# Math Help - appropriate tests for randomly selected data in spss?

1. ## appropriate tests for randomly selected data in spss?

Hi. I am having troubles with what test should I use in comparing randomly selected data using spss?

Cr concentrations----------------Cr concentration absorption
15.00 mg/kg-------------------------------3.54
45.00 mg/kg-------------------------------4.27
75.00 mg/kg-------------------------------2.63
105.00 mg/kg------------------------------3.76
135.00 mg/kg------------------------------2.23
165.00 mg/kg------------------------------3.88
195.00 mg/kg------------------------------6.39
225.00 mg/kg------------------------------8.18
255.00 mg/kg------------------------------9.15
285.00 mg/kg------------------------------5.30
315.00 mg/kg------------------------------4.33

I want to know a test that is much similar to One-way ANOVA. I cant use ANOVA because of too few cases. I want to know if there is a significant difference among Cr concentration absorptions. Thanks!

Followup question:

Which test is better for post-hoc tests? LSD, Tukey, or Games-Howell test?

2. ## Re: appropriate tests for randomly selected data in spss?

Okay, so you have 2 continuous variables.
The first is something you control, while the second is a result.
How about... a linear regression?

3. ## Re: appropriate tests for randomly selected data in spss?

Hello.

Cr concentrations = is the treatment that we have done for each pot of soil. we injected 15 mg/kg, 45 mg/kg of chromium and so forth to each pot of soil. We grow plants in each soil to see if chromium has an effect on plants.
Cr concentration absorption = is the amount that our plants absorb from each pot of soil.

We made it as triplicates (15-A mg/g, 15-B mg/kg, 15-C mg/kg), but due to budget constraints, we randomly selected from each concentration (we picked 15-B mg/kg, 45-C mg/kg, 75-A mg/kg and so forth).
I want to know if there is a significant difference among Cr concentration absorptions. I've been using SPSS software and I chose one-sample t-test, but the problem is i do not know what test value to use. If I could just enter this randomly selected data as means, so that I can use ANOVA for significant differences.
Any help is greatly appreciated.

Followup question:

Which test is better for post-hoc tests? LSD, Tukey, or Games-Howell test?

4. ## Re: appropriate tests for randomly selected data in spss?

And also, I want to know which concentrations have the significant differences. thanks!

5. ## Re: appropriate tests for randomly selected data in spss?

Hi, I took your advice to use linear regression and this is what showed in the output in SPSS. Please take a look at the attach document.
Where can I find the value in the results that indicate a significant difference or non-significant difference?
Please help me, this is for my thesis.

6. ## Re: appropriate tests for randomly selected data in spss?

You have a table "Coefficients".

From it you can see that you have:
Predicted Cr measurement = 2.847 + 0.012 * Concentration

In particular for the line related to Concentration, you have:
B: 0.012
Sig: 0.075

Since Sig > 0.05, the statistical conclusion is that you have insufficient proof to be able to say that the Cr measurement depends on the Concentration (in a linear regression).

Let's take a look at a graph of your data.

I can see that around 200-250 there seems to be some effect.
Below 180 and above 270 looks like random noise.

I guess that should match expectations.
There is a concentration that gives an optimal absorption.
Lower or higher concentrations will give less effect.
For something like that, a linear regression is the wrong test.

I guess you'd need for instance a non-linear regression test for that.

7. ## Re: appropriate tests for randomly selected data in spss?

I've been playing around with your data a bit, thinking what kind of curve you might want to fit.

The best I could think of, was a kind of bell curve (like the normal distribution) augmented with some constant effect.

Here's a result.

This is a fit with a curve of the form:

$Y = B_0 + B_1 \cdot e^{-({X - B_2 \over B_3})^2}$

The resulting numbers are:
B0 = 3.33
B1 = 5.84
B2 = 239.4
B3 = 49.5

This would mean a maximum effect at a concentration of 239.4 mg/kg.
And the effect would have a spread more or less equivalent to a standard deviation of 49.5 mg/kg.

Btw, this is a non-linear regression.

8. ## Re: appropriate tests for randomly selected data in spss?

I just realized there is yet another test you can do: the t-test on correlation.

$H0: \rho = 0$
$H1: \rho \ne 0$

$t = r \sqrt{n - 2 \over 1 - r^2}$

The t-distribution for this test has n-2 degrees of freedom.

In your case, you have t = 2,011 and the corresponding p-value is p = 0,038.
In a 2-sided t-test with $\alpha = 0.05$, this is not significant, although it would be significant in a 1-sided t-test.

9. ## Re: appropriate tests for randomly selected data in spss?

Hello again, I've been meaning to use t-test but I just don't know how to interpret data.

I just want to know if there is a significant difference among the concentrations.

H0: there is no significant difference among the concentrations
H1: there is a significant difference among the concentrations

BTW, you used the non-linear regression to know what concentration does the plant achieved the optimal absorption? or what concentration does the plant is comfortable with? It can be useful

10. ## Re: appropriate tests for randomly selected data in spss?

And also it would be very much appreciated if you know which concentrations are alike or not similar.

For example:

Statistics analysis (insert test) shows that Concentrations 15 to 165, and 285 to 315 mg/kg do not have a significant difference with one another while they differ from the 195-255 mg/kg which also do not have a significant difference with one another.

Thank you!!!

11. ## Re: appropriate tests for randomly selected data in spss?

Well, you could do a one-way ANOVA with the 3 categories (or some other category choice) you mentioned.
But I'd advise against it.
It does not look good if you use your sample to massage the data into a form just so you can find significance.

I think a graph like the one I showed with the bell-curve model would look good in a report.
However, I don't know how to properly support it with a t-test or any other test.

Sorry if this doesn't really help you.