scholarly journals Responses of non-eye-movement central vestibular neurons to sinusoidal yaw rotation in compensated macaques after unilateral semicircular canal plugging

2016 ◽  
Vol 116 (4) ◽  
pp. 1871-1884 ◽  
Author(s):  
Shawn D. Newlands ◽  
Min Wei ◽  
David Morgan ◽  
Hongge Luan
Keyword(s):  
Eye Movement ◽  
Semicircular Canal ◽  
Vestibular Nuclei ◽  
Type I ◽  
Type Ii ◽  
Central Type ◽  
Vestibular Neurons ◽  
Unilateral Labyrinthectomy ◽  
Resting Activity ◽  
The Difference

After vestibular labyrinth injury, behavioral measures of vestibular performance recover to variable degrees (vestibular compensation). Central neuronal responses after unilateral labyrinthectomy (UL), which eliminates both afferent resting activity and sensitivity to movement, have been well-studied. However, unilateral semicircular canal plugging (UCP), which attenuates angular-velocity detection while leaving afferent resting activity intact, has not been extensively studied. The current study reports response properties of yaw-sensitive non-eye-movement rhesus macaque vestibular neurons after compensation from UCP. The responses at a series of frequencies (0.1–2 Hz) and peak velocities (15–210°/s) were compared between neurons recorded before and at least 6 wk after UCP. The gain (sp/s/°/s) of central type I neurons (responding to ipsilateral yaw rotation) on the side of UCP was reduced relative to normal controls at 0.5 Hz, ±60°/s [0.48 ± 0.30 (SD) normal, 0.32 ± 0.15 ipsilesion; 0.44 ± 0.2 contralesion]. Type II neurons (responding to contralateral yaw rotation) after UCP have reduced gain (0.40 ± 0.27 normal, 0.35 ± 0.25 ipsilesion; 0.25 ± 0.18 contralesion). The difference between responses after UCP and after UL is primarily the distribution of type I and type II neurons in the vestibular nuclei (type I neurons comprise 66% in vestibular nuclei normally; 51% ipsilesion UCP; 59% contralesion UCP; 38% ipsilesion UL; 65% contralesion UL) and the magnitude of the responses of type II neurons ipsilateral to the lesion. These differences suggest that the need to compensate for unilateral loss of resting vestibular nerve activity after UL necessitates a different strategy for recovery of dynamic vestibular responses compared to after UCP.

Neuronal Activity in the Vestibular Nuclei After Contralateral or Bilateral Labyrinthectomy in the Alert Guinea Pig

1998 ◽  
Vol 80 (5) ◽  
pp. 2352-2367 ◽  
Author(s):  
Laurence Ris ◽  
Emile Godaux
Keyword(s):  
Guinea Pig ◽  
Vestibular Nuclei ◽  
Acute Stage ◽  
Second Order ◽  
Inhibitory Influence ◽  
Type I ◽  
Vestibular Neurons ◽  
Unilateral Labyrinthectomy ◽  
Resting Activity ◽  
Control State

Ris, Laurence and Emile Godaux. Neuronal activity in the vestibular nuclei after contralateral or bilateral labyrinthectomy in the alert guinea pig. J. Neurophysiol. 80: 2352–2367, 1998. In the guinea pig, a unilateral labyrinthectomy is followed by an initial depression and a subsequent restoration of the spontaneous activity in the neurons of the ipsilateral vestibular nuclei. In two previous works, we have established the time course of these changes in the alert guinea pig using electrical stimulation as a search stimulus to select the analyzed neurons. The latter criterion was important to capture the many ipsilateral neurons that are silent at rest during the immediate postlabyrinthectomy stage. Because it is known that a pathway originating from the vestibular nuclei on one side crosses the midline and functionally inhibits the activity of the vestibular nuclei on the other side, we investigated in the first part of this study the spiking behavior of the neurons in the vestibular nuclei contralateral to the labyrinthectomy using the same procedure as that used for the ipsilateral neurons. The spiking behavior of 976 neurons was studied during 4-h recording sessions in intact animals and 1 h, 1 day, 2 days, or 1 wk postlabyrinthectomy. Neurons selected according to the electrical activation criterion were classified further as type I (their firing rate increased during ipsilateral rotation), type II (their firing rate increased during contralateral rotation), or unresponsive. The resting activity of type I neurons, which was 38.1 ± 20.9 spikes/s (mean ± SD) in the control state, increased statistically significantly 1 h after the lesion (53.3 ± 29.1 spikes/s) and remained at this level 1 wk later (56.0 ± 20.3 spikes/s). The sensitivity of type I units, which was 0.80 ± 0.46 spikes/s per deg/s in the control population, decreased to 0.49 ± 0.26 spikes/s per deg/s 1 h after the lesion and remained at this level 1 wk later (0.50 ± 0.39 spikes/s per deg/s). When all monosynaptically activated neurons (type I, type II, unresponsive) were pooled, the sensitivity to horizontal rotation fell from 0.58 ± 0.51 spikes/s per deg/s in the control state to 0.15 ± 0.25 spikes/s per deg/s 1 h after the lesion and to 0.20 ± 0.32 spikes/s per deg/s 1 wk later. The major findings of the first part of this study in the alert guinea pig are thus in accord with those of Curthoys et al. and Smith and Curthoys in anesthetized guinea pigs. In the second part of this work, we studied the spiking behavior of the neurons in the vestibular nuclei after bilateral labyrinthectomy. After unilateral labyrinthectomy, the resting discharge of the ipsilateral monosynaptically activated vestibular neurons fell from 36.9 ± 21 spikes/s (basal activity) to 6.7 ± 17.0 spikes/s 1 h after the lesion and then recovered, reaching 17.4 ± 18.9 and 40.8 ± 23.7 spikes/s 1 day and 1 wk after the lesion, respectively. These observations raise the two following questions. What are the relative contributions of the loss of the excitatory influence from the ipsilateral labyrinth (destroyed) and of the persistence of the inhibitory influence from the contralateral labyrinth (intact) in the labyrinthectomy-induced depression of activity? And are the left-right asymmetries caused by a unilateral labyrinthectomy the driving force for restoration of activity? Here, we addressed these two questions by studying the spiking behavior of 473 second-order vestibular neurons in the alert guinea pig after a bilateral labyrinthectomy. In the acute stage, 1 h after bilateral labyrinthectomy, the resting discharge of the second-order vestibular neurons was 16.2 ± 22.4 spikes/s. From comparison with the results obtained in the acute stage after a unilateral labyrinthectomy, we inferred that the ipsilateral excitatory influence was between two and three times more powerful than the contralateral inhibitory influence. After bilateral labyrinthectomy as well as after unilateral labyrinthectomy, the resting activity of the second-order vestibular neurons returned to normal, reaching 20.8 ± 23.1 spikes/s 1 day after the lesion and 38.6 ± 21.1 spikes/s 1 wk after the lesion. From this fact, we concluded that the left-right asymmetries caused by a unilateral labyrinthectomy were not the error signals inducing the restoration of activity.

Encoding of head acceleration in vestibular neurons. I. Spatiotemporal response properties to linear acceleration

1993 ◽  
Vol 69 (6) ◽  
pp. 2039-2055 ◽  
Author(s):  
G. A. Bush ◽  
A. A. Perachio ◽  
D. E. Angelaki
Keyword(s):  
Semicircular Canal ◽  
Linear Acceleration ◽  
Vestibular Nuclei ◽  
Type I ◽  
Type Ii ◽  
Head Acceleration ◽  
Null Direction ◽  
Response Properties ◽  
Spatiotemporal Response ◽  
Horizontal Head

1. Extracellular recordings were made in and around the medial vestibular nuclei in decerebrated rats. Neurons were functionally identified according to their semicircular canal input on the basis of their responses to angular head rotations around the yaw, pitch, and roll head axes. Those cells responding to angular acceleration were classified as either horizontal semicircular canal-related (HC) or vertical semicircular canal-related (VC) neurons. The HC neurons were further characterized as either type I or type II, depending on the direction of rotation producing excitation. Cells that lacked a response to angular head acceleration, but exhibited sensitivity to a change in head position, were classified as purely otolith organ-related (OTO) neurons. All vestibular neurons were then tested for their response to sinusoidal linear translation in the horizontal head plane. 2. Convergence of macular and canal inputs onto central vestibular nuclei neurons occurred in 73% of the type I HC, 79% of the type II HC, and 86% of the VC neurons. Out of the 223 neurons identified as receiving macular input, 94 neurons were further studied, and their spatiotemporal response properties to sinusoidal stimulation with pure linear acceleration were quantified. Data were obtained from 33 type I HC, 22 type II HC, 22 VC, and 17 OTO neurons. 3. For each neuron the angle of the translational stimulus vector was varied by 15, 30, or 45 degrees increments in the horizontal head plane. In all tested neurons, a direction of maximum sensitivity was identified. An interesting difference among neurons was their response to translation along the direction perpendicular to that that produced the maximum response ("null" direction). For the majority of neurons tested, it was possible to evoke a nonzero response during stimulation along the null direction always had response phases that varied as a function of stimulus direction. 4. These spatiotemporal response properties were quantified in two independent ways. First, the data were evaluated on the basis of the traditional one-dimensional principle governed by the "cosine gain rule" and constant response phase at different stimulus orientations. Second, the response gain and phase values that were empirically determined for each orientation of the applied linear stimulus vector were fitted on the basis of a newly developed formalism that treats neuronal responses as exhibiting two-dimensional spatial sensitivity. Thus two response vectors were determined for each neuron on the basis of its response gain and phase at different stimulus directions in the horizontal head plane.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Tests of linearity in the responses of eye-movement-sensitive vestibular neurons to sinusoidal yaw rotation

2013 ◽  
Vol 109 (10) ◽  
pp. 2571-2584 ◽  
Author(s):  
Shawn D. Newlands ◽  
Min Wei
Keyword(s):  
Eye Movement ◽  
Dynamic Range ◽  
Peak Velocity ◽  
Vestibular Nuclei ◽  
Head Movements ◽  
Type I ◽  
Vestibular Neurons ◽  
Ocular Reflex ◽  
Vestibulo Ocular Reflex ◽  
Vestibular Nuclear Neurons

The rotational vestibulo-ocular reflex in primates is linear and stabilizes gaze in space over a large range of head movements. Best evidence suggests that position-vestibular-pause (PVP) and eye-head velocity (EHV) neurons in the vestibular nuclei are the primary mediators of vestibulo-ocular reflexes for rotational head movements, yet the linearity of these neurons has not been extensively tested. The current study was undertaken to understand how varying magnitudes of yaw rotation are coded in these neurons. Sixty-six PVP and 41 EHV neurons in the rostral vestibular nuclei of 7 awake rhesus macaques were recorded over a range of frequencies (0.1 to 2 Hz) and peak velocities (7.5 to 210°/s at 0.5 Hz). The sensitivity (gain) of the neurons decreased with increasing peak velocity of rotation for all PVP neurons and EHV neurons sensitive to ipsilateral rotation (type I). The sensitivity of contralateral rotation-sensitive (type II) EHV neurons did not significantly decrease with increasing peak velocity. These data show that, like non-eye-movement-related vestibular nuclear neurons that are believed to mediate nonlinear vestibular functions, PVP neurons involved in the linear vestibulo-ocular reflex also behave in a nonlinear fashion. Similar to other sensory nuclei, the magnitude of the vestibular stimulus is not linearly coded by the responses of vestibular neurons; rather, amplitude compression extends the dynamic range of PVP and type I EHV vestibular neurons.

Responses of Medullary Dorsal Horn Neurons to Corneal Stimulation by CO2 Pulses in the Rat

1999 ◽  
Vol 82 (5) ◽  
pp. 2092-2107 ◽  
Author(s):  
Harumitsu Hirata ◽  
James W. Hu ◽  
David A. Bereiter
Keyword(s):  
Thalamic Nucleus ◽  
Receptive Fields ◽  
Male Rats ◽  
Cervical Cord ◽  
Type I ◽  
Type Ii ◽  
Upper Cervical ◽  
The Difference ◽  
Evoked Activity ◽  
Stimulation Of

Corneal-responsive neurons were recorded extracellularly in two regions of the spinal trigeminal nucleus, subnucleus interpolaris/caudalis (Vi/Vc) and subnucleus caudalis/upper cervical cord (Vc/C1) transition regions, from methohexital-anesthetized male rats. Thirty-nine Vi/Vc and 26 Vc/C1 neurons that responded to mechanical and electrical stimulation of the cornea were examined for convergent cutaneous receptive fields, responses to natural stimulation of the corneal surface by CO2 pulses (0, 30, 60, 80, and 95%), effects of morphine, and projections to the contralateral thalamus. Forty-six percent of mechanically sensitive Vi/Vc neurons and 58% of Vc/C1 neurons were excited by CO2 stimulation. The evoked activity of most cells occurred at 60% CO2 after a delay of 7–22 s. At the Vi/Vc transition three response patterns were seen. Type I cells ( n = 11) displayed an increase in activity with increasing CO2 concentration. Type II cells ( n = 7) displayed a biphasic response, an initial inhibition followed by excitation in which the magnitude of the excitatory phase was dependent on CO2 concentration. A third category of Vi/Vc cells (type III, n = 3) responded to CO2 pulses only after morphine administration (>1.0 mg/kg). At the Vc/C1 transition, all CO2-responsive cells ( n = 15) displayed an increase in firing rates with greater CO2 concentration, similar to the pattern of type I Vi/Vc cells. Comparisons of the effects of CO2 pulses on Vi/Vc type I units, Vi/Vc type II units, and Vc/C1 corneal units revealed no significant differences in threshold intensity, stimulus encoding, or latency to sustained firing. Morphine (0.5–3.5 mg/kg iv) enhanced the CO2-evoked activity of 50% of Vi/Vc neurons tested, whereas all Vc/C1 cells were inhibited in a dose-dependent, naloxone-reversible manner. Stimulation of the contralateral posterior thalamic nucleus antidromically activated 37% of Vc/C1 corneal units; however, no effective sites were found within the ventral posteromedial thalamic nucleus or nucleus submedius. None of the Vi/Vc corneal units tested were antidromically activated from sites within these thalamic regions. Corneal-responsive neurons in the Vi/Vc and Vc/C1 regions likely serve different functions in ocular nociception, a conclusion reflected more by the difference in sensitivity to analgesic drugs and efferent projection targets than by the CO2 stimulus intensity encoding functions. Collectively, the properties of Vc/C1 corneal neurons were consistent with a role in the sensory-discriminative aspects of ocular pain due to chemical irritation. The unique and heterogeneous properties of Vi/Vc corneal neurons suggested involvement in more specialized ocular functions such as reflex control of tear formation or eye blinks or recruitment of antinociceptive control pathways.

scholarly journals Number of fiber bundles in the fetal anterior talofibular ligament

2021 ◽  
Author(s):  
Mutsuaki Edama ◽  
Tomoya Takabayashi ◽  
Hirotake Yokota ◽  
Ryo Hirabayashi ◽  
Chie Sekine ◽  
...  
Keyword(s):  
Fiber Bundle ◽  
Fiber Bundles ◽  
Anterior Talofibular Ligament ◽  
Type I ◽  
Type Ii ◽  
Crown Rump Length ◽  
Type Iii ◽  
The Difference ◽  
And Inversion

Abstract Background For the anterior talofibular ligament (ATFL), a three-fiber bundle has recently been suggested to be weaker than a single or double fiber bundle in terms of ankle plantarflexion and inversion braking function. However, the studies leading to those results all used elderly specimens. Whether the difference in fiber bundles is a congenital or an acquired morphology is important when considering methods to prevent ATFL damage. The purpose of this study was to classify the number of fiber bundles in the ATFL of fetuses. Methods This study was conducted using 30 legs from 15 Japanese fetuses (mean weight, 1764.6 ± 616.9 g; mean crown-rump length, 283.5 ± 38.7 mm; 8 males, 7 females). The ATFL was then classified by the number of fiber bundles: Type I, one fiber bundle; Type II, two fiber bundles; and Type III, three fiber bundles. Results Ligament type was Type I in 5 legs (16.7%), Type II in 21 legs (70%), and Type III in 4 legs (13.3%). Conclusions The present results suggest that the three fiber bundles of the structure of the ATFL may be an innate structure.

Convergent Properties of Vestibular-Related Brain Stem Neurons in the Gerbil

2000 ◽  
Vol 83 (4) ◽  
pp. 1958-1971 ◽  
Author(s):  
Galen D. Kaufman ◽  
Michael E. Shinder ◽  
Adrian A. Perachio
Keyword(s):  
Translational Motion ◽  
Stimulus Frequency ◽  
Head Rotation ◽  
Vestibular Nuclei ◽  
Inhibitory Input ◽  
Type I ◽  
Similar Response ◽  
Type Ii ◽  
Response Dynamics ◽  
Related Activity

Three classes of vestibular-related neurons were found in and near the prepositus and medial vestibular nuclei of alert or decerebrate gerbils, those responding to: horizontal translational motion, horizontal head rotation, or both. Their distribution ratios were 1:2:2, respectively. Many cells responsive to translational motion exhibited spatiotemporal characteristics with both response gain and phase varying as a function of the stimulus vector angle. Rotationally sensitive neurons were distributed as Type I, II, or III responses (sensitive to ipsilateral, contralateral, or both directions, respectively) in the ratios of 4:6:1. Four tested factors shaped the response dynamics of the sampled neurons: canal-otolith convergence, oculomotor-related activity, rotational Type (I or II), and the phase of the maximum response. Type I nonconvergent cells displayed increasing gains with increasing rotational stimulus frequency (0.1–2.0 Hz, 60°/s), whereas Type II neurons with convergent inputs had response gains that markedly decreased with increasing translational stimulus frequency (0.25–2.0 Hz, ±0.1 g). Type I convergent and Type II nonconvergent neurons exhibited essentially flat gains across the stimulus frequency range. Oculomotor-related activity was noted in 30% of the cells across all functional types, appearing as burst/pause discharge patterns related to the fast phase of nystagmus during head rotation. Oculomotor-related activity was correlated with enhanced dynamic range compared with the same category that had no oculomotor-related response. Finally, responses that were in-phase with head velocity during rotation exhibited greater gains with stimulus frequency increments than neurons with out-of-phase responses. In contrast, for translational motion, neurons out of phase with head acceleration exhibited low-pass characteristics, whereas in-phase neurons did not. Data from decerebrate preparations revealed that although similar response types could be detected, the sampled cells generally had lower background discharge rates, on average one-third lower response gains, and convergent properties that differed from those found in the alert animals. On the basis of the dynamic response of identified cell types, we propose a pair of models in which inhibitory input from vestibular-related neurons converges on oculomotor neurons with excitatory inputs from the vestibular nuclei. Simple signal convergence and combinations of different types of vestibular labyrinth information can enrich the dynamic characteristics of the rotational and translational vestibuloocular responses.

Blood clinicopathological differences between type I and II ketosis in dairy cows

2015 ◽  
Author(s):  
XU Chuang ◽  
Shen Tai-yu ◽  
YAO Yuan ◽  
Yu Hong-jiang ◽  
XIA Cheng ◽  
...  
Keyword(s):  
Dairy Cows ◽  
Dairy Cow ◽  
Plasma Concentrations ◽  
Elisa Test ◽  
Type I ◽  
Type Ii ◽  
Hydroxybutyric Acid ◽  
Cattle Farm ◽  
The Difference ◽  
Heilongjiang Of China

The purpose was to determine the difference of blood clinicopathological changes between type I and type II ketosis in dairy cow. Fifty-eight cows, from dairy cattle farm in Heilongjiang of China, were included. An ELISA test was used to evaluate the blood indicators. The plasma concentrations of beta-hydroxybutyric acid (BHBA) and insulin sensitivity decreased, and the plasma concentration of glucose (Glc), non-esterified fatty acid (NEFA) and bilirubin content increased in type II ketosis group compared with the type I ketosis group. These results showed that there was a difference in etiology between type II ketosis and type I ketosis. Type II ketosis was not only associated with energy metabolism and insulin resistance, but also with oxidative stress and liver function. It laid the foundation for further investigate the mechanism and prevention of type II ketosis in the future.

scholarly journals Analytic non-Abelian gravitating solitons in the Einstein–Yang–Mills–Higgs theory and transitions between them

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Fabrizio Canfora ◽  
Seung Hun Oh
Keyword(s):  
Energy Levels ◽  
Higgs Field ◽  
Scalar Fields ◽  
Family Type ◽  
Type I ◽  
Type Ii ◽  
Yang Mills ◽  
Completely Regular ◽  
The Difference ◽  
Abelian Fields

AbstractTwo analytic examples of globally regular non-Abelian gravitating solitons in the Einstein–Yang–Mills–Higgs theory in (3 + 1)-dimensions are presented. In both cases, the space-time geometries are of the Nariai type and the Yang–Mills field is completely regular and of meron type (namely, proportional to a pure gauge). However, while in the first family (type I) $$X_{0} = 1/2$$ X 0 = 1 / 2 (as in all the known examples of merons available so far) and the Higgs field is trivial, in the second family (type II) $$X_{0} = 1/2$$ X 0 = 1 / 2 is not 1/2 and the Higgs field is non-trivial. We compare the entropies of type I and type II families determining when type II solitons are favored over type I solitons: the VEV of the Higgs field plays a crucial role in determining the phases of the system. The Klein–Gordon equation for test scalar fields coupled to the non-Abelian fields of the gravitating solitons can be written as the sum of a two-dimensional D’Alembert operator plus a Hamiltonian which has been proposed in the literature to describe the four-dimensional Quantum Hall Effect (QHE): the difference between type I and type II solutions manifests itself in a difference between the degeneracies of the corresponding energy levels.

scholarly journals Genetic basis of the formation and identity of type I and type II neurons in Drosophila embryos

Development ◽  
1997 ◽  
Vol 124 (14) ◽  
pp. 2819-2828 ◽  
Author(s):  
M. Vervoort ◽  
D.J. Merritt ◽  
A. Ghysen ◽  
C. Dambly-Chaudiere
Keyword(s):  
Cell Communication ◽  
Sense Organ ◽  
Type I ◽  
Type Ii ◽  
Neuronal Fate ◽  
Late Step ◽  
Alternative Type ◽  
The Difference ◽  
Dependent Lineages ◽  
Multidendritic Neurons

The embryonic peripheral nervous system of Drosophila contains two main types of sensory neurons: type I neurons, which innervate external sense organs and chordotonal organs, and type II multidendritic neurons. Here, we analyse the origin of the difference between type I and type II in the case of the neurons that depend on the proneural genes of the achaete-scute complex (ASC). We show that, in Notch- embryos, the type I neurons are missing while type II neurons are produced in excess, indicating that the type I/type II choice relies on Notch-mediated cell communication. In contrast, both type I and type II neurons are absent in numb- embryos and after ubiquitous expression of tramtrack, indicating that the activity of numb and the absence of tramtrack are required to produce both external sense organ and multidendritic neural fates. The analysis of string- embryos reveals that when the precursors are unable to divide they differentiate mostly into type II neurons, indicating that the type II is the default neuronal fate. We also report a new mutant phenotype where the ASC-dependent neurons are converted into type II neurons, providing evidence for the existence of one or more genes required for maintaining the alternative (type I) fate. Our results suggest that the same mechanism of type I/type II specification may operate at a late step of the ASC-dependent lineages, when multidendritic neurons arise as siblings of the external sense organ neurons and, at an early step, when other multidendritic neurons precursors arise as siblings of external sense organ precursors.

Hypothesis Testing in Business Administration

2020 ◽  
Author(s):  
Rand R. Wilcox
Keyword(s):  
Hypothesis Testing ◽  
Empirical Evidence ◽  
Confidence Intervals ◽  
Error Probability ◽  
Type I Error ◽  
Type I ◽  
Type Ii ◽  
Practical Concern ◽  
Type I Error Probability ◽  
The Difference

Hypothesis testing is an approach to statistical inference that is routinely taught and used. It is based on a simple idea: develop some relevant speculation about the population of individuals or things under study and determine whether data provide reasonably strong empirical evidence that the hypothesis is wrong. Consider, for example, two approaches to advertising a product. A study might be conducted to determine whether it is reasonable to assume that both approaches are equally effective. A Type I error is rejecting this speculation when in fact it is true. A Type II error is failing to reject when the speculation is false. A common practice is to test hypotheses with the type I error probability set to 0.05 and to declare that there is a statistically significant result if the hypothesis is rejected. There are various concerns about, limitations to, and criticisms of this approach. One criticism is the use of the term significant. Consider the goal of comparing the means of two populations of individuals. Saying that a result is significant suggests that the difference between the means is large and important. But in the context of hypothesis testing it merely means that there is empirical evidence that the means are not equal. Situations can and do arise where a result is declared significant, but the difference between the means is trivial and unimportant. Indeed, the goal of testing the hypothesis that two means are equal has been criticized based on the argument that surely the means differ at some decimal place. A simple way of dealing with this issue is to reformulate the goal. Rather than testing for equality, determine whether it is reasonable to make a decision about which group has the larger mean. The components of hypothesis-testing techniques can be used to address this issue with the understanding that the goal of testing some hypothesis has been replaced by the goal of determining whether a decision can be made about which group has the larger mean. Another aspect of hypothesis testing that has seen considerable criticism is the notion of a p-value. Suppose some hypothesis is rejected with the Type I error probability set to 0.05. This leaves open the issue of whether the hypothesis would be rejected with Type I error probability set to 0.025 or 0.01. A p-value is the smallest Type I error probability for which the hypothesis is rejected. When comparing means, a p-value reflects the strength of the empirical evidence that a decision can be made about which has the larger mean. A concern about p-values is that they are often misinterpreted. For example, a small p-value does not necessarily mean that a large or important difference exists. Another common mistake is to conclude that if the p-value is close to zero, there is a high probability of rejecting the hypothesis again if the study is replicated. The probability of rejecting again is a function of the extent that the hypothesis is not true, among other things. Because a p-value does not directly reflect the extent the hypothesis is false, it does not provide a good indication of whether a second study will provide evidence to reject it. Confidence intervals are closely related to hypothesis-testing methods. Basically, they are intervals that contain unknown quantities with some specified probability. For example, a goal might be to compute an interval that contains the difference between two population means with probability 0.95. Confidence intervals can be used to determine whether some hypothesis should be rejected. Clearly, confidence intervals provide useful information not provided by testing hypotheses and computing a p-value. But an argument for a p-value is that it provides a perspective on the strength of the empirical evidence that a decision can be made about the relative magnitude of the parameters of interest. For example, to what extent is it reasonable to decide whether the first of two groups has the larger mean? Even if a compelling argument can be made that p-values should be completely abandoned in favor of confidence intervals, there are situations where p-values provide a convenient way of developing reasonably accurate confidence intervals. Another argument against p-values is that because they are misinterpreted by some, they should not be used. But if this argument is accepted, it follows that confidence intervals should be abandoned because they are often misinterpreted as well. Classic hypothesis-testing methods for comparing means and studying associations assume sampling is from a normal distribution. A fundamental issue is whether nonnormality can be a source of practical concern. Based on hundreds of papers published during the last 50 years, the answer is an unequivocal Yes. Granted, there are situations where nonnormality is not a practical concern, but nonnormality can have a substantial negative impact on both Type I and Type II errors. Fortunately, there is a vast literature describing how to deal with known concerns. Results based solely on some hypothesis-testing approach have clear implications about methods aimed at computing confidence intervals. Nonnormal distributions that tend to generate outliers are one source for concern. There are effective methods for dealing with outliers, but technically sound techniques are not obvious based on standard training. Skewed distributions are another concern. The combination of what are called bootstrap methods and robust estimators provides techniques that are particularly effective for dealing with nonnormality and outliers. Classic methods for comparing means and studying associations also assume homoscedasticity. When comparing means, this means that groups are assumed to have the same amount of variance even when the means of the groups differ. Violating this assumption can have serious negative consequences in terms of both Type I and Type II errors, particularly when the normality assumption is violated as well. There is vast literature describing how to deal with this issue in a technically sound manner.

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