Making a t interval for paired data (article) | Khan Academy (2024)

Log in

• Makara.p

  6 years agoPosted 6 years ago. Direct link to Makara.p's post “What is the difference be...”

  What is the difference between z* and t*? When to use z* and when to you t*?

  Button navigates to signup page•Button navigates to signup page

  (5 votes)

  • Angels Angels

    6 years agoPosted 6 years ago. Direct link to Angels Angels's post “To be more precise - if y...”

    

    To be more precise - if you know the standard deviation of the ENTIRE population, then use z*. Otherwise, calculate the standard deviation of the sample and use t*.

    Comment on Angels Angels's post “To be more precise - if y...”

    (21 votes)
• ahmedmetiaz

  4 years agoPosted 4 years ago. Direct link to ahmedmetiaz's post “"Since there was no contr...”

  "Since there was no control group for comparison we shouldn't say there's a causal relationship here" I didn't understand this explanation

  Button navigates to signup page•Button navigates to signup page

  (2 votes)

  • MFogleman

    4 years agoPosted 4 years ago. Direct link to MFogleman's post “The only way to tell if s...”

    

    The only way to tell if something causes something else (a causal relationship) is with a controlled experiment, where you can make sure that only one variable changes. In this example, we did an observational study instead of an experiment, so we don't know for sure if the program causes better performance. There could be a lurking variable in the mix, so we would need to assign treatments and perform an experiment to know more.

    A control group would be a group that doesn't use the program at all between the pretest and post test, so you can compare the performance between both groups and know that the only change was whether someone used the program or not. You would also need to take some more steps to make sure that this experiment is ironclad, which would let you do more with the results. I would recommend checking out the videos on experimental design, observational studies, and surveys, just to get a bit more depth.
    Hope this helps.

    Button navigates to signup page

    (22 votes)
• See Also

  7.7: t-Interval for a MeanConfidence Interval Calculator - with calculation stepsConfidence Interval Calculator - Calculate one-sample or two-sample (difference of means) CIT-Value Calculator / Critical Value Calculator - [100% Free] - Calculators.io

  Hieu Le

  5 years agoPosted 5 years ago. Direct link to Hieu Le's post “How did you find the stan...”

  How did you find the standard deviation in the table in step 2?

  Button navigates to signup page•Button navigates to signup page

  (5 votes)

  • deka

    2 years agoPosted 2 years ago. Direct link to deka's post “using our familiar genera...”

    using our familiar general formula for std,
    std_sample = sqrt{sum_on_all_data[(data_i-data_mean)^2]/n-1}
    this measures and tells you how each datapoint varies from the mean of them in general

    by the way, you can't use the concept and formula for std of the difference between two random variables that sqrt(std_var1^2 + std_var2^2) here. cause the two datasets (pre and post -tests) are not independent here. they are paired each other. thus the std of their difference may be less than that of those from two independent datasets using the formula above. and it is indeed

    please, hand on the numbers yourself. it will help you to grasp the concept of variance, standard deviation, and variables more clearly

    Comment on deka's post “using our familiar genera...”

    (3 votes)
• phillicia makanatleng

  4 years agoPosted 4 years ago. Direct link to phillicia makanatleng's post “how was the standard devi...”

  how was the standard deviations in example 1 calculated?

  Button navigates to signup page•Button navigates to signup page

  (4 votes)

  • daniella

    3 months agoPosted 3 months ago. Direct link to daniella's post “he standard deviations in...”

    he standard deviations in example 1 were likely calculated using the standard deviation formula for a sample, which divides by n-1 instead of n for unbiased estimation. Since the data are paired, the standard deviation of the differences can also be calculated directly from the differences themselves.

    Button navigates to signup page

    (1 vote)
• pfarheen

  5 years agoPosted 5 years ago. Direct link to pfarheen's post “You made a typo. You wrot...”

  You made a typo. You wrote "here are the data" instead of "here is the date." It's at Step 3.

  Button navigates to signup page•Button navigates to signup page

  (0 votes)

  • Saivishnu Tulugu

    See Also

    Confidence Interval Calculator

    5 years agoPosted 5 years ago. Direct link to Saivishnu Tulugu's post “Data is a plural word and...”

    

    Data is a plural word and thus the correct phrase would be "here are the data" instead of "here is the data". The singular form of "data" is "datum".

    Button navigates to signup page

    (14 votes)
• Chase McKinley

  5 months agoPosted 5 months ago. Direct link to Chase McKinley's post “Great explanation! Clarit...”

  Great explanation! Clarity is always super appreciated with complex statistical tests.

  Regarding using t-intervals for paired data, if you're dealing with a situation where the both the population mean and variance are not known but you have a large number of data pairs in your sample from the population of interest, is this still the best test to use?

  Specifically asking regarding a statistics assignment where the task is to test the claim that the mean heart rates of fraternal twin pairs are not significantly different. Despite having 130 pairs of recorded heart rates for the sample, my reasoning was that this (paired data t-test for differences) was a good choice to use/conduct a hypothesis test with. Should I have gone a different route than this?

  Button navigates to signup page•Button navigates to signup page

  (2 votes)

  • Chase McKinley

    3 months agoPosted 3 months ago. Direct link to Chase McKinley's post “Thanks for the response/a...”

    Thanks for the response/advice. The test seemed to fit very nicely for what I needed to draw inferences about for the project, so I’m definitely glad I stuck with it/didn’t abandon for some other less suitable method.

    Button navigates to signup page

    (1 vote)
• Mike Papadakis

  4 years agoPosted 4 years ago. Direct link to Mike Papadakis's post “Is it okay to use the dif...”

  Is it okay to use the difference of watch a - watch b? this results in negative numbers but if one keeps in mind we talk about the difference in time intervals, no problem should come up. Isn't that right?( example 1)

  Button navigates to signup page•Button navigates to signup page

  (2 votes)

  • daniella

    3 months agoPosted 3 months ago. Direct link to daniella's post “Using the difference of w...”

    Using the difference of watch A - watch B is indeed appropriate for paired data analysis, especially when the focus is on comparing the effects or measurements between two related conditions or treatments. Negative differences simply indicate that watch B reported a shorter distance than watch A, which is meaningful in the context of the study.

    Button navigates to signup page

    (1 vote)
• jk3109

  6 years agoPosted 6 years ago. Direct link to jk3109's post “In my opinion, Step 2 of ...”

  In my opinion, Step 2 of Example 1 shouldn't be considered independent because I don't believe they "shouldn't influence each other's results". They are running at the same time so isn't it likely they are pressured to keep up at the group pace and thus influenced by each other? If this type of question were on the AP exam, should I state this opinion or assume they aren't going to be influenced and go through with the calculations?

  Button navigates to signup page•Button navigates to signup page

  (1 vote)

  • Jesse Johnson

    6 years agoPosted 6 years ago. Direct link to Jesse Johnson's post “I hope this helps, It s...”

    I hope this helps,

    It states that they are wearing both watches at the same time, not that they are running in a group together at the same time. Since the runners were randomly selected, and the runners according to the study were not running together, they weren't able to reasonably influence each other's results.

    Comment on Jesse Johnson's post “I hope this helps, It s...”

    (3 votes)
• B H

  4 years agoPosted 4 years ago. Direct link to B H's post “How did you calculate the...”

  How did you calculate the standard deviation of the difference between means? You show 8.07; I get 4.49 = [6.48/SQRT(6) + 8.89/SQRT(6)]. Thanks.

  At

  5:55

  pm CDT: Math AP®︎ Statistics Confidence intervals Confidence intervals for means, example 2.

  Button navigates to signup page•Button navigates to signup page

  (1 vote)

  • daniella

    3 months agoPosted 3 months ago. Direct link to daniella's post “To calculate the standard...”

    To calculate the standard deviation of the difference between means, you need to first compute the standard deviation of each group (watch A and watch B), then divide each by the square root of the sample size, and finally apply the formula for combining standard deviations. Your calculation of 4.49 seems correct.

    Button navigates to signup page

    (1 vote)
• shadiaroberts.srr

  3 years agoPosted 3 years ago. Direct link to shadiaroberts.srr's post “how did he get the standa...”

  how did he get the standard deviation if it wasnt given?

  Button navigates to signup page•Button navigates to signup page

  (1 vote)

  • daniella

    3 months agoPosted 3 months ago. Direct link to daniella's post “The standard deviation mi...”

    The standard deviation might not have been explicitly given in the problem statement, but it can be calculated from the provided data. In example 1, the standard deviation of the differences can be computed directly from the differences recorded for each runner.

    Button navigates to signup page

    (1 vote)