EXAMPLE 1: One-Way ANOVA One-Way ANOVA - one factor with at least two levels, where levels are independent. Researchers want to test a new anti-anxiety medication. They split participants into three conditions {0, 50. and 100 mg), then ask them to rate their anxiety level on a scale of 1-10. Are there any differences between the three conditions, using or. = 0.05? EXAMPLE 1: One-Way ANOVA Researchers want to test a new anti-anxiety medication. They split participants into three conditions (0, 50, and 100 me), then ask them to rate their anxiety level on a scale of 1-10. Are there any differences between the three conditions, using a. = 0.05? 1. Define Hull and Alternative Hypotheses 2. State a . Calculate degrees of freedom . State decision rule . Calculate test statistic . State Results . State Conclusion 540*me 0.05 120 161 4476 199 000 315 2073 324 5832 230 1616 239 9850 236 3684 298 6827 240 5438 241 8817 342 9835243. 245 9490 248 0131 249 0518 250 0951 251 1492 252 1957 353 2529 (254 3137 18 5128 19 0900 10 1280 9.5 21 F Distribution Table 7.7056 6.9 43 5 9874 3.1 33 6019 514 . A right-skewed distribution used most commonly in Analysis of Variance 5.5914 4.7 14 5.3177 4.4 90 . When reference the F distribution, the numerator degrees of freedom 5.1174 4.3 63 are always given first, as switching the order of degrees of freedom 10 4.9646 4.1 28 4.8443 3.9 23 changes the distribution, ie., F(18,2) # F(2, 18) 4 7472 3.5 53 4 6572 3.5 56 . To determine the 0.05 critical value for an F distribution with 2 and 18 14 4 6001 3.7 89 4.5431 3.6 23 degrees of freedom, look in the 2 column (numerator) and 18 row 15 16 4.4940 3.6 37 (denominator) of an F Table for a=0.05 4 4513 35075 15 1 4139 3.5546 . F(0. 05,2, 18) = 3.5546 19 4 3907 3.5219 10 4 3512 3.4928 3.0984 28661 2.7109 2 3990 2 5140 2 4471 2 3926 23479 23100 2 2776 2 2495 2 2250 2 2033 21242 20825 20391 1 9938 1.9464 1.8963 1.8432 21 4 3248 3.4668 3.0725 28401 26848 25727 24876 24205 23650 23210 2 2829 2 2504 2 2222 2 1975 21757 20960 20540 20102 1 9645 19165 1.8657 18118 21 4 3009 3.4414 3 0491 28167 2.6613 2 5491 24638 2 3965 2 3419 2 2967 2 2585 2 2258 21975 21727 21508 20707 20283 19842 1 9180 1.8894 1.8380 1.7832 21 4 2793 3.4321 30230 2.7955 3.6400 2 5277 24432 2 3748 2 3201 2 2747 2 2364 2 3036 2 1752 2 1903 2 1282 20476 20050 1.9605 1 9139 | 1 8645 1.8125 1.7571 24 4.2597 3.4028 3.0098 2.7763 2.6207 2 5082 24226 23551 23002 2 2547 22163 21834 21548 21298 21077 20267 1.9838 1.9390 1 8920 1.8424 1.7896 1.7331 25 42417 3.3852 2 9912 2.7587 2.6030 2 4904 2 4047 2 3371 2 2821 2 2365 2 1979 2 1649 21362 21111 20689 20075 1.9643 19192 18718 18217 17684 17111 26 4 2252 3 3690 29752 2.7426 2.5868 24741 2 3883 23205 2 2655 22197 21811 21479 21192 20939 20716 19898 1.9464 19010 1 8533 1 8027 17488 1.6907 4.2100 3.3541 29604 2.7278 2.5719 24591 23732 2 3053 2 2501 2 2043 2.1655 2 1323 21035 20781 20558 1.9736 1.9299 1.8842 1 8361 1.7851 17306 1.6718 25 4 1960 3 3404 2 9467 27141 23581 2 4453 2 3593 2 2913 2 2360 21900 21512 21179 20859 20635 20411 1.9585 1.9147 18657 18203 17659 1.7138 16542 29 4 1830 3.3277 29340 2.7014 25454 24324 23463 2 2783 2 2229 21768 21379 2 1045 20755 20500 20275 19445 1.9005 18543 1 5055 17537 16981 1.6377 4 1709 3 3158 2 9273 26896 2.5336 24205 2 3343 2 2662 2 2107 21646 21256 20921 20630 20374 20148 1.9317 1.8874 1.8409 17918 1.7396 1.6835 1.6271 4 0847 3.2317 28387 2 6060 2.4495 2 3359 2 2490 2.1802 21240 20772 20376 20035 1 9738 19476 19245 1.8359 1.2929 1.7444 1 6928 1.6373 1.5756 1.5090 40343 3.1826 2.7900 2 5572 2.4004 2 2864 2.1992 2.1299 20734 20261 1 9561 19515 19214 1 8949 18714 1.7841 1.7371 1.6872 16337 15757 15115 1.4384 3.9685 3.1156 2.7265 2.4937 2 3365 2 2321 2 1343 20644 20073 1 9594 1 9185 1 5836 1 8530 1 8359 1 5018 17121 16633 16112 1 5548 14926 14221 1.3381 100 3 9361 3.0873 2 6955 2.4626 2 3053 21906 21025 20323 19748 19267 1 8857 1 8503 1 8193 1.7919 1.7675 1.6764 1.6267 15733 15151 1.4504 1.3757 1.2833 3.8416 2.9958 2.6050 23720 2.2142 20987 20097 1.9385 1.8800 18308 1.7887 17523 17203 1.6919 16565 1.5706 1.5174 1.4592 1 3941 13182 1.2216 1.0105 16 Activ