Question

construct a persuasive argument for the value (conditional probability, odds, odds ratio, etc.) that, intuitively, makes the most sense for you to report as a result to your audience. Be sure to provide a specific rationale for your choice

Answer 1

1. Binary logistic regression will allow you to answer questions where you can predict the odds of an event occurring from a combination of categorical and continual variables.The relationship between conditional probability, odds as well as odds ratio makes these values the most easily to report.

2. DEFINITIONS:-

odds - express the likelihood of an event taking place compared to the likelihood of an event not happening.

odds ratio - is a method of comparing whether the chances of a certain event is similar for two groups. The value of odds range between zero and one and are normally determined from probabilities.

Conditional probability -the occurrence of an event depending on the occurrence of an event that occurred before.

3. ANALYSIS:-

The odds are ratios of probabilities of "success" and "failure" for a given row, or a ratio of conditional probabilities of the same conditional distribution. Odds of getting a cold versus not getting a cold given that a person took a placebo:

odds1=P(Z=1|Y=1) / P(Z=2|Y=1)

=?1|1 / ?2|1

=?1|1 / (1??1|1)

Properties of odds:

• If odds equal to 1, "success" and "failure" are equally likely.
• If odds > 1, then "success" is more likely than "failure".
• If odds < 1, then "success" is less likely than "failure".

The odds ratio, is the ratio of odds₁and odds₂ (or vice versa):

4.EXAMPLE:-

odds of "success" (i.e., getting a cold) given that that a skier took vitamin C, 0.12/0.88 = 0.14

odds of "success" (i.e., getting a cold) given that a skier took a placebo pill, 0.22/0.78 = 0.28.

The odds ratio is 0.14/0.28 = 0.49.

?^=0.49 means that

• the odds of getting a cold given vitamin C are .49 times the odds of getting cold given a placebo
• the odds of getting a cold given a placebo are 1/.49 = 2.04 times greater than the odds of given vitamin C
• getting cold is less likely given vitamin C than give a placebo.

5. an odds ratio of 0.75 means that in one group the outcome is 25%less likely. An odds ratio of 1.33 means that in one group the outcome is 33% more likely." ... “An Odds Ratio of less than 1 means that the first group was less likely to experience the event.

6. The coccidioidomycosis OR of (20×362)÷(35×39)=5.30 indicates that the odds of disease when exposed to dust is 5 times its odds when not exposed.