1. 1 Competence and a new baby, M | mastery baby | 0 1 | Total -----------+----------------------+---------- 0 | 67 84 | 151 | 44.37 55.63 | 100.00 | 67.00 80.77 | 74.02 -----------+----------------------+---------- 1 | 33 20 | 53 | 62.26 37.74 | 100.00 | 33.00 19.23 | 25.98 -----------+----------------------+---------- Total | 100 104 | 204 | 49.02 50.98 | 100.00 | 100.00 100.00 | 100.00

2. 2 Competence and a new baby, F | mastery baby | 0 1 | Total -----------+----------------------+---------- 0 | 74 77 | 151 | 49.01 50.99 | 100.00 | 73.27 74.76 | 74.02 -----------+----------------------+---------- 1 | 27 26 | 53 | 50.94 49.06 | 100.00 | 26.73 25.24 | 25.98 -----------+----------------------+---------- Total | 101 103 | 204 | 49.51 50.49 | 100.00 | 100.00 100.00 | 100.00

3. 3 Depression and a new baby, M | depress baby | 0 1 | Total -----------+----------------------+---------- 0 | 92 59 | 151 | 60.93 39.07 | 100.00 | 75.41 71.95 | 74.02 -----------+----------------------+---------- 1 | 30 23 | 53 | 56.60 43.40 | 100.00 | 24.59 28.05 | 25.98 -----------+----------------------+---------- Total | 122 82 | 204 | 59.80 40.20 | 100.00 | 100.00 100.00 | 100.00

4. 4 Depression and a new baby, F | depress baby | 0 1 | Total -----------+----------------------+---------- 0 | 91 60 | 151 | 60.26 39.74 | 100.00 | 76.47 70.59 | 74.02 -----------+----------------------+---------- 1 | 28 25 | 53 | 52.83 47.17 | 100.00 | 23.53 29.41 | 25.98 -----------+----------------------+---------- Total | 119 85 | 204 | 58.33 41.67 | 100.00 | 100.00 100.00 | 100.00

5. 5 Central Limit Theorem Know the sampling distribution of means from properties of the population Mean of sampling distribution of means is mean of the population Standard deviation of sampling distribution of means is times sd of population Sampling distribution is normal

6. 6 Normal Distribution 95% Mean Standard deviation

7. 7 Normal Distribution

8. 8 Normal Probabilities z p 1. -3.0013499 2. -2.0227501 3. -1.1586553 4. 0.5 5. 1.8413448 6. 2.9772499 7. 3.9986501 Why we have a normal table!!! Z score

9. 9 Translation 100116 Mean = 100 sd = 16 Mean = 0 sd = 1 0123 132148

10. 10 Translation (part 1) Original metric of variable, IQ: mean is 100, std. dev. is 16 New metric (z score), mean is 0, std. dev. is 1. To make the new variable, z, have a mean of zero, subtract the mean of the old variable from all observations

11. 11 Translation (part 2) To make the new variable, z, have a standard deviation of 1, divide each deviation by the sd of X

12. 12 Translation (Part 3) 100116 Mean = 100, sd = 16 132148 Mean = 0, sd = 16 Mean = 0, sd = 1 0 163248 0123 Subtract mean of 100 Divide by sd of 16 The order in which you do these steps is important!

13. 13 Not all distributions are normal We have already looked at the binomial The same principles hold in looking at the binomial distribution. The formulae are different.

14. 14 Binomial, p =.3

15. 15 Binomial example Let p =.3 and n = 7 In this case f can be 0,1,2,3,4,5,6, or 7 This creates a discrete distribution with a probability for each separate outcome.082

16. 16 Binomial example (cont.) 7.3.118=.247 21.09.168=.318

17. 17 Binomial Results f comb pf qnf p 0 1 1.0823543.082 1 7.3.117649.247 2 21.09.16807.317 3 35.027.2401.226 4 35.0081.343.097 5 21.00243.49.025 6 7.000729.7.004

18. 18 Binomial Normal approximation with large sample A large sample? np/q > 9 & nq/p > 9 If p=.3 then n > 21

19. 19 Binomial with p =.32, n = 21 Mean = np = 6.3 Sd = sqrt(npq) = 2.1 Note normal curve