Hypothesis testing and confidence intervals with two samples Video transcript In the last couple of videos we were trying to figure out whether there was a meaningful difference between the proportion of men likely to vote for a candidate and the proportion of women. What I want to do in this video is just to ask the question more directly.
Upon successful completion of this lesson, you will be able to: So far in our course, we have only discussed measurements taken in one variable for each sampling unit.
This is referred to as univariate data. In this lesson, we are going to talk about measurements taken in two variables for each sampling unit.
This is referred to as bivariate data. In this lesson, we are going to talk about the very practical problem of situations where two measurements are being compared. If the measurements are categorical e. Yes or No to the question "Do you smoke? Female, Male the analysis will involve comparing two independent proportions.
If the measurements are quantitative e. GPA and taken from two distinct groups e. Graduate, Undergraduate the analysis will involve comparing two independent means. Weight and taken twice from each subject e.
Finally, there are situations that involve dependent proportions e. However, we will not discuss this last situation. To begin, just as we did in the case for one-proportion or one-mean, one has to first decide whether the problem you are investigating requires the analysis of categorical or quantitative data.
Next, one has to determine if the samples are independent samples or dependent samples in order to choose between a 2-sample test and the paired test.
We will start with comparing two independent population proportions, move to comparing two independent population means, from there to paired population means, and ending with the comparison of two independent population variances.
The latter can help us determine in the analysis of two independent population means whether to use the equal variances 2-sample t-test or pooled variances 2-sample t-test.
You will find that much of what we discuss here will be an extension to our previous lessons on confidence intervals and hypothesis testing for one-proportion and one-mean. We will want to check necessary conditions in order to use Z-methods for comparing two proportions or to use t-methods for comparing two means independent and dependent.
If conditions are satisfied, we calculate the specific test statistic and again compare this to a critical value rejection region approach or find the probability of observing this test statistic or one more extreme p-value approach.
The decision process will be the same as well: The interpretation of an confidence intervals in support of the hypothesis decision will also be familiar: One departure we will take from our prior lesson on hypothesis testing is how we will treat the null value.
In the previous lesson the null value could vary. In this lesson when comparing two proportions or two means, we will use a null value of 0 i. Although we can test for a specific difference, for example does the diet result in an average weight loss of more than 10 pounds.
However, common applications commonly research only for a difference i. Unlike prior lessons where we introduced software at the end of the lesson, here will will introduce software within the specific topic. The motivation for this change are the more complex expressions.
Though the formulas are not strenuous - if you think about it the expressions are more like "puzzles" where you need to input numbers into their specific location - doing them by hand can be cumbersome.
Therefore, while we will provide the formulas and examples by hand, we will use software to complete the analysis.
The Software is Only as Good as the User! After reading the prior paragraph students often feel some relief because they will move to using computers over by-hand methods. Be careful of what you wish for! We frequently tell students that despite the speed of the software, the user is ultimately smarter.
That is, the software will perform the complicated math, but we are responsible for telling the computer what is the correct math to perform.
The software will not provide prompts such as, "Are you sure this is the right analysis"?Jul 27, · This feature is not available right now. Please try again later. In hypothesis testing, we assume that the null hypothesis holds until proven otherwise. We therefore need to determine the likelihood of observing a sample mean of or higher when the true population mean is (i.e., if the null hypothesis is true or under the null hypothesis).
And all that means, and we've done this multiple times, is we're going to assume the null hypothesis. And then assuming the null hypothesis is true, we're going to figure out the probability of getting the actual difference of our sample proportions. Hypothesis Testing for Two Means and Two Proportions.
Hypothesis Testing for Two Means and Two Proportions Class Time: Names: Student Learning Outcomes. The student will select the appropriate distributions to use in each case.
The student will conduct hypothesis tests and interpret the results. HYPOTHESIS TESTING FOR DIFFERENCE OF POPULATION PARAMETERS Part of important studies within business and decision‐making are the ones related to hypothesis for difference of population parameters; it is testing the difference between .
The procedure for hypothesis testing is based on the ideas described above. Specifically, we set up competing hypotheses, select a random sample from the population of interest and compute summary statistics. We then determine whether the sample data supports the null or alternative hypotheses.