Essentials

INTRODUCTION TO NULL HYPOTHESIS TESTING 39The Type I error rate and, therefore, your alpha, would be .10 instead of .05 becauseyou are performing a two-tailed test.To keep alpha down to .05 when performing a two-tailed test you have to dividealpha in half and put .025 area in each tail (as in panel B of Figure 2.2). Thecritical zs for the two-tailed .05 test are 1.96 and –1.96 (you can see in Table A.1that the area beyond z 1.96 is .0250). The price you pay for being able to test aresult in both directions is that you need a stronger result to reach significance.The one- and two-tailed distinction affects p values as well as the critical values.When we looked up the area beyond z 1.67 and found that our p value was .0475we were finding a one-tailed p value. The two-tailed p value would be twice asmuch (we are allowing for results as extreme as ours on both sides of the distribution):the two-tailed p equals 2 .0475 .095. Notice that a z of 1.67 is significantif a one-tailed test is performed ( p .0475 .05), but not for a two-tailed test ( p .095 .05). Thus, it is understandable that statistics texts often tell students thata two-tailed test should only be performed when you have no hypothesis aboutwhich way the results will go, and that a one-tailed test should be used when youhave a clear prediction about the direction of the results. However, this is anotherone of those cases where common practice tends not to match the textbooks.It is rare that a researcher compares two experimental conditions without hypothesizingabout which condition will have the higher mean on some dependentvariable. However, it is also true that paradoxical results are common in the socialsciences. The publication of one-tailed tests implies a trust that the researcherwould not have tested results in the unpredicted direction no matter how interesting.If, for instance, researchers routinely performed one-tailed .05 tests for resultsin the predicted direction, and then turned around and performed two-tailedtests whenever the results turned out opposite to prediction, the overall Type Ierror rate would really be .05 .025 .075, more than the generally agreed-uponalpha of .05.To be conservative (in statistics, this means being especially cautious about TypeI errors), the more prestigious journalsusually require the two-tailed testto be used as the default and allowone-tailed tests only in special circumstances(e.g., results in the oppositedirection would not only beunpredicted, but they would be ridiculousor entirely uninteresting). Ifyou did plan to use a one-tailed testbut the results came out significant inCAUTIONTo find a critical value for a two-tailedtest, first divide alpha by two, and thenfind the z score with half of alpha inthe “beyond z” column of Table A.1.To find a two-tailed p value, first findthe area “beyond” your z score, andthen multiply that area by two.