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# Phi (φ) Correlation

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### Phi (φ) Correlation

1. 1. Sounds like fee.
2. 2.  ad  bc a  b c  d a  c b  d 
3. 3.  Significance testing:  Use chi-square table › N = number of participants › df = 1 (always)
4. 4. Country Denmark Total 36b (31%) 21c 79d (25%) Suspicious 64a (75%) Attitudes of People Trusting France (69%) 85 (100%) 115(100%)
5. 5. • 75% percent of Danish sampled(64/85*100) were trusting, whereas 31 % of French sampled (36/115*100) were trusting. • Approximately 25% (21/85*100) of Danish were suspicious, whereas 69% (79/115*100) of French were suspicious.
6. 6. HO (φ) =0  HA (φ) ≠ 0  In plain English, null hypothesis means attitude of people and national origin are independent of one another, they don’t influence each other.  Alternative hypothesis- attitude of people and national origin are dependent on one another, they do, in fact, influence each other. 
7. 7.   Significance testing: Use chi-square table › N = number of participants › df = 1 (always) for 2X2 table › Why?? (r-1) (c-1) where r=rows and c= columns. In 2X2 table there are 2 rows and 2 columns; › (2-1) (2-1)=1X1=1 › For .05 level of significance and 1 df, critical value =3.84; › For .01 level of significance and 1 df, critical value =6.63; › If Chi obtained is greater than critical value, we reject null hypothesis of independence between the variables.
8. 8. Training Stimulus Food as Reward Affection as Reward 28a 48b (74%) (30%) 10c 114d Could They Dance After Stimulus Presented? Yes No (26%) Total 38 (100%) (70%) 162 (100%)
9. 9. Test the significance of correlation between sex and opinion on capital punishment at 0.05 level of significance. Use the table given below. Sex Female Opinion Male total For 15 9 24 Against 10 17 27 Total 25 26 51
10. 10. Test statistics for testing the significance of phi coefficient is given by: z = r n