On the Pearson Chi-Squared Goodness-Of-Fit Test Statistic

Biometrika ◽  
1971 ◽  
Vol 58 (3) ◽  
pp. 685 ◽  
Author(s):  
Ram C. Dahiya
Keyword(s):  
Goodness Of Fit ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Chi Squared

Reversing the Friday peak in metastatic cord compression referrals: Not as simple as previously thought?

2021 ◽  
Vol 39 (15_suppl) ◽  
pp. e14050-e14050
Author(s):  
Olusola Michael Adeleke ◽  
Rubyyat A Hakim ◽  
Laurence Dean ◽  
Huma Zahid ◽  
Rongyu Lin ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Single Point ◽  
District General Hospital ◽  
Cord Compression ◽  
Radiology Reporting ◽  
Goodness Of Fit Test ◽  
Tertiary Centre ◽  
Chi Squared ◽  
Early Case ◽  
The Uk

e14050 Background: Historically, metastatic spinal cord compression (MSCC) referrals trend towards a Friday peak in incidence (Koiter E, Radioth Onc 2013). However, data from a single, tertiary centre in the UK showed a reversal in the Friday peak (Adeleke S, Annals of Oncology 2020). This was attributed to early case referrals and quicker treatment decisions. In this new study, we explored whether a similar pattern was apparent in multiple district general hospital (DGH) settings and attempt to identify underlying causes. DGHs manage a larger proportion of cancer patients in the UK. Methods: 1,069 patients between 1 Jan 2015 and 31 Dec 2020 were identified across 4 hospitals in Kent, UK with a population of 1.6 million people. 220, 181, 182, 159, 134 and 193 MSCC patients were identified annually (2015-2020). Commonest cancers were prostate (24.1%), lung (19.3%) and breast (12.3%). Thoracic and lumbar regions constituted 80% of MSCC sites. Kruskal Wallis was used to compare differences in referrals across weekdays. Data was then dichotomised to Fridays only vs. other days of the week combined, as previously reported (De Bono B, Acta Neurochir 2019). Chi squared was used to compare frequency of referrals between the two groups. Chi squared goodness of fit test was conducted to detect if Friday reflected the day with highest referrals across the week. Results: Across the region, 2015 saw the highest number of Friday referrals relative to other days, p= 0.002. Friday referrals continued to drop, year on year, until 2018 with a corresponding increase in mid-week referrals. After 2018, there was a return in trend to a further Friday peak across the region, though p= 0.836. On an individual hospital basis, the persistent Friday peak in the region was driven by two hospitals. Having a 7-day acute oncology service (AOS), 7-day radiology reporting and single referral point of contact in the department, were factors identified that kept the referrals across the week uniform. On another note, a substantial shift towards a single 8Gy fraction vs. 20Gy in 5 fractions was observed across the region. This change coincided with SCORAD III data (Hoskin P, ASCO 2017) and demonstrates adherence to evidence-based practice in the region. Conclusions: This large multi-centre retrospective study shows a differential referral pattern in the region, with hospitals with 7-day AOS/Radiology reporting and single point of referral (e.g, similar to MSCC coordinator role) having a quicker treatment turnaround and uniform referrals across the week. The MSCC coordinator has been shown to streamline service, ensure timely decision-making and improved survival outcomes (Richards L, Spine J 2017). The role is recommended by NICE UK. DGHs should consider appointing an MSCC coordinator when designing/auditing their service. The shift towards single 8Gy fraction can provide a ‘one-stop’ service where patients are scanned, planned and treated on the same day.

A test for fuzzy exponentiality based on Kullback-Leibler information

2021 ◽  
pp. 1-8
Author(s):  
Lingtao Kong
Keyword(s):  
Biological Sciences ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Experimental Studies ◽  
Real Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Higher Power ◽  
Leibler Information

The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

scholarly journals Testing in Nonparametric Accelerated Life Time Models

2016 ◽  
Vol 37 (1) ◽  
Author(s):  
Hannelore Liero
Keyword(s):  
Limit Distribution ◽  
Goodness Of Fit ◽  
Bootstrap Method ◽  
Life Time ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Time Model ◽  
Power Of The Test ◽  
Accelerated Life ◽  
Type Test

A goodness-of-fit test for testing the acceleration function in a nonparametric life time model is proposed. For this aim the limit distribution of an L2-type test statistic is derived. Furthermore, a bootstrap method is considered and the power of the test is studied.

scholarly journals Tracking Pandemic Severity Using Data on the Age Structure of Mortality: Lessons From the 1918 Influenza Pandemic in Michigan

2021 ◽  
Vol 111 (S2) ◽  
pp. S149-S155
Author(s):  
Siddharth Chandra ◽  
Julia Christensen
Keyword(s):  
Public Health ◽  
Age Structure ◽  
Goodness Of Fit ◽  
Influenza Pandemic ◽  
Age Distribution ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
1918 Influenza ◽  
Death Data ◽  
Excess Deaths

Objectives. To test whether distortions in the age structure of mortality during the 1918 influenza pandemic in Michigan tracked the severity of the pandemic. Methods. We calculated monthly excess deaths during the period of 1918 to 1920 by using monthly data on all-cause deaths for the period of 1912 to 1920 in Michigan. Next, we measured distortions in the age distribution of deaths by using the Kuiper goodness-of-fit test statistic comparing the monthly distribution of deaths by age in 1918 to 1920 with the baseline distribution for the corresponding month for 1912 to 1917. Results. Monthly distortions in the age distribution of deaths were correlated with excess deaths for the period of 1918 to 1920 in Michigan (r = 0.83; P < .001). Conclusions. Distortions in the age distribution of deaths tracked variations in the severity of the 1918 influenza pandemic. Public Health Implications. It may be possible to track the severity of pandemic activity with age-at-death data by identifying distortions in the age distribution of deaths. Public health authorities should explore the application of this approach to tracking the COVID-19 pandemic in the absence of complete data coverage or accurate cause-of-death data.

scholarly journals Demographic Seasonality

2019 ◽  
Vol 22 (03) ◽  
pp. 187-194 ◽  
Author(s):  
Johan Fellman
Keyword(s):  
At Risk ◽  
Goodness Of Fit ◽  
Extreme Values ◽  
Demographic Data ◽  
Climatic Conditions ◽  
Data Sets ◽  
Test Statistic ◽  
Population At Risk ◽  
Chi Squared ◽  
Number Of Births

AbstractThe seasonality of demographic data has been of great interest. It depends mainly on the climatic conditions, and the findings may vary from study to study. Commonly, the studies are based on monthly data. The population at risk plays a central role. For births or deaths over short periods, the population at risk is proportional to the lengths of the months. Hence, one must analyze the number of births (and deaths) per day. If one studies the seasonality of multiple maternities, the population at risk is the total monthly number of confinements and the number of multiple maternities in a given month must be compared with the monthly number of all maternities. Consequently, when one considers the monthly rates of multiple maternities, the monthly number of births is eliminated and one obtains an unaffected seasonality measure of the rates. In general, comparisons between the seasonality of different data sets presuppose standardization of the data to indices with common means, mainly 100. If one assumes seasonality as ‘non-flatness’ throughout a year, a chi-squared test would be an option, but this test calculates only the heterogeneity and the same test statistic can be obtained for data sets with extreme values occurring in consecutive months or in separate months. Hence, chi-squared tests for seasonality are weak because of this arbitrariness and cannot be considered a model test. When seasonal models are applied, one must pay special attention to how well the applied model fits the data. If the goodness of fit is poor, nonsignificant models obtained can erroneously lead to statements that the seasonality is slight, although the observed seasonal fluctuations are marked. In this study, we investigate how the application of seasonal models can be applied to different demographic variables.

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