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Comparison of Two Means
Published in Marcello Pagano, Kimberlee Gauvreau, Heather Mattie, Principles of Biostatistics, 2022
Marcello Pagano, Kimberlee Gauvreau, Heather Mattie
Recall that α is the significance level of the test, is the desired power, μ0 is the population mean given that the null hypothesis is true, μ1 is the population mean given that the alternative hypothesis is true, and σ is the population standard deviation. Because the paired t-test is just a one-sample t-test performed on differences, the same formula can be applied to paired data, with a slight change in notation. Since we are working with differences, we replace by . Furthermore, we indicate that the population standard deviation is a standard deviation of differences by labeling it σd. Therefore, the sample size formula becomes
Statistics for Genomics
Published in Altuna Akalin, Computational Genomics with R, 2020
However, we should note that how we constructed the confidence interval using standard normal distribution, , only works when we know the population standard deviation. In reality, we usually have only access to a sample and have no idea about the population standard deviation. If this is the case, we should estimate the standard deviation using the sample standard deviation and use something called the t distribution instead of the standard normal distribution in our interval calculation. Our confidence interval becomes , with t distribution parameter , since now the following quantity is t distributed instead of standard normal distribution.
Extrapolation
Published in Shein-Chung Chow, Innovative Statistics in Regulatory Science, 2019
In clinical research, it is often of interest to generalize clinical results obtained from a given target patient population (or medical center) to a similar but different patient population (or another medical center). Denote the original target patient population by where and are the population mean and population standard deviation, respectively. Similarly, denote the similar but different patient population by . Since the two populations are similar but different, it is reasonable to assume that and , where is referred to as the shift in location parameter (population mean) and is the inflation factor of the scale parameter (population standard deviation). Thus, the (treatment) effect size adjusted for the standard deviation of population can be expressed as follows:
Debridement, antibiotics and implant retention (DAIR) is successful in the management of acutely infected unicompartmental knee arthroplasty: a case series
Published in Annals of Medicine, 2023
Angela Brivio, Talal Al-Jabri, Jurgen Martin, David Barrett, Nicola Maffulli
Patients failing to complete the therapeutic regimen through non-attendance or failure of therapy were excluded, and recurrence of infection was noted. Failure to eradicate the infection was defined as recurrent infection from the same or different organisms. FU was continued in successful cases until inflammatory markers had returned to normal and the patient reported cessation of infective symptoms. Yearly FU appointments were then scheduled. The overall survivorship free from reoperation for infection and the overall survivorship free from reoperation for any reason is reported. The mean and standard deviations are provided using a population standard deviation formula. We used a Kaplan Meier survivorship curve to present survivorship free from reinfection following the primary DAIR procedure. This mode of analysis is similar to that used in previous literature in this field and allows direct comparison to other previous publications and different techniques for treating PJI.
Impaired health-related quality of life, psychological distress, and productivity loss in younger people with persistent shoulder pain: a cross-sectional analysis
Published in Disability and Rehabilitation, 2022
Ilana N. Ackerman, Kathy Fotis, Lauren Pearson, Peter Schoch, Nigel Broughton, Sharon L. Brennan-Olsen, Andrew Bucknill, Emily Cross, Nicola Bunting-Frame, Richard S. Page
AQoL data were compared to overall and age- and sex-matched Australian population norms [13] using one-sample t-tests. As the overall population norm was based on data from people aged 15–80 years and over, we calculated a weighted mean for the overall, male and female populations aged 20–59 years using published AQoL means and sample sizes for the 20–29, 30–39, 40–49, and 50–59 years age groups. For each t-test, the largest population standard deviation within these age strata was used. This approach has been used previously [1]. K10 scores were categorised into levels of psychological distress according to 2017–2018 National Health Survey definitions [24] and compared to age- and sex-matched data for the population aged 18–54 years from the 2017–2018 National Health Survey [25]. An online calculator [26] was used to estimate relative risk for the presence of high or very high psychological distress (K10 score ≥ 22) in the sample, compared with the population. Non-parametric tests (Kruskal–Wallis or Mann–Whitney) were used to examine whether shoulder-related parenting disability differed according to age group of the children, or sex of the study participant.
Pathogenesis of pelvic pain syndrome associated with endometriosis in patients resistant to surgical treatment
Published in Gynecological Endocrinology, 2020
Victor Radzinsky, Mekan Orazov, Olga Sharapova, Marina Khamoshina
The resulting data were statistically processed using the SPSS 7.5 program for Windows statistical software package (IBM Analytics, Armonk, NY, USA). The variation series, the arithmetic mean, the population standard deviation, the mean error, and the probability of difference were determined. Then, the conformity/non-conformity of the results obtained to the normal distribution was evaluated using the Kolmogorov–Smirnov criterion. When statistical processing, the following non-parametric criteria were used to assess the reliability of differences in mean values between the following groups: Mann–Whitney U-test, Kruskal–Wallis H-test. In the absence of normal data distribution, the non-parametric F. Wilcoxon criterion (Statistical Methods for Research Workers) with a significance level of p < .05 was used.