Since the x2 tests of goodness of fit and of association in contingency tables are presented in many courses on statistical methods for beginners in the subject, it is not surprising that x2 has become one of the most commonly-used techniques, even by scientists who profess only a smattering of knowledge of statistics. It is also not surprising that the technique is sometimes misused, e.g. by calculating x2 from data that are not frequencies or by errors in counting the number of degrees of freedom. A good catalogue of mistakes of this kind has been given by Lewis and Burke (1). In this paper I want to discuss two kinds of failure to make the best use of x2 tests which I have observed from time to time in reading reports of biological research. The first arises because x2 tests, as has often been pointed out, are not directed against any specific alternative to the null hypothesis. In the computation of x2, the deviations (fi mi) between observed and expected frequencies are squared, divided by mi in order to equalize the variances (approximately), and added. No attempt is made to detect any particular pattern of deviations (fi mi) that may hold if the null hypothesis is false. One consequence is that the usual x2 tests are often insensitive, and do not indicate significant results when the null hypothesis is actually false. Some forethought about the kind of alternative hypothesis that is likely to hold may lead to alternative tests that are more powerful and appropriate. Further, when the ordinary x2 test does give a significant result, it does not direct attention to the way in which the null hypothesis disagrees with the data, although the pattern of deviations may be informative and suggestive for future research. The remedy here is to supplement the ordinary test by additional tests that help to reveal the significant type of deviation. In this paper a number of methods for strengthening or supplementing the most common uses of the ordinary x2 test will be presented and illustrated by numerical examples. The principal devices are as follows:

Recently, Lancaster (1949, 1950) and Irwin (1949) showed how x2 may be partitioned exactly into single degrees of freedom when expected frequencies are estimated from the data. In particular they considered the case of an r X s (r rows, s columns) contingency table in which the expected frequencies are computed from the marginal totals. Their work suggests several different methods of carrying out the necessary computations, some of which they have illustrated. For tables of any order, their con...

In studying the occurrence of plants and animals in nature, the number of individuals may be counted in each of many equal units of space or time. The original counts can be summarized in a frequency distribution, showing the number of units containing x = 0, 1, 2, 3, ... individuals of a given species. If every unit in the series were exposed equally to the chance of containing the organism, the distribution would follow the Poisson series, each unit having the population mean as its expected f...

This paper contains an expository discussion of the chi square test of goodness of fit, intended for the student and user of statistical theory rather than for the expert. Part I describes the historical development of the distribution theory on which the test rests. Research bearing on the practical application of the test--in particular on the minimum expected number per class and the construction of classes--is discussed in Part II. Some varied opinions about the extent to which the test actu...

1. The statistician is often confronted with data in which the measurement of interest is the proportion of units possessing a certain attribute. Such data can arise in factorial arrangements in either designed experiments or survey work. An example of the former is given by an experiment on a number of varieties of bulbs which have been infested with eelworm. Treatments of hot water at two temperatures are applied for two lengths of time, these treatments together with two sizes of bulb forming...

It is an important inferential problem to test no association between two binary variables based on data. Tests based on the sample odds ratio are commonly used. We bring in a competing test based on the Pearson correlation coefficient. In particular, the odds ratio does not extend to higher order contingency tables, whereas Pearson correlation does. It is important to understand how Pearson correlation stacks against the odds ratio in 2 x 2 contingency tables. Another measure of association is ...

#1Colette M Gnade(UIHC: University of Iowa Hospitals and Clinics)

#2Emily K. Hill(UIHC: University of Iowa Hospitals and Clinics)H-Index: 8

Last. Colleen K. Stockdale(UIHC: University of Iowa Hospitals and Clinics)H-Index: 13

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Abstract Objectives The objective of this study was to determine if there has been an increase in the age of diagnosis of cervical cancer over time, specifically in the proportion of patients over 65 years old, given decreasing rates of hysterectomy. Materials and Methods A retrospective review of a single institution was conducted including cervical cancer patients seen between 1986 and 2016. Data included demographic variables including age of diagnosis, last cervical cancer screening, and can...

Abstract Exposure to forest environment is beneficial to human health and has complex physiological and psychological effects. Here, we synthesized the results from 40 peer-reviewed publications, and conducted a meta-analysis to evaluate the general responses of 15 variables related to physiological and psychological functions to forest exposure. We summarized the evidence that forest exposure was beneficial to health, such as reducing systolic blood pressure (SMD = −0.27), diastolic blood press...

Last. Chien-Chang Lee(NTU: National Taiwan University)H-Index: 37

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Background null Few population-based studies assess the impact of cancer on sepsis incidence and mortality. null Objectives null To evaluate epidemiological trends of sepsis in patients with cancer. null Methods null This retrospective cohort study included adults (≥20 years old) identified using sepsis-indicator International Classification of Diseases codes from the Nationwide Inpatient Sample database (2006-2014). A generalized linear model was used to trend incidence and mortality. Outcomes ...

Argonaute 2 (AGO2) is an indispensable component of the RNA-induced silencing complex, operating at the translational or posttranscriptional level. It is compartmentalized into structures such as GW- and P-bodies, stress granules and adherens junctions as well as the midbody. Here we show using immunofluorescence, image and bioinformatic analysis and cytogenetics that AGO2 also resides in membrane protrusions such as open- and close-ended tubes. The latter are cytokinetic bridges where AGO2 colo...

This article estimates a count-data model on the flight behaviour of Austrian holiday-makers based on information from a large representative quarterly survey spanning the years 2014–2016. On average, the number of holiday flights ranges between 0.6 and 1.2 per year for residents in the least populated region and the capital, respectively. Results of the estimations reveal that the number of holiday flights is highest for persons with tertiary degrees, of a young age (16–24 years) and capital ci...

Background null Conventional dynamic contrast enhanced (DCE) magnetic resonance (MR) hardly achieves a good imaging performance of arteries and lymph nodes in the breast area. Therefore, a new imaging method is needed for the assessment of breast arteries and lymph nodes. null Methods null We performed prospective research. The research included 52 patients aged from 25 to 64 between June 2019 and April 2020. The isotropic e-THRIVE sequence scanned in the coronal direction after DCE-THRIVE. Reco...

Dual-energy X-ray absorptiometry (DXA)-based bone mineral density testing is standard to diagnose osteoporosis to detect individuals at high risk of fracture. A radiomics approach to extract quantifiable texture features from DXA hip images may improve hip fracture prediction without additional costs. Here, we investigated whether bone radiomics scores from DXA hip images could improve hip fracture prediction in a community-based cohort of older women. The derivation set (143 women who sustained...

Last. Maria Iannario(University of Naples Federico II)H-Index: 16

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Aim of the contribution is analyzing potential events that may negatively impact individuals, assets, and/or the environment, and making judgments about the perceived personal and social riskiness ...