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Paired t-interval

This version was saved 9 years, 4 months ago View current version     Page history
Saved by Julie Schaufler
on December 1, 2014 at 9:10:25 am
 

When comparing two sets of data, you subtract one from the other to find the difference for every group in the set. This doesn't make sense in general. It only works for certain kinds of data. These differences are the means of paired data. Makes no sense. After finding the mean differences, we want to know how close to the true mean we are for the matched pairs. This is not what a confidence interval accomplishes. A paired t-interval constructs a confidence interval to estimate the mean difference between matched pairs of data. Yes, this is much closer. This confidence level tells us how far away we are from the true mean. Incorrect. Before we can create a confidence interval, we need to check our conditions.

 

Rather than format it like this, just write a few paragraphs. Use full sentences that flow one to another. Your presentation is too choppy.

 

Conditions

Paired Data Condition - the data must be paired.

Independence Assumption - if the data are paired, the groups are not independent. Rather, the differences must be independent of each other.

Randomization Condition - the groups must be random.

Nearly Normal Condition - assume the population of differences follows a Normal Model. We can check this condition with a histogram. Or a QQ-plot.

 

Put this in your own words. I don't have a copy of the book with me, but I'd bet some money that you just copied this right out of the book. That's a huge problem.

 

Confidence Equations

If all of our conditions are met, we can calculate a confidence interval:


                                                                                          where  is the mean difference,

                                                                                                                               is the critical value with  degrees of freedom.

                                                                                                                              n-1 finds the degree of freedom, and

                                                                                                                              SE is the standard error

The standard error of the mean difference is:                          SE(dbar) = sd /sqrt(n)   where sd is the standard deviation of the differences, and

                                                                                                                             n is the sample size

 

The formatting here is awful. Did you really align these by just inserting dozens of spaces?

 

Steps for Finding the Confidence Interval

In order to conduct the test, we need to follow the appropriate steps to find a solution and come to a conclusion.

Plan - state what we want to know.

Model - check the conditions, draw a picture, state the sampling distribution model, and choose your method.

Mechanics - estimate the standard error of dbar, and calculate the margin of error.

Conclusion - interpret the confidence interval in context.

 

Again, don't bullet point these steps. Just write what needs to be done. This should be incorporated into the exposition above and not listed as a separate section.

 

No need to introduce the example. Just start writing about it.

Example

 

This is suppose to be the same example you use in the video. Why isn't it?

 

I won't comment much about it because you'll have to change all of it. But like I said above, you need a much more expository style, organized into flowing paragraphs. Don't just copy the book. Put it in your own words and follow the rubric.

 

 

Looking at married couples, husbands tend to be slightly older than wives. How much older, on average, are husbands? We have data from a random sample of 200 British couples. Only 170 couples provided ages for both husband and wife. Form a confidence interval for the mean difference of husband's and wife's ages for these 170 couples.

 

Plan - I want to estimate the mean difference in age between husbands and wives. I have a random sample of 200 British couples, 170 of whom provided both ages.

Model - Paired Data Condition: the data are paired because they are testing on members of married couples.

         - Independence Assumption: the data are from a randomized survey, so couples should be independent of each other.

         - Nearly Normal Condition: a histogram is best.

         The conditions are met, so we can use Student's t-model with (n-1)=169 degrees of freedom and find a paired t-interval.

Mechanics - n=170

               - dbar=2.2

               - sd=4.1 years

               - standard error of dbar: SE(dbar) = sd /sqrt(n)

                                                                = 4.1/sqrt(170) = 0.31 years

                                                                degree of freedom(df): n-1=169

                - the 95% critical value for t169 is 1.97

                - the margin of error: ME = t*169 X SE(dbar)

                                                     = 1.97(0.31) = 0.61

                So the 95% confidence interval is 2.2 + 0.6, or an interval of (1.6,2.8) years

Conclusion - I am 95% confident that British husbands are, on average, 1.6 to 2.8 years older than other wives.

 

Using SPSS to find Confidence Intervals for Matched Pairs

  • First open the file that you will be working with on SPSS We're assuming this has already been done. (By the way, each step is a sentence and, therefore, requires a period.)
  • Select the Analyze drop down menu and choose Compare Means
  • Under the Compare Means menu, select Paired-Sample T Test
  • A menu will pop up, place the two different variables into the variable 1 and variable 2 boxes. Run-on sentence.
  • SPSS has the confidence interval set to 95%, but if you would like to change the interval select the options button and replace the 95 with the percentage that you want
  • After you have replaced the 95% with your intended interval click continue to return to the Paired-Sample T Test menu
  • Select the OK button and SPSS will produce the output for the Paired-Sample T Test
  • Scrolling through the output, in the Paired Samples Test box there is a column for the interval that you specified that breaks it into the upper and lower ends of the interval  

 

 

Unable to display content. Adobe Flash is required.

 

Again, you can assume the data set is open already. As you work through the steps, explain a little about the example. So introduce the data and make sure the viewer understands what they're looking at.

 

You can check one of the conditions in SPSS by calculating the differences in a new column and looking at a histogram and QQ-plot. It would be wise considering that you only have 12 data points.

 

You need to explain the choice you made to put July first and then January. The viewer will want to know how to make that decision and why one choice might be better than the other.

 

You need to help the viewer interpret the interval they see. What do those numbers mean in context? 

 

                                                                                                                           

 

 

 

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