide this result by the standard deviation. (For instance, 8.5/12.5 = 0.68) This is a z score, and it is the basic form of standard score from which all others are derived. (That includes IQ scores, T scores, stanines, and so forth.) The mean score will be 0. Most of the values will be between -1 and +1; about 95% will be between -2 and +2.

Personally, I would stop there. But if you really want to force this onto a 0 to 1 scale, you could do as follows:

4. Change all values greater than 2 to 2 and all values lower than -2 to -2. You now have a four-point range. You lose a bit of information at the extremes, but not much.

5. Divide all values by 5. You now have a 1-point range. However, the mean is still 0.

6. Add 0.5 to all values. You now have a mean of 0.5 and a range extending from 0 to 1. About 2/3 of your cases will probably fall between 0.25 and 0.75.

Stephen's directions are very good. His advice to stop at step 3 is very wise. When people talk about normalized scores, they usually mean the results that you get at the end of step 3.

Dear Professor Stephen Joy, 

Thank you so much.  I really appreciate.

I did step 1-3 before  , its there in the doc. i attached,  if you tried to open it you could see that.

1. Is it right to use normalized data if i want to compute Pearson correlation ?

2,  Is it possible for me to use my  normalized data if i want to do a k-means clustering?

Sizyoongo

Dear  David Dunaetz,

Thank you. i still have some few questions below.

1. Is it right to use normalized data if i want to compute Pearson correlation ?

2,  Is it possible for me to use my  normalized data if i want to do a k-means clustering?

Thank you so much.

Sizyoonngo·

No real disadvantages except the slight loss of information at the extremes. But no gains either. As David says, a z score will be instantly recognizable to researchers; z scores are also the basic metric underlying correlation coefficients and beta-weights in regression equations. But if there is some reason to prefer a 0 - 1 scale, it's fine. Just make sure your readers know what you've done.

Dear Professor Stephen Joy ,

Thank you. i still have some few questions below.

1. Is it right to use normalized data if i want to compute Pearson correlation ?

2,  Is it possible for me to use my  normalized data if i want to do k-means clustering?

Sizyoongo

Sure, it's fine.

Too complicated. Just divide all numbers on the maximal value ;-))

Dear Igor I Katkov ,

What do you mean by "Too complicated"?

His suggestion is simpler, because it involves only one step and does put everything on a 0 - 1 scale. But it would not "normalize" the data in the sense of placing everything on an interval scale.

Dear Sizyoongo,

Those guys have given you hard time, haven't they. I've proposed a very simple answer, which in 95% is a proper one. The Occam razor rules! ;-))

• He is proposing to use so called non-parametric methods. It makes sense if you don't have exact score/numbers at the beginning but you can range the serious and group similar/same qualities together. For example, you a bouquet competition judge. You'd rank all competitors giving them scores. Then, you can now place them in equal interwals. Still, you can normalize them to the highest score and got rank of intervals say
• 0-0.2
• >0.2-0.4
• >0.4-0.6
• >0.6-0.8
• >0.8-1.0
• So, now, your data are normalized and placed in equal intervals.
• This methods is also widely used that one can prove that the distribution of the parameter is non-Gaussian ("abnormal") and all those criteria (t, p) are not applicable. If you have further Q's, we can meet at bldg 12 one day.

IK

 Dear Igor I Katkov,

Thank you for the input and your offer.

Sure  we can meet.  I can come to building 12.

Building 12 main entrance (facing the fountain) of the university, right?

Just give me the details what time,when i can come and how i will know that this is the person am meeting? I will really appreciate. Thanks in advance.

Sizyoongo

Правильно, тот, что выходит на фонтан, давайте во пятницу в 12:00. Сформулируйте Ваши вопросы.

До встречи,

Игорь Иванович

Уважаемый Игорь Иванович,

огромное вам спасибо.

До встречи!

Cизьенго М.

Договорились. Я буду с бородой и в джинсах по-амрикански наивной физиономией ;-))) Как Ваше име произносить по-русски: Сизийонго? По-моему, звучит как один из языков банту, так? Вы из шона, ндебеле?

(x - min(x)) / (max(x) - min(x))

xi−mean(x)/sd(x)

(A - min(A)) / (max(A) - min(A))

Om Raj Sapkota Thank you, though I’m done with this problem, but it can be useful for others.

Sizyoongo Munenge it would be nice if you could share your solution as it could be useful for others :)

Agree with Ali Rahmani and Om Raj Sapkota . Alternatively, it can be normalized by the maximum value only since there is no data in the negative zone.