scholarly journals Reaction Times and other Skewed Distributions

2020 ◽  
Vol 4 ◽  
Author(s):  
Guillaume A Rousselet ◽  
Rand R Wilcox
Keyword(s):  
Reaction Times ◽  
Small Sample ◽  
Careful Examination ◽  
Shift Function ◽  
Central Tendency ◽  
Skewed Distributions ◽  
Experimental Conditions ◽  
Sample Mean ◽  
Sample Median ◽  
The Mean

To summarise skewed (asymmetric) distributions, such as reaction times, typically the mean or the median are used as measures of central tendency. Using the mean might seem surprising, given that it provides a poor measure of central tendency for skewed distributions, whereas the median provides a better indication of the location of the bulk of the observations. However, the sample median is biased: with small sample sizes, it tends to overestimate the population median. This is not the case for the mean. Based on this observation, Miller (1988) concluded that "sample medians must not be used to compare reaction times across experimental conditions when there are unequal numbers of trials in the conditions". Here we replicate and extend Miller (1988), and demonstrate that his conclusion was ill-advised for several reasons. First, the median's bias can be corrected using a percentile bootstrap bias correction. Second, a careful examination of the sampling distributions reveals that the sample median is median unbiased, whereas the mean is median biased when dealing with skewed distributions. That is, on average the sample mean estimates the population mean, but typically this is not the case. In addition, simulations of false and true positives in various situations show that no method dominates. Crucially, neither the mean nor the median are sufficient or even necessary to compare skewed distributions. Different questions require different methods and it would be unwise to use the mean or the median in all situations. Better tools are available to get a deeper understanding of how distributions differ: we illustrate the hierarchical shift function, a powerful alternative that relies on quantile estimation. All the code and data to reproduce the figures and analyses in the article are available online.

scholarly journals Reaction times and other skewed distributions: problems with the mean and the median

2019 ◽  
Author(s):  
Guillaume A Rousselet ◽  
Rand R. Wilcox
Keyword(s):  
Reaction Times ◽  
Small Sample ◽  
Careful Examination ◽  
Shift Function ◽  
Central Tendency ◽  
Skewed Distributions ◽  
Experimental Conditions ◽  
Sample Mean ◽  
Sample Median ◽  
The Mean

To summarise skewed (asymmetric) distributions, such as reaction times, typically the mean or the median are used as measures of central tendency. Using the mean might seem surprising, given that it provides a poor measure of central tendency for skewed distributions, whereas the median provides a better indication of the location of the bulk of the observations. However, the sample median is biased: with small sample sizes, it tends to overestimate the population median. This is not the case for the mean. Based on this observation, Miller (1988) concluded that ”sample medians must not be used to compare reaction times across experimental conditions when there are unequal numbers of trials in the conditions.” Here we replicate and extend Miller (1988), and demonstrate that his conclusion was ill-advised for several reasons. First, the median’s bias can be corrected using a percentile bootstrap bias correction. Second, a careful examination of the sampling distributions reveals that the sample median is median unbiased, whereas the mean is median biased when dealing with skewed distributions. That is, on average the sample mean estimates the population mean, but typically this is not the case. In addition, simulations of false and true positives in various situations show that no method dominates. Crucially, neither the mean nor the median are sufficient or even necessary to compare skewed distributions. Different questions require different methods and it would be unwise to use the mean or the median in all situations. Better tools are available to get a deeper understanding of how distributions differ: we illustrate the hierarchical shift function, a powerful alternative that relies on quantile estimation. All the code and data to reproduce the figures and analyses in the article are available online.

scholarly journals Reaction times and other skewed distributions: problems with the mean and the median

2018 ◽  
Author(s):  
Guillaume A. Rousselet ◽  
Rand R. Wilcox
Keyword(s):  
Reaction Times ◽  
Small Sample ◽  
Careful Examination ◽  
Central Tendency ◽  
Skewed Distributions ◽  
Experimental Conditions ◽  
Sample Mean ◽  
Sample Median ◽  
The Mean ◽  
Small Sample Sizes

ABSTRACTTo summarise skewed (asymmetric) distributions, such as reaction times, typically the mean or the median are used as measures of central tendency. Using the mean might seem surprising, given that it provides a poor measure of central tendency for skewed distributions, whereas the median provides a better indication of the location of the bulk of the observations. However, the sample median is biased: with small sample sizes, it tends to overestimate the population median. This is not the case for the mean. Based on this observation, Miller (1988) concluded that “sample medians must not be used to compare reaction times across experimental conditions when there are unequal numbers of trials in the conditions.” Here we replicate and extend Miller (1988), and demonstrate that his conclusion was ill-advised for several reasons. First, the median’s bias can be corrected using a percentile bootstrap bias correction. Second, a careful examination of the sampling distributions reveals that the sample median is median unbiased, whereas the mean is median biased when dealing with skewed distributions. That is, on average the sample mean estimates the population mean, but typically this is not the case. In addition, simulations of false and true positives in various situations show that no method dominates. Crucially, neither the mean nor the median are sufficient or even necessary to compare skewed distributions. Different questions require different methods and it would be unwise to use the mean or the median in all situations. Better tools are available to get a deeper understanding of how distributions differ: we illustrate a powerful alternative that relies on quantile estimation. All the code and data to reproduce the figures and analyses in the article are available online.

scholarly journals Another Warning about Median Reaction Time --- Version of 11 Feb 2020

2020 ◽  
Author(s):  
Jeff Miller
Keyword(s):  
Type I Error ◽  
Reaction Times ◽  
Error Rates ◽  
Type I ◽  
Experimental Conditions ◽  
Type I Error Rates ◽  
Correction Technique ◽  
Inflated Type ◽  
The Mean ◽  
Rt Distributions

Contrary to the warning of Miller (1988), Rousselet and Wilcox (2020) argued that it is better to summarize each participant’s single-trial reaction times (RTs) in a given condition with the median than with the mean when comparing the central tendencies of RT distributions across experimental conditions. They acknowledged that median RTs can produce inflated Type I error rates when conditions differ in the number of trials tested, consistent with Miller’s warning, but they showed that the bias responsible for this error rate inflation could be eliminated with a bootstrap bias correction technique. The present simulations extend their analysis by examining the power of bias-corrected medians to detect true experimental effects and by comparing this power with the power of analyses using means and regular medians. Unfortunately, although bias-corrected medians solve the problem of inflated Type I error rates, their power is lower than that of means or regular medians in many realistic situations. In addition, even when conditions do not differ in the number of trials tested, the power of tests (e.g., t-tests) is generally lower using medians rather than means as the summary measures. Thus, the present simulations demonstrate that summary means will often provide the most powerful test for differences between conditions, and they show what aspects of the RT distributions determine the size of the power advantage for means.

scholarly journals Land snails as experimental animals: a study of the variability and distribution of individual weights in Helix aspersa snails born from the same clutch

1990 ◽  
Vol 24 (1) ◽  
pp. 1-4 ◽  
Author(s):  
R. Sanz Sampelayo ◽  
J. Fonolla ◽  
F. Gil Extremera
Keyword(s):  
Normal Distribution ◽  
Growth Curve ◽  
Original Data ◽  
Helix Aspersa ◽  
Land Snails ◽  
Central Tendency ◽  
Experimental Conditions ◽  
Experimental Animals ◽  
Coefficients Of Variation ◽  
The Mean

A study was carried out to examine the distribution of individual weights in Helix aspersa snails, the aims being to establish the best estimate of the ponderal growth and also to obtain a model growth curve. Four groups of 20 snails from the same clutch were analysed and kept under experimental conditions from birth up to 6 months. The variability of their individual weights within groups was studied by calculating the coefficients of variation every 15 days. At the same time, the assumed normal distribution of those weights was being tested. The coefficients of variation increased with age and the assumed normal distribution of individual weights had to be rejected. By means of a log transformation of the original data, a model growth curve was constructed, and was used to assess the possibility of estimating age from weight. We finally reached the conclusion that median weight, rather than the mean, would be a better measure of central tendency to use until it is possible to obtain selected populations. The difficulty of estimating age from weight is emphasized.

scholarly journals Estimating the sample mean and standard deviation from commonly reported quantiles in meta-analysis

2020 ◽  
Vol 29 (9) ◽  
pp. 2520-2537 ◽  
Author(s):  
Sean McGrath ◽  
XiaoFei Zhao ◽  
Russell Steele ◽  
Brett D. Thombs ◽  
Andrea Benedetti ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Meta Analysis ◽  
Outcome Variable ◽  
Sample Mean ◽  
Sample Median ◽  
Common Effect ◽  
The Mean ◽  
Novel Approaches ◽  
Summary Data ◽  
Better Than

Researchers increasingly use meta-analysis to synthesize the results of several studies in order to estimate a common effect. When the outcome variable is continuous, standard meta-analytic approaches assume that the primary studies report the sample mean and standard deviation of the outcome. However, when the outcome is skewed, authors sometimes summarize the data by reporting the sample median and one or both of (i) the minimum and maximum values and (ii) the first and third quartiles, but do not report the mean or standard deviation. To include these studies in meta-analysis, several methods have been developed to estimate the sample mean and standard deviation from the reported summary data. A major limitation of these widely used methods is that they assume that the outcome distribution is normal, which is unlikely to be tenable for studies reporting medians. We propose two novel approaches to estimate the sample mean and standard deviation when data are suspected to be non-normal. Our simulation results and empirical assessments show that the proposed methods often perform better than the existing methods when applied to non-normal data.

Predation by house cats, Felis catus (L.), in Canberra, Australia. II. Factors affecting the amount of prey caught and estimates of the impact on wildlife

1998 ◽  
Vol 25 (5) ◽  
pp. 475 ◽  
Author(s):  
D. G. Barratt
Keyword(s):  
Significant Influence ◽  
Felis Catus ◽  
Potential Prey ◽  
Sample Mean ◽  
Sample Median ◽  
Factors Affecting ◽  
Source Areas ◽  
Residential Developments ◽  
The Mean ◽  
The Impact

Information on the amount of vertebrate prey caught by house cats in Canberra was collected by recording prey deposited at cat owners’ residences over 12 months. The amount of prey taken was not significantly influenced by cat gender, age when neutered, or cat breed. Nor did belling or the number of meals provided per day have a significant influence on the amount of prey caught. The age of the cat and the proportion of nights spent outside explained approximately 11% of the variation in the amount of prey caught by individual cats. In all, 43% of variation in predation on introduced species (predominantly rodents) was explained by distance from potential prey source areas (i.e. rural/grassland habitat) and cat density. The mean number of prey reported per cat over 12 months (10.2) was significantly lower than mean predation per cat per year based on estimates made by cat owners before the prey survey began (23.3). Counts of the amount of prey caught by house cats were highly positively skewed. In all, 70% of cats were observed to catch less than 10 prey over 12 months, but for 6% of cats, more than 50 prey were recorded. Estimates of predation by house cats, particularly extrapolated estimates, should be treated with caution. The total number of prey caught by house cats in Canberra estimated using the sample median was approximately half the estimate based on the sample mean. Predation estimates alone do not prove that prey populations are detrimentally affected, especially in highly disturbed and modified environments such as suburbs. Impacts on native fauna are likely to be most significant in undisturbed habitat adjacent to new residential developments.

Articulatory Behavior Pre and Post Full-Mouth Tooth Extraction and Alveoloplasty

1980 ◽  
Vol 23 (3) ◽  
pp. 630-645 ◽  
Author(s):  
Gerald Zimmermann ◽  
J.A. Scott Kelso ◽  
Larry Lander
Keyword(s):  
Control Subject ◽  
High Speed ◽  
Tooth Extraction ◽  
Kinematic Parameters ◽  
Experimental Conditions ◽  
Mean Values ◽  
Articulatory Movements ◽  
The Mean ◽  
Experimental Subjects ◽  
Normal Speech

High speed cinefluorography was used to track articulatory movements preceding and following full-mouth tooth extraction and alveoloplasty in two subjects. Films also were made of a control subject on two separate days. The purpose of the study was to determine the effects of dramatically altering the structural dimensions of the oral cavity on the kinematic parameters of speech. The results showed that the experimental subjects performed differently pre and postoperatively though the changes were in different directions for the two subjects. Differences in both means and variabilities of kinematic parameters were larger between days for the experimental (operated) subjects than for the control subject. The results for the Control subject also showed significant differences in the mean values of kinematic variables between days though these day-to-day differences could not account for the effects found pre- and postoperatively. The results of the kinematic analysis, particularly the finding that transition time was most stable over the experimental conditions for the operated subjects, are used to speculate about the coordination of normal speech.

Modeling Within-Person Variance in Reaction Time Data of Older Adults

GeroPsych ◽  
2011 ◽  
Vol 24 (4) ◽  
pp. 169-176 ◽  
Author(s):  
Philippe Rast ◽  
Daniel Zimprich
Keyword(s):  
Reaction Time ◽  
Cognitive Aging ◽  
Reaction Times ◽  
Reaction Time Task ◽  
Reaction Time Data ◽  
Scale Model ◽  
Time Data ◽  
Time Task ◽  
The Mean ◽  
Second Wave

In order to model within-person (WP) variance in a reaction time task, we applied a mixed location scale model using 335 participants from the second wave of the Zurich Longitudinal Study on Cognitive Aging. The age of the respondents and the performance in another reaction time task were used to explain individual differences in the WP variance. To account for larger variances due to slower reaction times, we also used the average of the predicted individual reaction time (RT) as a predictor for the WP variability. Here, the WP variability was a function of the mean. At the same time, older participants were more variable and those with better performance in another RT task were more consistent in their responses.

scholarly journals Recovery of Platinum from a Spent Automotive Catalyst through Chloride Leaching and Solvent Extraction

Recycling ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 27
Author(s):  
Ana Méndez ◽  
Carlos A. Nogueira ◽  
Ana Paula Paiva
Keyword(s):  
Solvent Extraction ◽  
Environmental Sustainability ◽  
Catalytic Converter ◽  
Reaction Times ◽  
Model Solution ◽  
Critical Metals ◽  
Experimental Conditions ◽  
Chloride Leaching ◽  
Good Potential ◽  
Hydrometallurgical Treatment

Considering economics and environmental sustainability, recycling of critical metals from end-of-life devices should be a priority. In this work the hydrometallurgical treatment of a spent automotive catalytic converter (SACC) using HCl with CaCl2 as a leaching medium, and solvent extraction (SX) with a thiodiglycolamide derivative, is reported. The aim was to develop a leaching scheme allowing high Pt recoveries and minimizing Al dissolution, facilitating the application of SX. The replacement of part of HCl by CaCl2 in the leaching step is viable, without compromising Pt recovery (in the range 75–85%), as found for the mixture 2 M CaCl2 + 8 M HCl when compared to 11.6 M HCl. All leaching media showed good potential to recover Ce, particularly for higher reaction times and temperatures. Regarding SX, results achieved with a model solution were promising, but SX for Pt separation from the real SACC solution did not work as expected. For the adopted experimental conditions, the tested thiodiglycolamide derivative in toluene revealed a very good loading performance for both Pt and Fe, but Fe removal and Pt stripping from the organic phases after contact with the SACC solution were not successfully accomplished. Hence, the reutilization of the organic solvent needs improvement.

scholarly journals Comparison of Bite Force in Patients After Treatment of Mandibular Fractures With 3-Dimensional Locking Miniplate and Standard Miniplates

2019 ◽  
Vol 1 (1) ◽  
pp. 7-10
Author(s):  
Gaurav Singh ◽  
Madan Mishra ◽  
Amit Gaur ◽  
Dhritiman Pathak
Keyword(s):  
Treatment Strategies ◽  
Bite Force ◽  
Mandibular Fractures ◽  
Time Intervals ◽  
Experimental Conditions ◽  
3 Dimensional ◽  
The Mean ◽  
Group 2 ◽  
Drilling Conditions ◽  
Group 1

Background: Fractures of the mandible can be studied and described in anatomic terms, functional considerations, treatment strategies, and outcome measures. The performance of any fixation system depends on multiple factors including plate adaptation, screw placement, bone quality, drilling conditions, and postoperative patient compliance. Bite force assesses masticatory muscle function under clinical and experimental conditions. Method: 30 patients with isolated, noncomminuted mandibular fractures were randomly divided into two equal groups. Group 1 patients were treated using 3-dimensional locking miniplates and group 2 patients were treated with standard miniplates. The bite forces were recorded at definite time intervals: preoperatively, and second week, sixth week, third month, and sixth month postoperatively. Result: At 6 weeks postoperative, 3 month postoperative, and 6 month postoperative, the mean bite force was found to be significantly higher among group 1 patients as compared to those in group 2 in all the sites. While at 2 week postoperative, the mean bite force was found to be significantly higher in Group 2 as compared to Group 1 at incisor region. Conclusion: The overall results of the present study show better performance in bite force for the 3-dimensional locking miniplate when compared with standard miniplates.

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