scholarly journals Effects of Number of Genetic Marker Alleles, Marker Interval, Degree of Substitution Effect and Paternal Half-sib Family Size on Type I Error Probability in the Test of the Presence of a QTL

1997 ◽  
Vol 68 (10) ◽  
pp. 911-916
Author(s):  
Kenji TOGASHI ◽  
Naoyuki YAMAMOTO ◽  
Osamu SASAKI
Keyword(s):  
Genetic Marker ◽  
Family Size ◽  
Error Probability ◽  
Type I Error ◽  
Substitution Effect ◽  
Degree Of Substitution ◽  
Type I ◽  
Marker Interval ◽  
Type I Error Probability ◽  
Marker Alleles

scholarly journals On the Performances of Trend and Change-Point Detection Methods for Remote Sensing Data

2020 ◽  
Vol 12 (6) ◽  
pp. 1008 ◽  
Author(s):  
Ana Militino ◽  
Mehdi Moradi ◽  
M. Ugarte
Keyword(s):  
Error Probability ◽  
Type I Error ◽  
Remote Sensing Data ◽  
Change Point Detection ◽  
Change Points ◽  
Detection Methods ◽  
Type I ◽  
Power Of The Test ◽  
Type I Error Probability ◽  
Point Detection

Detecting change-points and trends are common tasks in the analysis of remote sensing data. Over the years, many different methods have been proposed for those purposes, including (modified) Mann–Kendall and Cox–Stuart tests for detecting trends; and Pettitt, Buishand range, Buishand U, standard normal homogeneity (Snh), Meanvar, structure change (Strucchange), breaks for additive season and trend (BFAST), and hierarchical divisive (E.divisive) for detecting change-points. In this paper, we describe a simulation study based on including different artificial, abrupt changes at different time-periods of image time series to assess the performances of such methods. The power of the test, type I error probability, and mean absolute error (MAE) were used as performance criteria, although MAE was only calculated for change-point detection methods. The study reveals that if the magnitude of change (or trend slope) is high, and/or the change does not occur in the first or last time-periods, the methods generally have a high power and a low MAE. However, in the presence of temporal autocorrelation, MAE raises, and the probability of introducing false positives increases noticeably. The modified versions of the Mann–Kendall method for autocorrelated data reduce/moderate its type I error probability, but this reduction comes with an important power diminution. In conclusion, taking a trade-off between the power of the test and type I error probability, we conclude that the original Mann–Kendall test is generally the preferable choice. Although Mann–Kendall is not able to identify the time-period of abrupt changes, it is more reliable than other methods when detecting the existence of such changes. Finally, we look for trend/change-points in land surface temperature (LST), day and night, via monthly MODIS images in Navarre, Spain, from January 2001 to December 2018.

scholarly journals Locally adaptive change-point detection (LACPD) with applications to environmental changes

2021 ◽  
Author(s):  
Mehdi Moradi ◽  
Manuel Montesino-SanMartin ◽  
M. Dolores Ugarte ◽  
Ana F. Militino
Keyword(s):  
Time Series ◽  
Change Point ◽  
Error Probability ◽  
Type I Error ◽  
Change Point Detection ◽  
Alternative Methods ◽  
Change Points ◽  
Type I ◽  
Type I Error Probability ◽  
Point Detection

AbstractWe propose an adaptive-sliding-window approach (LACPD) for the problem of change-point detection in a set of time-ordered observations. The proposed method is combined with sub-sampling techniques to compensate for the lack of enough data near the time series’ tails. Through a simulation study, we analyse its behaviour in the presence of an early/middle/late change-point in the mean, and compare its performance with some of the frequently used and recently developed change-point detection methods in terms of power, type I error probability, area under the ROC curves (AUC), absolute bias, variance, and root-mean-square error (RMSE). We conclude that LACPD outperforms other methods by maintaining a low type I error probability. Unlike some other methods, the performance of LACPD does not depend on the time index of change-points, and it generally has lower bias than other alternative methods. Moreover, in terms of variance and RMSE, it outperforms other methods when change-points are close to the time series’ tails, whereas it shows a similar (sometimes slightly poorer) performance as other methods when change-points are close to the middle of time series. Finally, we apply our proposal to two sets of real data: the well-known example of annual flow of the Nile river in Awsan, Egypt, from 1871 to 1970, and a novel remote sensing data application consisting of a 34-year time-series of satellite images of the Normalised Difference Vegetation Index in Wadi As-Sirham valley, Saudi Arabia, from 1986 to 2019. We conclude that LACPD shows a good performance in detecting the presence of a change as well as the time and magnitude of change in real conditions.

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.

Fixed sized samples for type-specific surveillance of human papillomavirus in genital warts

Sexual Health ◽  
2013 ◽  
Vol 10 (1) ◽  
pp. 95
Author(s):  
Edward K. Waters ◽  
Andrew J. Hamilton ◽  
Anthony M. A. Smith ◽  
David J. Philp ◽  
Basil Donovan ◽  
...  
Keyword(s):  
Human Papillomavirus ◽  
Sample Size ◽  
Error Probability ◽  
Type I Error ◽  
Hpv Vaccination ◽  
Genital Warts ◽  
Type I ◽  
Post Vaccination ◽  
Hpv Types ◽  
Type I Error Probability

Surveillance data suggest that human papillomavirus (HPV) vaccination in Australia is reducing the incidence of genital warts. However, existing surveillance measures do not assess the proportion of the remaining cases of warts that are caused by HPV types other than 6 or 11, against which the vaccine has no demonstrated effectiveness. Using computer simulation rather than sample size formulae, we established that genotyping at least 60 warts can accurately test whether the proportion of warts due to HPV types not targeted by the vaccine has increased (Type I error probability ≤0.05, Type II error probability <0.07). Standard formulae for calculating sample size, in contrast, suggest that a sample size of more than 130 would be required for this task, but using these formulae entails making several strong assumptions. Our methods require fewer assumptions and demonstrate that a smaller sample size than anticipated could be used to address the question of what proportion of post-vaccination cases of warts are due to nonvaccine types. In conjunction with indications of incidence and prevalence provided by existing surveillance measures, this could indicate the number of cases of post-vaccination warts due to nonvaccine types and hence whether type replacement is occurring.

Effects of Differential Genotyping Error Rate on the Type I Error Probability of Case-Control Studies

2006 ◽  
Vol 61 (1) ◽  
pp. 55-64 ◽  
Author(s):  
Valentina Moskvina ◽  
Nick Craddock ◽  
Peter Holmans ◽  
Michael J. Owen ◽  
Michael C. O’Donovan
Keyword(s):  
Error Rate ◽  
Error Probability ◽  
Type I Error ◽  
Case Control ◽  
Type I ◽  
Genotyping Error ◽  
Case Control Studies ◽  
Genotyping Error Rate ◽  
Type I Error Probability

Teacher’s Corner: A Note on Interpretation of the Paired-Samples t Test

1997 ◽  
Vol 22 (3) ◽  
pp. 349-360 ◽  
Author(s):  
Donald W. Zimmerman
Keyword(s):  
Error Probability ◽  
Degrees Of Freedom ◽  
Type I Error ◽  
T Test ◽  
Experimental Designs ◽  
Type I ◽  
Significance Level ◽  
Advantages And Disadvantages ◽  
Paired Samples ◽  
Type I Error Probability

Explanations of advantages and disadvantages of paired-samples experimental designs in textbooks in education and psychology frequently overlook the change in the Type I error probability which occurs when an independent-samples t test is performed on correlated observations. This alteration of the significance level can be extreme even if the correlation is small. By comparison, the loss of power of the paired-samples t test on difference scores due to reduction of degrees of freedom, which typically is emphasized, is relatively slight. Although paired-samples designs are appropriate and widely used when there is a natural correspondence or pairing of scores, researchers have not often considered the implications of undetected correlation between supposedly independent samples in the absence of explicit pairing.

scholarly journals Spatial Scan Statistics Adjusted for Multiple Clusters

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Zhenkui Zhang ◽  
Renato Assunção ◽  
Martin Kulldorff
Keyword(s):  
Error Probability ◽  
Type I Error ◽  
Statistical Significance ◽  
Scan Statistics ◽  
Type I ◽  
Spatial Scan Statistic ◽  
Scan Statistic ◽  
Study Region ◽  
Type I Error Probability ◽  
Spatial Scan

The spatial scan statistic is one of the main epidemiological tools to test for the presence of disease clusters in a geographical region. While the statistical significance of the most likely cluster is correctly assessed using the model assumptions, secondary clusters tend to have conservatively highP-values. In this paper, we propose a sequential version of the spatial scan statistic to adjust for the presence of other clusters in the study region. The procedure removes the effect due to the more likely clusters on less significant clusters by sequential deletion of the previously detected clusters. Using the Northeastern United States geography and population in a simulation study, we calculated the type I error probability and the power of this sequential test under different alternative models concerning the locations and sizes of the true clusters. The results show that the type I error probability of our method is close to the nominalαlevel and that for secondary clusters its power is higher than the standard unadjusted scan statistic.

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