# Statistical terminology: Is my wording correct?

I have written:

A predetermined level of significance ($$\alpha$$ – level) was set to assess the null hypothesis based on a probability value ($$p$$ value). If the $$p$$-value is greater than the $$\alpha$$-level, then the null hypothesis can be accepted. If the $$p$$-value is less than or equal to the $$\alpha$$-level then the null hypothesis is rejected. For this analysis the $$\alpha$$-level was set at $$0.025$$ giving a $$95%$$ confidence of the result.

For the $$\alpha$$-level of $$0.025$$, it is $$95%$$ certain that the true difference between population mean values lies within the confidence interval. The estimate for difference is the difference between the population mean values as calculated from the sample data.

The $$p$$ value was calculated as shown:

$$\displaystyle p = \frac{\bar{x_1} - \bar{x_2}}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$$

using $$n-2$$ degrees of freedom.

Is the terminology in that correct? Have I used "$$p$$ values" correctly there or should it be $$t$$ value? I'm pretty sure my formula is correct as I can't justify equal variances for both samples. Also, is my conclusion to my hypothesis test correct?

Also, am I right in comparing my $$p$$ values to my $$\alpha$$ values or should that say something else?

• An alpha level of 0.025 would correspond to a 97.5% confidence interval -- an alpha of 0.05 would correspond to a 95% confidence interval (i.e. the 0.05 rejection area is split between the two tails of the t-distribution.) Apr 16, 2013 at 20:06
• @JamesStanley Would I be able to compare my test statistic to "alpha values from the table" or would I need to reword this to something along the lines of "I can get criticial value corresponding to my alpha value.." and then talk about whether to accept or reject my alternative hypothesis from that? Apr 17, 2013 at 8:19
• yes, you should be able to check your t-statistic (with n - 2) degrees of freedom with a critical value from a table (with a two-sided alpha of 0.05) to see whether the p-value is < 0.05. Apr 17, 2013 at 21:11

• So where I have mentioned $p$ values in my text, not the formula, is that correct or should that be $z$ values aswell? Apr 16, 2013 at 23:30