I have observed values (80 in total) in different measured circumstances (80 in total). I want to test whether my observed values are the result of chance or do measured values affect my observed values.

My problem is that measured values are non-normally distributed and observed values are normally distributed according to Shapiro-Wilk test which I run on SPSS. Measured values' p-value was 0,001 in that test and observed values' p-value was 0,102 in that test.

What test should I use that I would know that are my observed values statistically significant? All I need to test is that are my observed values result of chance or did measured values affect them.

If I use t-test, are both measured and observed values required to be normally distributed?

Thank you for reading, any help is appreciated

  • $\begingroup$ If you have 80 values and 80 conditions there is little or nothing you can do. Is that a typo? $\endgroup$
    – Peter Flom
    Commented May 18, 2014 at 10:40
  • $\begingroup$ I meant that I have 80 values which I observed when I was doing my research. To each observed value I have one measured value. I changed the testing environment, so I have 80 different measurements when I did 80 different observations. Condition is probably a wrong word, maybe circumstance is better. I changed it now. $\endgroup$
    – Timmy
    Commented May 18, 2014 at 10:52
  • $\begingroup$ This doesn't make sense. Observed variables are measured values. How many conditions do you have? It sounds like you have 2, but it isn't clear. Try explaining your data as you would to people who aren't statisticians. $\endgroup$
    – Peter Flom
    Commented May 18, 2014 at 10:57
  • $\begingroup$ Well I studied that does relative humidity affect to adhesion strength on solid substance against surface. So I increased relative humidity and observed how much adhesion strength increases. So I have 80 measured values of relative humidity and 80 observed values of adhesion strength. Maybe I have wrong terms here, but my instrument did a measurement and I observed the adhesion strength. Maybe I should say that I have two measured values? So I have then two sets of measured values. $\endgroup$
    – Timmy
    Commented May 18, 2014 at 11:10
  • $\begingroup$ Failing to reject normality doesn't imply your data are normal. Please clarify what the distinction between 80 observed values and 80 measurements is. Are they measuring the same quantity? What is the null hypothesis? What alternatives do you seek power against? In short, what do you actually want to find out about your data? $\endgroup$
    – Glen_b
    Commented May 18, 2014 at 11:22

1 Answer 1


Your comments clarified things.

You have two variables (relative humidity and adhesion strength) measured on 80 objects. To see if the two variables are related you probably want some form of regression, with adhesion strength being the dependent variable and adhesion strength the independent variable. You may have other independent variables as well.

Before proceeding with the regression I would make a scatterplot of the two variables to see if the relationship is roughly linear.

And regression does not make assumptions about the distribution of either variable; it does make assumptions about the distribution of the errors, as measured by the residuals.

  • $\begingroup$ Yes I have done a regression analysis and linear regression seems to fit best, since it gives best correlation. But this correlation is weak still (0,2544) and I do think that my results should not be statistically significant. This was one of the substances which I tested and relative humidity does not seem to affect its adhesion strength. But I tested its correlation with t=√(n-2)*(r/(√(1-r^2))) equation and I get a significant result on 0,05 alpha level (p-value is 0,0228 then). I'm not sure though that which test I really should use. $\endgroup$
    – Timmy
    Commented May 18, 2014 at 11:46
  • $\begingroup$ This is the correct analysis, I think. A small effect can be significant. A significant effect is not necessarily important. Don't change your analysis just because the results are not what you expect. $\endgroup$
    – Peter Flom
    Commented May 18, 2014 at 13:02
  • $\begingroup$ Okay, then if there is a possibility that my both measurements are not normally distributed, then can I rely on this result? I asked my teacher, and he said that I would need to check that are my measurements normally distributed and it now looks like at least one of them is not. Since this is the case, then is there some test which I can use which does not require that my measurements are normally distributed? I know there are some, but I'm not sure do I need to use such a test and if I need to, then which one. $\endgroup$
    – Timmy
    Commented May 18, 2014 at 13:35
  • $\begingroup$ Your teacher is not correct. Regression does not make assumptions about the normality of the data. It makes assumptions about the normality of the residuals. All statistical packages have tools to help you analyze these. What package are you using? $\endgroup$
    – Peter Flom
    Commented May 18, 2014 at 13:45
  • $\begingroup$ I am using SPSS. My teacher meant that if I check the significance of correlation then my data should be normally distributed. This is also what my book says. Should I analyze the normality of residuals? Also thanks for helping me $\endgroup$
    – Timmy
    Commented May 18, 2014 at 14:04

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