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*? • (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*. (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 • (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. (22 votes) 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? • (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, 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 (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? • (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. (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. • (0 votes) Saivishnu Tulugu 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". (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? • (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. (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) • (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. (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? • (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. (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 • (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. (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? • (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. (1 vote)Want to join the conversation?
Hope this helps.
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
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FAQs
How to calculate confidence interval for paired t test? ›
A 95% confidence interval for the true mean difference is: ¯ d ± t∗ sd √ n or, equivalently ¯d± (t∗ × SE(¯d)) where t∗ is the 2.5% point of the t-distribution on n − 1 degrees of freedom.
When to construct at interval? ›T interval is good for situations where the sample size is small and population standard deviation is unknown. When the sample size comes to be very small (n≤30), the Z-interval for calculating confidence interval becomes less reliable estimate. And here the T-interval comes into place.
When to use matched pairs t interval? ›- You take one random sample to study two paired variables. These paired variables are DEPENDENT. Usually, you are studying some measurable quality about the same subject before and after a treatment.
- Your goal is to find the mean difference (ˉxd).
Paired Data. • Data are paired when the observations are collected in. pairs or the observations in one group are naturally. related to observations in the other group.
How to calculate t value for paired t-test? ›- Calculate the sample mean. ¯d = d1 + d2 + ⋯ + dnn.
- Calculate the sample standard deviation. ˆσ = √(d1 − ¯d)2 + (d2 − ¯d)2 + ⋯ + (dn − ¯d)2n − 1.
- Calculate the test statistic. t = ¯d − 0ˆσ/√n.
- Calculate the probability of observing the test statistic under the null hypothesis.
95% confidence interval
This means that at the 5% significance level, the true median difference lies between 0.50 and 1.50.
If the population standard deviation is known, use the z-distribution. If the population standard deviation is not known, use the t-distribution.
How to do T intervals? ›- Choose the significance level based on your desired confidence level. ...
- Find the critical value of t in the two-tailed t table.
- Multiply the critical value of t by s/√n.
Strictly speaking a 95% confidence interval means that if we were to take 100 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value (μ).
When not to use a paired t-test? ›If there are two different samples, and you wish to test whether they come from the same population we go with an unpaired t-test. If it is a single sample and we are measuring a scenario of before/after and wish to compare the significance of the results we go with a paired t-test.
When it is appropriate to use paired t procedures versus two sample t procedures? ›
3.3 Differences between the two-sample t-test and paired t-test. As discussed above, these two tests should be used for different data structures. Two-sample t-test is used when the data of two samples are statistically independent, while the paired t-test is used when data is in the form of matched pairs.
Which is the correct condition for the paired t-test? ›To apply the paired t-test to test for differences between paired measurements, the following assumptions need to hold: Subjects must be independent. Measurements for one subject do not affect measurements for any other subject. Each of the paired measurements must be obtained from the same subject.
What is the formula for paired data? ›The formula for the paired t-test is given by t=∑d√n(∑d2)−(∑d)2n−1, where ∑d is the sum of the differences. The data is taken from subjects who have been measured twice. 95% confidence interval is obtained from the difference between the two sets of joined observations.
How do you tell if data is paired or not? ›There are two types: paired and unpaired. Paired means that both samples consist of the same test subjects. A paired t-test is equivalent to a one-sample t-test. Unpaired means that both samples consist of distinct test subjects.
What is the p-value for paired data? ›The P-value is the probability of finding the observed difference (or larger) between the paired samples, under the null-hypothesis. The null-hypothesis is the hypotheses that in the population (from which the samples are drawn) the difference between similarly paired observations is 0.
What is the formula for the confidence interval of the t-test? ›Multiply the critical value of t by s/√n. Add this value to the mean to calculate the upper limit of the confidence interval, and subtract this value from the mean to calculate the lower limit.
How do you find the confidence interval using the t value? ›Steps to calculate the confidence interval (CI) from the p value (p) and the estimate (Est) for a difference where data are continuous: Calculate the test statistic for a normal distribution test (z) from p: z = −0.862 + √[0.743 − 2.404×log(p)] Calculate the standard error, ignoring the minus sign: SE = Est/z.
What is P 0.05 in paired t-test? ›In the paired samples t-test the null hypothesis is that the average of the differences between the paired observations in the two samples is zero. If the calculated P-value is less than 0.05, the conclusion is that, statistically, the mean difference between the paired observations is significantly different from 0.
What is the confidence interval of a two tailed t-test? ›For a two-tailed test, the critical value is 1.96 . So the confidence interval is |Z|<1.96 and the critical regions are where |Z|>1.96 .