This one-tailed value would be significant at the conventional level (because 0.03 is less than 0.05). Had you done this test one-tailed, however, the p you would have got would be half of the two-tailed value (0.03). Also, if you do a two-tailed test and find that your p is 0.06, then you would conclude that your results were not significant (because 0.06 is bigger than the critical value of 0.05). If you don’t do this, then you have done a two-tailed test using a different level of significance from the one you set out to use, which is cheating therefore, one-tailed tests temp people to cheat. If you do a one-tailed test and the results turn out to be in the opposite direction to what you predicted you must ignore them and accept the null hypothesis. What are the arguments for not using one-tailed tests? The significance of a test statistic is directly linked to the sample size: the same effect will have different p-values in different-sized samples: small differences can be deemed ‘significant’ in large samples, and large effects might be deemed ‘non-significant’ in small samples. What effect does sample size have on statistical significance?
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