# How to draw conclusions based on Statistically Equal data sets?

I just have a question about statistical significance that I can't wrap my mind around.

So lets say we put out a survey comparing male and females and their frustration levels doing any sort of tasks. from like lets say a scale of 1-5 with 5 being highest level of frustration/anger and whatever

The results come back and lets say....males have a mean score of like 4 while females have a lower mean score of lets say 2.

Now I want to compare the data from the sample of males and females and draw the conclusion that hey males have a higher frustration level on average to do whatever task. But first I complete a t-test lets say Welchs to make sure taht the data is okay to compare.

So I compute a tvalue of .264 and a t value at 90% confidence interval with whatever degrees of freedom of 1.943. Became my t90CI value is greater than my tvalue I draw the conclusion that the female and male data sets are statistically equal.

Does this now mean that I can now effective draw the conclusion from my data collection that "hey males experience significantly higher frustration levels on average"?

Sorry for making this post so long

• a tvalue of .264 means you cannot say "males experience significantly higher frustration levels on average". – user158565 Nov 2 '18 at 15:53
• so if my t90CI value I calculate is less than my tvalue I can then say that the data is statistically difference and draw the conclusion i want right? – Tommy Nov 2 '18 at 15:57
• Whose CI will you calculate? difference of the means? If so, based on 0.264, the CI will include 0. So you still cannot get what you want. If you calculated you t value correctly (=0.264), absolutely, you cannot get what you want. – user158565 Nov 2 '18 at 16:07

Your null hypothesis (assuming a two tailed test) is that the mean for the men $$\mu_{m}$$ equals the mean for the women $$\mu_{w}$$, that is $$H_{0}: \mu_{m}=\mu_{w}$$ against the alternative $$H_{1}: \mu_{m}\neq\mu_{w}$$.
Your test statistic is calculated assuming the null hypothesis is true. Since you didn't get an "extreme" value for your test statistic you have little evidence that the null is actually false (that is your statistic isn't bigger than your critical value.) The same idea holds for a one sided test if that is actually what you are interested in. Essentially your data is not extreme enough to reject your null hypothesis. All you can conclude is that, "we failed to reject the null hypothesis with $$\alpha = 0.1$$".