Statistics problem

[ManOfSteel]

Hello,

 

I have 9 means for 9 separate samples. I would like to compare them (with a software) to know if they are significantly different.

 

What test(s) should I use? A Student t-test for mean comparison?

 

Can it be done with Excel, as it's the only software I've got right now?

 

But if it can't be done with Excel could you show me how to do it with SPSS?

 

Thank you for your help.

[Glider]

There are a couple of problems:

 

1) A t-test will only test for a difference between two samples.

 

Are these means from measures of the same thing over time, or are they measures of different things? To compare three or more samples you need to use ANOVA. You need to give a bit more information to tell what type of ANOVA you can use.

 

2) You can't dirtectly compare means using a t-test.

 

You need the raw data as t-tests (and ANOVA) need to calculate the variance around the means in order to work out whether the means are significantly different.

 

I'm guessing you have the raw data, but as you only say you have the means, I just thought I'd make sure.

 

I don't know about Excel, but I can talk you through ANOVA or t-test on SPSS if you tell me what these measures are (what has been measured and how).

[ManOfSteel]

Hello and thanks for your reply.

 

Are these means from measures of the same thing over time, or are they measures of different things?

The latter. I'm trying to compare the average number of cigarettes smoked in 9 countries. So I have 9 averages/means, each for a different country (sample).

 

I'm guessing you have the raw data, but as you only say you have the means, I just thought I'd make sure.

It's actually an imaginary example and the 9 numbers are fictious. I'm just trying to understand if and how such a particular case would work, because I might need it later.

So if I have nothing but the 9 means, is there any way to do it or is it just impossible?

[Glider]

Hello and thanks for your reply.

 

The latter. I'm trying to compare the average number of cigarettes smoked in 9 countries. So I have 9 averages/means, each for a different country (sample).

Ok, then the research question would be 'Is there a difference in the number of cigarettes smoked according to country?' To put it another way, 'Is there an effect of the factor 'country' on the number of cigarettes smoked?

 

So 'country' is your factor (Independent Variable) and it has 9 levels (each different country). Having only one factor (IV) with more than two levels means you need to run a One-Way ANOVA (see below).

 

 

It's actually an imaginary example and the 9 numbers are fictious. I'm just trying to understand if and how such a particular case would work, because I might need it later.

 

So if I have nothing but the 9 means, is there any way to do it or is it just impossible?

You cannot compare single values for statistical difference. ANOVA stands for Analysis Of Variance and it basically tests the variance around the means and compares them for each cell (level of the IV) to see if any vary significantly from the others, so you need the raw data.

 

However, it's easy enough to make up. For the sake of the exercise, all you need to do is to make up around 20 numbers for each level (country) where each group of 20 numbers adds up to one of the means you have for each country. In reality, you would have asked 20 people from each country, how many cigarettes they smoke per day.

 

In SPSS, you will need to create two variables. The first is your grouping variable which you would name COUNTRY. In the ‘variable view’ window of SPSS, you would apply value labels in the ‘values’ column. This is where you apply a numerical value to each level of your IV (i.e. each country), for example, 1 = USA; 2 = Germany; 3 = Italy; 4 = Spain and so-on (using whatever countries you used, obviously).

 

The next variable you would name CIGARETTES. This contains the values of your dependent variable (DV). You don’t need to label this variable, it is ratio data so you can just enter the values (no coding needed).

 

Then, switching to the DATA VIEW window (using the tab at the bottom left), you just enter your data. In the first column you enter your country codes, so in this exercise you would enter 20 ‘1’s, then 20 ‘2s’ then 20 ‘3s’ and so-on.

 

In the DV column (you named CIGARETTES), you enter the raw data, where each row (case) is one person’s answer to the question ‘How many cigarettes do you smoke per day?’. There will be 20 people from the USA (in this example), so those values will be entered in the first 20 rows, next to the value ‘1’ in your grouping variable. The next 20 from Germany would be entered in the next 20 rows, next to the value ‘2’ in your grouping variable and so-on.

 

Your data sheet should look something like this (I have cut the groups of 20 to three, just to illustrate).

 

____COUNTRY____CIGARETTES

.........1......................20

.........1......................40

.........1......................30

.........2......................20

.........2......................10

.........2........................5

.........3........................8

.........3......................10

.........3......................15

 

And so-on, down to 9 (ignore the dotted lines, it's the only way I could get the columns to space out).

 

Then all you need to do is to go to the menu bar and click on ‘Analyse’ – ‘Compare Means’ – One-Way ANOVA’ and a dialogue box will come up.

 

Select the DV (CIGARETTES) and place it in the 'Dependent List' using the arrow.

 

Select the factor (COUNTRY) and place it in the 'Factor' box using the arrow.

 

Then click ‘OK’ and SPSS will run the ANOVA.

[ManOfSteel]

It's all clear now. Your explanation is very interesting and helpful. Thank you.

[iNow]

Wow. That brought back some memories. I haven't used SPSS in a while. Great post, and good help, Glider. Well done, sir.

[Glider]

It's all clear now. Your explanation is very interesting and helpful. Thank you.

You're welcome.

 

There is one other thing, if you were to run a One-Way ANOVA, the output would only tell you whether or not there is an effect, but if there is, it won't tell you where the effect is (i.e. [/i]which[/i] group(s) smokes the most/least cigarettes).

 

If you want to find out which group(s) differ the most, you'll need to obtain some descriptive stats, a table of means or a bar chart. The differences should become obvious then.

 

If it's still not obvious, you might need to run some post-hoc analyses (t-tests or something) between the higher and lower groups to find out exactly which differ significantly.

 

Tukey's test of Honestly Significant Differences which can be found in the One-Way ANOVA 'post hoc' analyses box (it's listed as 'Tukey') will run pairwise comparisons, comparing each group with every other group. That tends to be the quickest way I think.

 

Wow. That brought back some memories. I haven't used SPSS in a while. Great post, and good help, Glider. Well done, sir.

Why, thank you sir. You're a gent.

[ManOfSteel]

There is one other thing' date=' if you were to run a One-Way ANOVA, the output would only tell you whether or not there is an effect, but if there is, it won't tell you where the effect is (i.e. [i']which[/i] group(s) smokes the most/least cigarettes).

 

If you want to find out which group(s) differ the most, you'll need to obtain some descriptive stats, a table of means or a bar chart. The differences should become obvious then.

Yes, of course.

I don't know yet how the output looks in SPSS (I will get it tomorrow), but in Excel there's a SUMMARY table right before the ANOVA table that shows the sample size, sum, average and variance.

 

 

If it's still not obvious' date=' you might need to run some post-hoc analyses (t-tests or something) between the higher and lower groups to find out exactly which differ significantly.

 

Tukey's test of Honestly Significant Differences which can be found in the One-Way ANOVA 'post hoc' analyses box (it's listed as 'Tukey') will run pairwise comparisons, comparing each group with every other group. That tends to be the quickest way I think.

[/quote']

This Tukey test seems interesting. As far as I know, there's no such test in Excel. SPSS obviously provides many more options.

 

 

Thanks again.