# Conditional probability, odds, and odds ratios are all values that can be used to report results. To determine which value to use to report results depends on the question of interest. Conditional probability is the probability that an event will occur given that another event has already occurred.

you need to reply to 2 of the classmates on the subject .you need to reply directly to the students using their names and also you have to have a reference page for each response.

Thanks.

Here are the students posts:

Tina

WK4 – Main Discussion Post

COLLAPSE

Conditional probability, odds, and odds ratios are all values that can be used to report results. To determine which value to use to report results depends on the question of interest. Conditional probability is the probability that an event will occur given that another event has already occurred. The probability that a high school student (condition of being a high school student) will be a smoker (smoker vs. nonsmoker) is an example of a conditional probability. For example, if there are 120 high school students, 20 smokers and 100 nonsmokers, I can figure out the probability of a student being a smoker to be .167 (20/120 = .167). Conversely, the probability that a student is not a smoker is .833 (100/120 = .833). Probabilities are represented by a number between 0 and 1.

The odds of an event occurring are produced by dividing the number of times the event occurs by the number of times it does not occur. For example, if out of 120 high school students there are 20 that smoke and 100 that do not smoke, the odds of smoking are .2 (20/100 = .2). In contrast, the odds of being a nonsmoker is 5 (100/20). In other words, the odds that a high school student won’t smoke is 5 to 1. Odds’ values fall between 0 and positive infinity (Warner, 2013). Although there is a wide range of potential odds’ values, the value of 1 is telling. Specifically, odds less than 1 indicate that the event of interest is less likely to occur than the alternative, while odds greater than 1 indicate that the event of interest is more likely to occur than an alternative (Warner, 2013). When an odds of 1 occurs, the likelihood of outcomes is equal.

Whereas probability and odds provide a measure of the likelihood that an event will occur, an odds ratio compares odds across two groups (Warner, 2013). For example, if I want to compare the odds of a high school student being a smoker to the odds of a college student being a smoker I could use an odds ratio. In social science research, we are often interested in comparing groups, therefore, I think odds ratios are results I would share. However, Warner (2013) states that odds ratios lack utility because they are usually not evenly distributed and they usually lack a linear relationship to predictor variables. Fortunately, these limitations can be corrected by using natural logarithmic transformations (Warner, 2013). Because odds ratios are used to compare group odds and because they can be transformed into statistically useful values, I would pick odds ratios as my value of choice.

Reference

Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.

Tim

RE: Discussion – Week 4

COLLAPSE

Are mindfulness practitioners more likely to brush their teeth on a daily basis? Exercise? Make healthier food choices? Are mindfulness practitioners more likely to download an app that would help them track their meditation practice? If so, how likely? What would the odds of that prediction be? In order to answer these questions, we need to dive into the basics of and assumptions of binomial logistic regression.

Laerd (n.d.) lists several assumptions for a logistic regression to be an appropriate statistical measure: you have one dependent variable that is dichotomous in nature. You have one or more independent variables that are either continuous or nominal variables. You have independence of observations in the categories of the dichotomous dependent variable, and all of the nominal independent variables are mutually exclusive and exhaustive. And, there needs to be a linear relationship between the independent variable and the logit transformation of the dependent variable. These will ensure the sound application of a binomial logistic regression and the calculations of odds, odds ratios, and probabilities.

Warner (2013) thoroughly discusses odds, which are obtained by dividing the number of times an outcome interest does happen by the number of times it does not happen. A minimal odds value is zero. The maximum value is the maximum number of times the outcome could occur. When the odds are less than one, the target event is more likely to happen than the alternative outcome. An odds ratio has an advantage over the probability and has no fixed upper limit, but a fixed and stable lower limit. The ratio assumes that values do not tend to be normally distributed. Also, values of the ratio do not tend to be linearly related to quantitative predictor scores. This would help develop a natural logarithm with exponential functioning. This transforms the dependent variable into the natural and logical odds conversion. There is no fixed upper or lower limit, scores are normally distributed, and could be linearly related to the quantitative predictor. Particularly in this case, does mindfulness training predict whether a person brushes their teeth, exercises, or even downloads an app. The perfect tool is binomial logistic regression.

References

Laerd Statistics. (n.d.). Binomial Logistic Regression. Retrieved from: https://statistics.laerd.com/premium/spss/blr/binomial-logistic-regression-in-spss-5.php

Warner, R. M. (2013). Applied Statistics: From Bivariate through Multivariate Techniques. Thousand Oaks, CA. Sage.