# How do I test statistical significance between normally distributed data and non normally distributed data?

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

• If you have 80 values and 80 conditions there is little or nothing you can do. Is that a typo? Commented May 18, 2014 at 10:40
• 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. Commented May 18, 2014 at 10:52
• 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. Commented May 18, 2014 at 10:57
• 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. Commented May 18, 2014 at 11:10
• 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? Commented May 18, 2014 at 11:22