Deliverable 05 Worksheet Instructions

Deliverable 05 Worksheet instructionsthe Following Worksheet Describ

The worksheet requires demonstrating solutions to two statistical scenarios: one involving independent samples and the other involving dependent samples. For the independent samples, you will formulate hypotheses, identify the test type, calculate the critical value and test statistic, and make a decision regarding the null hypothesis to determine if a new drug reduces blood pressure. For the dependent samples, you will perform a hypothesis test using the P-value approach to evaluate if the drug decreases blood pressure based on paired measurements. Your explanations should be detailed and in your own words, covering each step clearly.

Sample Paper For Above instruction

The statistical analysis of blood pressure data involves two distinct approaches: one for independent samples and another for dependent samples. Carefully executing these tests requires understanding the proper hypotheses formulation, choosing the correct test type, calculating test statistics and critical values or P-values, and making informed decisions about the null hypothesis.

Analysis of Independent Samples

Consider a study where a researcher aims to ascertain whether a new drug can effectively lower systolic blood pressure in individuals with high blood pressure. The researcher gathers data from two groups: a treatment group receiving the drug and a control group not receiving it. The sample sizes are denoted as nT for treatment and nC for control, with their respective sample means (x̄T and x̄C) and sample standard deviations (sT and sC). Since the population standard deviations are unknown, a t-test is suitable.

Formulating Hypotheses

The null hypothesis (H0) posits no difference in mean blood pressure reduction due to the drug:

  • H0: μT ≥ μC

The alternative hypothesis (HA) claims that the drug reduces blood pressure, i.e., the mean in the treatment group is less than in the control:

  • HA: μT C

This is a left-tailed test since we're testing for a reduction.

Calculating the Critical Value and Test Statistic

Using a significance level α = 0.01, we determine the critical t-value from the t-distribution table based on degrees of freedom estimated via the Welch's approximation. The test statistic (t) is calculated as:

t = (x̄T - x̄C) / SE

where SE is the standard error of the difference between means, computed as:

SE = sqrt( (sT)2 / nT + (sC)2 / nC ).

Calculating these values yields the t-statistic, which is then compared to the critical t-value to evaluate the hypothesis.

Decision and Conclusion

If the calculated t is less than the critical value, we reject H0, concluding that evidence supports the drug's effectiveness in reducing blood pressure. If not, we fail to reject H0, and there is insufficient evidence to confirm the drug's effect at the 0.01 significance level.

Analysis of Dependent Samples

In the second scenario, the same group of subjects is measured before and after administering the drug, allowing for a paired t-test. Each subject provides a pair of measurements, and the difference (d = after - before) is calculated for each individual.

Formulating Hypotheses

The null hypothesis states that the mean difference in blood pressure before and after the drug is zero or less, indicating no reduction:

  • H0: μd ≤ 0

The alternative hypothesis asserts that the drug decreases blood pressure, so:

  • HA: μd > 0

This is a right-tailed test as we are testing if the mean difference is greater than zero, indicating a decrease in blood pressure.

Calculating the Test Statistic and P-Value

The mean and standard deviation of the differences are computed, and the t-statistic is calculated by:

t = (mean difference) / (standard deviation of differences / sqrt(n))

The P-value is then obtained from the t-distribution table or software, corresponding to the calculated t-value and degrees of freedom (n-1).

Decision and Conclusion

If the P-value is less than the significance level α = 0.05, we reject H0, concluding that there is sufficient evidence the drug lowers blood pressure. Otherwise, we fail to reject H0.

Final Reflections

In both analyses, proper formulation of hypotheses rooted in the research question and the choice of appropriate statistical tests are critical for valid conclusions. The independent samples test assesses if the treatment group differs from a control, while the dependent samples test evaluates whether the same individuals show improvement after treatment. Correct interpretation of results in nontechnical terms ensures meaningful communication of findings relevant to healthcare decisions.

References

  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage.
  • Gravetter, F., & Wallnau, L. (2016). Statistics for the Behavioral Sciences. Cengage Learning.
  • Howell, D. C. (2012). Statistical Methods for Psychology. Cengage Learning.
  • Laerd Statistical Guides. (2020). Independent samples t-test in SPSS. Laerd.com.
  • Laerd Statistical Guides. (2020). Paired-samples t-test in SPSS. Laerd.com.
  • Moore, D. S., Notz, W., & Fligner, M. (2013). The Basic Practice of Statistics. W.H. Freeman.
  • Ott, R. L., & Longnecker, M. (2015). An Introduction to Statistical Methods and Data Analysis. Cengage Learning.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson.
  • Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing. Academic Press.
  • Woolson, R. F. (2002). Statistical Methods for the Analysis of Data from a Paired T-Test. Journal of Educational and Behavioral Statistics.

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