Matched or Paired Samples T-Test - Hypothesis Testing

The Organic Chemistry Tutor
15 Nov 201912:55
EducationalLearning
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TLDRThis video tutorial guides viewers through the process of analyzing the effectiveness of a weight loss program using a paired sample t-test. By comparing the before and after weights of 10 subjects, the video demonstrates how to calculate the mean difference, standard deviation, and construct hypotheses. Using a significance level of 5%, it walks through the calculation of the critical t-value, and the comparison of the calculated t-value to determine the program's effectiveness. The video concludes by constructing a confidence interval, reinforcing the statistical evidence that the weight loss program is effective in reducing weight, thus providing viewers with a practical application of statistical analysis in real-world scenarios.

Takeaways
  • ๐Ÿ˜€ The video explains how to solve problems with matched or paired sample data using a weight loss program example.
  • ๐Ÿ“Š The data consists of before and after weights of 10 subjects in the program.
  • ๐Ÿค” The goal is to determine if the program is effective at reducing weight using a t-test.
  • ๐Ÿ’ก The differences between before and after weights are calculated first.
  • ๐Ÿ“ˆ The sample mean and standard deviation of the differences are then calculated.
  • ๐Ÿ“œ The null and alternative hypotheses are stated based on the goal of the test.
  • ๐Ÿ” The critical t value is looked up in a t-distribution table based on the degrees of freedom and alpha.
  • ๐Ÿงฎ The calculated t value is compared to the critical value to determine if the null hypothesis should be rejected.
  • ๐Ÿ“Š A confidence interval is constructed around the sample mean difference.
  • ๐ŸŽ“ The margin of error is determined, and conclusions about the effectiveness of the program are made.
Q & A
  • What is the purpose of the study described in the video?

    -The purpose is to determine if a specific weight loss program is effective at reducing weight.

  • How many subjects participated in the weight loss program study?

    -There were 10 subjects that participated.

  • What data was collected from the subjects?

    -The before and after weights of the 10 subjects were collected.

  • What is the null hypothesis and alternative hypothesis for this study?

    -The null hypothesis is that the mean difference is equal to or greater than 0. The alternative hypothesis is that the mean difference is less than 0.

  • How is the mean difference and standard deviation of the differences calculated?

    -The mean difference is calculated by finding the difference between the before and after weights for each subject, summing those differences, and dividing by the number of subjects. The standard deviation is calculated using the STDEV.S function in Excel on the list of differences.

  • What test statistic is used to analyze the data?

    -A left-tailed t-test is used since the alternative hypothesis states the mean difference is less than 0. The test statistic is the sample mean difference minus 0 divided by the standard error.

  • What is the conclusion from the statistical test?

    -Since the calculated t statistic falls in the rejection region, we reject the null hypothesis. There is evidence that the weight loss program is effective at reducing weight.

  • What is the confidence interval calculated?

    -The 95% confidence interval is -20.65 to -5.55. This means we are 95% confident the true mean difference lies within that interval.

  • What is the margin of error for the study?

    -The margin of error is 7.55.

  • What sample size would be needed to reduce the margin of error?

    -A larger sample size would reduce the margin of error. For example, with a sample size of 25 instead of 10, the margin of error would decrease to about 5.9.

Outlines
00:00
๐Ÿ˜€ Calculating weight differences

The paragraph describes calculating the difference in before and after weights for each of the 10 subjects in a weight loss program study to determine the program's effectiveness. It steps through subtracting the after weight from the before weight for each subject to populate a difference column. It also states the null and alternative hypotheses.

05:02
๐Ÿ˜Š Calculating mean and standard deviation

The paragraph discusses calculating the sample mean and standard deviation of the weight differences using formulas initially then shows how to simplify the calculation using Excel. It highlights that the standard deviation helps determine the standard error to then calculate a test statistic.

10:03
๐Ÿ“ˆ Analyzing results and drawing conclusions

The paragraph analyzes the test statistic calculated from the mean difference and standard error and compares it to the critical t-value to determine that the null hypothesis can be rejected. It then constructs a 95% confidence interval for the true mean difference and explains how this also rejects the null. Finally, it states the margin of error.

Mindmap
Keywords
๐Ÿ’กMatched sample
A matched sample refers to measuring two things from the same group of participants. In this case, it is the before and after weights of participants in a weight loss program. This allows for a matched analysis by comparing weights within each individual.
๐Ÿ’กSignificance level
The significance level, set at 5% here, is the threshold probability for determining whether a result is statistically significant. If the p-value is below this level, the null hypothesis is rejected.
๐Ÿ’กNull hypothesis
The null hypothesis states that the weight loss program has no effect, meaning the average weight change is equal to or greater than zero. This is tested against the alternative hypothesis.
๐Ÿ’กAlternative hypothesis
The alternative hypothesis states that the weight loss program reduces weight on average, meaning the average weight change is less than zero. This is what the analysis aims to prove.
๐Ÿ’กMean difference
The mean difference of -13.1 pounds refers to the average amount of weight lost per participant in the program. This is a key statistic tested to evaluate the program's effectiveness.
๐Ÿ’กStandard deviation
The standard deviation of 13.025 pounds measures the amount of variation in weight changes among participants. This is used to calculate the standard error and test statistic.
๐Ÿ’กLeft-tailed test
This is a one-sided test checking only for a reduction in weight, in line with the alternative hypothesis. So only the left tail of the t distribution is relevant.
๐Ÿ’กDegrees of freedom
With 10 data points, the degrees of freedom is 10 - 1 = 9. This determines which row to use in the t distribution table.
๐Ÿ’กConfidence interval
The 95% confidence interval around the mean difference lets us say with 95% confidence that the true average weight change lies between -20.65 and -5.55 pounds.
๐Ÿ’กMargin of error
The margin of error of ยฑ7.55 pounds reflects the precision of our estimated mean weight change. A smaller margin means more precision.
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Transcripts
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