# Thread: One-tailed pearson's chi-square H1 and Ho as well as Fisher's exact test

1. ## One-tailed pearson's chi-square H1 and Ho as well as Fisher's exact test

Hi, I have numerous chi-squares to run. A couple of the expected frequencies are less than 5 so I have decided to go with Fisher's exact test for them. I have a couple of questions pertaining to these tests. First, I am conducting a Pearson's chi-square, which I believe to be a one tailed test because previous research tells me that people are likely to answer correctly when stimulus A is used than when stimulus B is used. So I have a 2 (stimuli A, stimuli B) x 2 (correct, incorrect) Chi-square contingency table and have generated the associated stats in SPSS. However, rather than finding that the alternative hypothesis is true (Stimuli A => correct answering, Stimuli B => incorrect answering) I have found the opposite is true and significantly so. Therein lies my conundrum. I can't say that there was no effect (Ho), because there was, but can I now report the significant effect because isn't this technically shifting toward testing a two tailed hypothesis now? It wouldn't be my alternative hypothesis either.... The second query I have pertains to the use of Fisher's exact test. Do I report the odds ratio and Phi for Fisher's exact test. If not, how do I describe the strength and direction of the effect? Many thanks. Kate

2. ## Re: One-tailed pearson's chi-square H1 and Ho as well as Fisher's exact test

Hey Kate.

For a Pearson Chi-square, the usual test is that variation between two distributions (expected and observed) is too large and thus we usually make a 1 tailed test as opposed to say an F-test where the ratio can either be very high or very low.

Maybe you should point out what you are doing in plain English and what you are trying to accomplish.

3. ## Re: One-tailed pearson's chi-square H1 and Ho as well as Fisher's exact test

Perhaps my explanation was a bit confusing. My apologies.

I have received a test result where the outcome is contrary to my hypothesis and in the opposite direction. Writing this up now sounds as though I am interpreting a two-tailed test. I.e. I was only supposed to be testing whether it was significant in one direction but I have a significant result in the other direction, so, now the interpretation sounds bidirectional. I am wondering if I only have a significant one-sided test statistic because the stats have been run in a computer program (SPSS), through which I have not specified which direction I am talking about?

Using an example from my data: One preliminary piece of research suggests that people will recognise a mental health problem more accurately when they receive a written vignette, as opposed to a videotaped one. So, my hypothesis is that there will be a significant association between whether people can correctly recognise a problem and the type of vignette received, such that, written vignettes will produce more accuracy. This is based on a 2 (accuracy: correct vs incorrect) x 2 (vignette type: written vs videotaped) contingency table with 2 cells having low expected frequencies. So, I have used a one-sided Fisher's Exact Test. Using SPSS, the Fisher's one-sided test result is p<.05. However, the result is in the opposite direction. So, I go on to say that contrary to the hypothesis, participants were significantly more likely to recognise the mental health problem incorrectly than correctly, when written (rather than videotaped) vignettes were used. I then report the one-sided p-value (since it was a one-sided hypothesis), the odds ratio (indicating that there is more incorrect responding when they were written), as well as Phi. The two problems I was trying to outline in the post above are a) I am concerned that I am now interpreting the data in a two-sided way, thus, misrepresenting the statistics; and b) I am not sure whether to report the odds ratio and phi.