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Can't miss: conquer any number task by making important statistics simple. Part 6. Tests of statistical significance (z test statistic, rejecting the null hypothesis, p value), t test, z test for proportions, statistical significance versus meaningful difference.

Healthcare quality professionals need to understand and use inferential statistics to interpret sample data from their organizations. Since in quality improvement and healthcare research studies all the data from a population often are not available, investigators take samples and make inferences about that population using inferential statistics. This series of six articles will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals and tests of statistical significance for samples of data. This article, Part 6, merges the four concepts of the (1) standard error of the difference between sample means, (2) the z test statistic, (3) rejecting the null hypothesis, and (4) the p value to provide a comprehensive view of tests of statistical significance. This is followed by a description of t tests, statistical tests for comparing two sample proportions, and Type I and Type II errors. The series of articles concludes with a description of statistical significance versus meaningful difference.

Confidence Intervals↗
PubMed1993

A log-rank test for equivalence of two survivor functions.

We consider a hypothesis testing problem in which the alternative states that the vertical distance between the underlying survivor functions nowhere exceeds some prespecified bound delta > 0. Under the assumption of proportional hazards, this hypothesis is shown to be (logically) equivalent to the statement [beta[ < log(1 + epsilon), where beta denotes the regression coefficient associated with the treatment group indicator, and epsilon is a simple strictly increasing function of delta. The testing procedure proposed consists of carrying out in terms of beta (i.e., the standard Cox likelihood estimator of beta) the uniformly most powerful level alpha test for a suitable interval hypothesis about the mean of a Gaussian distribution with fixed variance. The computation of the critical constant of this test is very easy in practice since it admits a representation as the root of the alpha th quantile of a noncentral chi-square distribution with a single degree of freedom.

Biometry↗
PubMed1993

Seasonal changes in rule infractions among prisoners: a preliminary test of the temperature-aggression hypothesis.

To test the temperature-aggression hypothesis, seasonal changes in aggression as indexed by reported rule infractions were studied for prisoners located at the Patuxent Institution, Jessup, Maryland. 5383 reports of rule infractions occurred between July 1987 and March 1991. Rule infractions occurred more frequently during the hot summer months than the three other seasons of the year. This summer effect, though significant, is only a few percent above a theoretical chance level based on the number of days comprising the seasons. A much stronger monthly effect over 45 months was found, but the bases of erratic fluctuations are not known.

Aggression↗
PubMed2002

Multiplicity, directional (type III) errors, and the null hypothesis.

L. V. Jones and J. W. Tukey (2000) pointed out that the usual 2-sided, equal-tails null hypothesis test at level alpha can be reinterpreted as simultaneous tests of 2 directional inequality hypotheses, each at level alpha/2, and that the maximum probability of a Type I error is alpha/2 if the truth of the null hypothesis is considered impossible. This article points out that in multiple testing with familywise error rate controlled at alpha, the directional error rate (assuming all null hypotheses are false) is greater than alpha/2 and can be arbitrarily close to alpha. Single-step, step-down, and step-up procedures are analyzed, and other error rates, including the false discovery rate, are discussed. Implications for confidence interval estimation and hypothesis testing practices are considered.

Humans↗
PubMed2001

Communication and consistency: AIDS talk and AIDS attitudes.

The main hypothesis tested in this study is that the frequency of talk about a particular domain is related to the consistency of attitudes in that domain. This hypothesis was developed by viewing talk as one of the ways in which people express their identities and by exploring the interpersonal processes involved in the construction of consistency. The hypothesis was tested with a questionnaire completed by 73 students at Oxford University. The first part of the questionnaire consisted of items related to attitude, and the second part contained questions about respondents' conversations about AIDS and related topics. Strong support was found for the hypothesis relating frequency of talk with consistency of attitudes. Data about who the respondents talked to about AIDS and the perceived agreement between them and their discussion partners demonstrated the homogeneity of the discussion environment. The implications for understanding attitude formation and change in everyday social contexts are considered.

Acquired Immunodeficiency Syndrome↗
PubMed2002

pH and rate of "dark" events in toad retinal rods: test of a hypothesis on the molecular origin of photoreceptor noise.

Thermal activation of the visual pigment constitutes a fundamental constraint on visual sensitivity. Its electrical correlate in the membrane current of dark-adapted rods are randomly occurring discrete "dark events" indistinguishable from responses to single photons. It has been proposed that thermal activation occurs in a small subpopulation of rhodopsin molecules where the Schiff base linking the chromophore to the protein part is unprotonated. On this hypothesis, rates of thermal activation should increase strongly with rising pH. The hypothesis has been tested by measuring the effect of pH changes on the frequency of discrete dark events in red rods of the common toad Bufo bufo. Dark noise was recorded from isolated rods using the suction pipette technique. Changes in cytoplasmic pH upon manipulations of extracellular pH were quantified by measuring, using fast single-cell microspectrophotometry, the pH-dependent metarhodopsin I-metarhodopsin II equilibrium and subsequent metarhodopsin III formation. These measurements show that, in the conditions of the electrophysiological experiments, changing perfusion pH from 6.5 to 9.3 resulted in a cytoplasmic pH shift from 7.6 to 8.5 that was readily sensed by the rhodopsin. This shift, which implies an 8-fold decrease in cytoplasmic [H(+)], did not increase the rate of dark events. The results contradict the hypothesis that thermal pigment activation depends on prior deprotonation of the Schiff base.

Animals↗
PubMed2003

Prognostic value of exercise echocardiography: validation of a new risk index combining echocardiographic, treadmill, and exercise electrocardiographic parameters.

Exercise (Ex) echocardiography has been shown to have significant prognostic power, independent of other known predictors of risk from an Ex stress test. The purpose of this study was to evaluate a risk index, incorporating echocardiographic and conventional Ex variables, for a more comprehensive risk stratification and identification of a very low-risk group. Two consecutive, mutually exclusive populations referred for treadmill Ex echocardiography with the Bruce protocol were investigated: hypothesis-generating (388 patients; 268 males; age 55 +/- 13 years) and hypothesis-testing (105 patients; 61 males age: 54 +/- 14 years).Cardiac events included cardiac death, myocardial infarction, late revascularization (>90 days), hospital admission for unstable angina, and admission for heart failure. Mean follow-up in the hypothesis-generating population was 3.1 years. There were 38 cardiac events. Independent predictors of events by multivariate analysis were: Ex wall motion score index (odds ratio [OR] = 2.77/Unit; P <.001); ischemic S-T depression > or = 1 mm (OR = 2.84; P =.002); and treadmill time (OR = 0.87/min; P =.037). A risk index was generated on the basis of the multivariate Cox regression model as: risk index = 1.02 (Ex wall motion score index) + 1.04 (S-T change) - 0.14 (treadmill time). The validity of this index was tested in the hypothesis-testing population. Event rates at 3 years were lowest (0%) in the lower quartile of risk index (-1.22 to -0.47), highest (29.6%) in the upper quartile (+0.66 to +2.02), and intermediate (19.2% to 15.3%) in the intermediate quartiles. The OR of the risk index for predicting cardiac events was 2.94/Unit ([95% confidence interval: 1.4 to 6.2]; P =.0043). Echocardiographic and Ex parameters are independent powerful predictors of cardiac events after treadmill stress testing. A risk index can be derived with these parameters for a more comprehensive risk stratification with Ex echocardiography.

Adult↗
PubMed2003

Validation of measures of middle schoolers' self-efficacy for physical and emotional health, and academic tasks.

The development and psychometric study of a measure of middle schoolers' perceptions of self-efficacy for physical, emotional, and academic behaviors appropriate to their age and developmental tasks are described. The validation of the Middle School Self-Efficacy Questionnaire (MISSE) included the adaptation of existing items and the generation of new ones. Items were subjected to judges' review by two expert panels and were tested with a large, geographically diverse sample of youngsters aged 11-14. Statistical analyses included factor analysis, internal consistency estimations, t tests, and analyses of variance for hypothesis testing related to construct validity. Results showed support for the expected factors and provided evidence of the validity of the MISSE.

Adolescent↗
PubMed1991

The Patient Intensity for Nursing Index: a validity assessment.

The psychometric assessment of a new measure of nursing intensity, The Patient Intensity for Nursing Index (PINI) is reported. Four dimensions of nursing intensity are measured by the PINI: (a) severity of illness, (b) dependency, (c) complexity of care, and (d) time. There are 10 items rated on a 5-point ordinal scale. A purposively drawn sample of 6,445 patients was obtained from five hospitals, with 487 registered nurses (RNs) providing daily patient ratings from 29 medical-surgical and intensive care units. Substantial interrater reliability was demonstrated. Validity testing included confirmatory factor analysis, hypothesis-testing, contrasted groups, and an observational study of time. The factor structure confirmed specified components of severity, dependency, and complexity, with time loading on all three factors. PINI scores were significantly related to medical severity of illness, length of hospital stay, disposition at discharge, number of secondary medical diagnoses and specialty consults, and scores on three different hospital classification systems used for staffing. PINI scores were significantly different for high- and low-intensity DRGs. Observed time spent delivering nursing care to specific patients was significantly correlated with nurse estimates of time.

Dependency, Psychological↗
PubMed2007

A spatial scan statistic for ordinal data.

Spatial scan statistics are widely used for count data to detect geographical disease clusters of high or low incidence, mortality or prevalence and to evaluate their statistical significance. Some data are ordinal or continuous in nature, however, so that it is necessary to dichotomize the data to use a traditional scan statistic for count data. There is then a loss of information and the choice of cut-off point is often arbitrary. In this paper, we propose a spatial scan statistic for ordinal data, which allows us to analyse such data incorporating the ordinal structure without making any further assumptions. The test statistic is based on a likelihood ratio test and evaluated using Monte Carlo hypothesis testing. The proposed method is illustrated using prostate cancer grade and stage data from the Maryland Cancer Registry. The statistical power, sensitivity and positive predicted value of the test are examined through a simulation study.

Cluster Analysis↗
PubMed1997

Consensus analysis: reliability, validity, and informant accuracy in use of American and Mandarin Chinese pain descriptors.

A quantitative method for validating qualitative interview results and checking sample parameters is described and illustrated using common pain descriptions among a sample of Anglo-American and mandarin Chinese patients and dentists matched by age and gender. Assumptions were that subjects were members of a sociocultural group (e.g. ethnic or professional/lay) and answered questions independently about a monotonic domain (e.g. pain). Subjects answered 18 true/false items derived from and selected to reflect pain perceptions consistent with published and unpublished interview data. Estimates of consistency in use of descriptors within groups, validity of description, accuracy of individuals compared with others in their group, and minimum required sample size were calculated using Cronbach's alpha, factor analysis, and Bayesian probability. Ethnic and professional differences within and across groups were also tested using multidimensional scaling (MDS) and hypothesis testing. Consensus (consistency of subject response by group) was .99 among Anglo-Americans and .97 among Chinese. Mean subject accuracy was .81 for Americans and .57 for Chinese, indicating the need for larger numbers of Chinese to supplement each others' statements. However, larger numbers of subjects were recruited than actually required for each ethnic group at .95 confidence limits. MDS showed similarities in use of descriptors within ethnic groups, while there were differences (p < .001) between Chinese and American groups. Use of covalidating questionnaires that reflect results of qualitative interviews are recommended in order to estimate sample parameters such as intersubject agreement, individual subject accuracy, and minimum required sample sizes.

Adult↗
PubMed1990

Eysenck's incubation of fear hypothesis: an experimental test.

The present experiment was designed to test Eysenck's hypothesis that repeated exposure to an unreinforced CS of brief duration following acquisition of a classical aversive CR may lead to a progressive increase in the strength of that CR, provided that the UCS is intense and the CR has drive-like properties. Using a between-groups design, normal human subjects were given identical classical acquisition trials, followed by extinction trials where CS duration was either 2, 8 or 16 sec. The UCS was of fixed high intensity. Dependent measures were tonic and phasic heart rate and skin conductance. No evidence of incubation was found as a function of CS duration. Nor was there any indication that CS duration differentially affected resistance to extinction. A small number of subjects showed evidence of incubation with heart rate measures during extinction. However, there was no indication that this enhancement was governed by the parameters suggested by Eysenck. UCR amplitude, which showed a positive correspondence with CS-bound activity throughout the trials, did not reliably predict incubation. Problems concerning both the definition and the demonstration of incubation are discussed.

Adolescent↗
PubMed2006

Phylogenetic systematics of the colorful, cyanide-producing millipedes of Appalachia (Polydesmida, Xystodesmidae, Apheloriini) using a total evidence Bayesian approach.

Here, we provide an exemplar-approach phylogeny of the xystodesmid millipede tribe Apheloriini with a focus on genus-group relationships-particularly of the genus Brachoria. Exemplars for the phylogenetic analysis were chosen to represent the maximum breadth of morphological diversity within all nominal genera in the tribe Apheloriini, and to broadly sample the genus Brachoria. In addition, three closely related tribes were used (Rhysodesmini, Nannariini, and Pachydesmini). Morphological and DNA sequence data were scored for Bayesian inference of phylogeny. Phylogenetic analysis resulted in polyphyletic genera Brachoria and Sigmoria, a monophyletic Apheloriini, and a "southern clade" that contains most of the tribal species diversity. We used this phylogeny to track morphological character histories and reconstruct ancestral states using stochastic character mapping. Based on the findings from the character mapping study, the diagnostic feature of the genus Brachoria, the cingulum, evolved independently in two lineages. We compared our phylogeny against prior classifications using Bayes factor hypothesis-testing and found that our phylogenetic hypothesis is inconsistent with the previous hypotheses underlying the most recent classification. With our preferred total-evidence phylogeny as a framework for taxonomic modifications, we describe a new genus, Appalachioria; supply phylogenetic diagnoses of monophyletic taxa; and provide a phylogeny-based classification for the tribe Apheloriini.

Animals↗
PubMed2003

Identification of genetic alterations related to chemoresistance in epithelial ovarian cancer.

OBJECTIVE: After the completion of primary chemotherapy, the majority of advanced ovarian cancer patients have persistent, chemoresistant disease. Comparative genomic hybridization (CGH) has been used to study genetic alterations that may be responsible for chemoresistance in ovarian cancer. CGH is a useful, genomewide screen but resolution is limited to 5-10 Mb. Recently, quantitative microsatellite analysis (QuMA), a TaqMan-based quantitative PCR technology, has been used for higher resolution of DNA copy number abnormalities. Our goal is to identify specific chromosomal aberrations correlated with platinum resistance. METHODS: Snap-frozen ovarian tissue samples taken from 22 patients with ovarian cancer between 1994 and 1998 were analyzed. Patients whose ovarian cancer actually demonstrated growth during platinum-combination treatment or no objective evidence of regression following four to six cycles of therapy were considered to have clinically defined platinum-resistant disease. QuMA was carried out at the following loci using the ABI Prism 7700 (TaqMan) instrument with a microsatellite repeat probe: D3S1553, D3S1617, D5S464, D5S630, D6S1581, D6S446, D8S557, D19S208, D20S196, DXS1068. Fisher's exact test, exact logistic regression, and the Cochran-Armitage trend test were used. Because of multiple hypothesis testing, the P values were adjusted with the Bonferroni procedure to limit the familywise error rate to at most 5%. RESULTS: Of the 22 patients, 12 (54.5%) were platinum-sensitive and 10 (45.5%) were platinum-resistant. When comparing sensitive and resistant patients, no statistically significant difference was noted among stage, grade, histology, and age (P = 0.1292, P = 1.0000, P = 1.0000, P = 1.0000, respectively). In the QuMA analysis, 10 of the 14 (71.4%) patients who had a low copy number of D6S1581 were platinum-resistant, while none of the patients with a normal or high copy number of D6S1581 were platinum-resistant. This was statistically significant when the marker data were treated as either a continuous or a categorical variable (P = 0.0410 and P = 0.0170, respectively). No other loci correlated significantly with platinum resistance. CONCLUSIONS: D6S1581 was the only genetic marker, of those examined, significantly related to chemoresistance. Patients with a loss of D6S1581 are more likely to be platinum-resistant. Identification of genetic alterations associated with platinum resistance detected by QuMA may contribute to a better understanding of clinical behavior and chemotherapy treatment options for patients.

Adenocarcinoma↗
PubMed2006

Testing the homocysteine hypothesis in end-stage renal disease: Problems and a possible solution.

The homocysteine hypothesis states that circulating homocysteine is a vascular toxin in concentrations that occur in the general population and in renal failure. This hypothesis is currently being tested in the Kidney and End State Renal Disease Study (HOST), but data have emerged since the HOST began that suggest its results will be inconclusive. The crucial treatment component in the HOST is folic acid, but its effect is likely to be lost because the American food supply is now fortified with folic acid. A second concern is that the very high doses of folic acid and pyridoxine being used in the HOST may confound the results. Finally, confounding due to 'reverse epidemiology' was not considered when the HOST was designed. Parenteral vitamin B(12) is a highly promising therapy for homocysteine reduction in end-stage renal disease that merits careful investigation. Clinical trials using it to test the homocysteine hypothesis will avoid the problems inherent in the HOST.

Clinical Trials as Topic↗
PubMed1977

Cognition and commissurotomy.

Cognitive functioning was extensively evaluated in a recent callosum-sectioned patient. A number of standardized and specialized experimental memory tests, as well as a sophisticated hypothesis testing task, were administered both before and after operation. No post-operative deficits were obtained. In fact, this patient showed marked improvement on almost every measure utilized. These results demonstrate that the cognitive processing of complex information is not necessarily dependent on the integrity of the corpus callosum, but rather suggest that cognitive functioning is largely an intrahemispheric process.

Adolescent↗