ANOVA and sig. question

#1
I have a question about ANOVA and statistical significance.

I have a 18 question Likert style survey, with about 400 replies. I am analysing replies from 3 age groups, looking at the differences between age cohorts.

Some questions are obvious with signficances less than .05. These
questions I can conclude that there is signficant variances between age groups.

My question is can I consider a sig. of .09 or .11 as looser evidence to significant variances between age cohorts?

My text seems to be focused on a 95% confidence interval, however seems silly to throw out what seem like significant findings over a few percent.

I am using SPSS for my analysis.
Thoughts? Thanks,
 
#2
Your p-value tells you the probability of sampling a test statistic greater than the one you obtained by chance. If you reject your null hypothesis, then your p-value gives you a level of confidence in your rejection. Even at p<0.05, there is still a 5% probability of being wrong in rejecting the null hypothesis. This is the so-called type I error. Of course, there is also the probabiliy of being right in rejecting your null hypothesis - this is called power. To answer your question, it is a bit arbitrary which alpha you decide to use- in stats courses they tell you to use 0.05 but you could make it whatever you wanted to. If you used an alpha of 0.1 then you could accept your test statistic with a p value of 0.09. You could also say in your results section that 'x question' was answered differently beween age groups (P=0.09) and let the reader make up his own mind whether this is sigificant. You could also then say "however, this difference is not significant at alpha = 0.05. A P-value of 0.09 indicates the presence of a trend." Note that saying there is a difference between groups is not the same as saying that there is significant difference between groups. Clearly there are differences between the groups for all questons answered but how confident can you be that the difference is "real". The p-value gives you a level of confidence that these differences are "real".
 
#4
For those analyses where your p-value is above .05, you could report that it was approaching significance (if it was say, .09), or you could say it was one-tailed and report it as significant (though you should have an a priori reason for doing one-tailed tests).