The Distribution of the Difference Between the Extreme Observation and the Sample Mean in Samples of n from a Normal Universe

Biometrika ◽  
1935 ◽  
Vol 27 (3/4) ◽  
pp. 466 ◽  
Author(s):  
A. T. McKay
Keyword(s):  
Sample Mean ◽  
The Difference ◽  
Extreme Observation

scholarly journals StaTips Part VIII: Confidence interval for the sample mean

2020 ◽  
Vol 7 (1) ◽  
pp. 2-3
Author(s):  
Giuseppe Perinetti
Keyword(s):  
Confidence Interval ◽  
Small Group ◽  
Statistical Significance ◽  
P Value ◽  
Sample Mean ◽  
Type Population ◽  
The Difference ◽  
Conducting Research

When conducting research on a given type of patients, it is impossible to examine all the existing subjects of that type (population)to derive the true mean of the parameter of interest. More realistically, by the investigation of a small group of subjects (sample) fromthe whole population, researchers can estimate an interval into which the true mean of the population lies. In statistics, such interval isreferred to as confidence interval (CI). The calculation of the CI from a sample mean is simple and gives important information, not onlyregarding the true mean of the population, but also on the statistical significance of the difference between groups being compared. Forthese reasons, the reporting of the CIs is preferred over the p value alone.

Putting applicant faking effects on personality tests into context

2017 ◽  
Vol 32 (6) ◽  
pp. 460-468 ◽  
Author(s):  
Gary N. Burns ◽  
Elizabeth A. Shoda ◽  
Mark A. Roebke
Keyword(s):  
Mathematical Proof ◽  
Computational Simulation ◽  
Effect Sizes ◽  
Personality Testing ◽  
Personality Tests ◽  
Sample Mean ◽  
Content Type ◽  
Applicant Faking ◽  
The Difference ◽  
The Impact

Purpose Estimates of the effects of faking on personality scores typically represent the difference from one sample mean to another sample mean in terms of standard deviations. While this is technically accurate, it does put faking effects into the context of the individuals actually engaging in faking behavior. The purpose of this paper is to address this deficiency. Design/methodology/approach This paper provides a mathematical proof and a computational simulation manipulating faking effect size, prevalence of faking, and the size of the applicant pool. Findings The paper illustrates that reported effects of faking are underestimates of the amount of faking that individual test takers are engaging in. Results provide researchers and practitioners with more accurate estimates of how to interpret faking effects sizes. Practical implications To understand the impact of faking on personality testing, it is important to consider both faking effect sizes as well as the prevalence of faking. Originality/value Researchers and practitioners do not often consider the real implications of faking effect sizes. The current paper presents those results in a new light.

scholarly journals Explorations in statistics: the assumption of normality

2017 ◽  
Vol 41 (3) ◽  
pp. 449-453 ◽  
Author(s):  
Douglas Curran-Everett
Keyword(s):  
Normal Distribution ◽  
T Test ◽  
Theoretical Distribution ◽  
Sample Mean ◽  
Quantile Plots ◽  
The Difference

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This twelfth installment of Explorations in Statistics explores the assumption of normality, an assumption essential to the meaningful interpretation of a t test. Although the data themselves can be consistent with a normal distribution, they need not be. Instead, it is the theoretical distribution of the sample mean or the theoretical distribution of the difference between sample means that must be roughly normal. The most versatile approach to assess normality is to bootstrap the sample mean, the difference between sample means, or t itself. We can then assess whether the distributions of these bootstrap statistics are consistent with a normal distribution by studying their normal quantile plots. If we suspect that an inference we make from a t test may not be justified—if we suspect that the theoretical distribution of the sample mean or the theoretical distribution of the difference between sample means is not normal—then we can use a permutation method to analyze our data.

Parametric Sequential Sampling Based on Multistage Estimation of the Negative Binomial Parameterk

Weed Science ◽  
1996 ◽  
Vol 44 (3) ◽  
pp. 555-559 ◽  
Author(s):  
Gregg A. Johnson ◽  
David A. Mortensen ◽  
Linda J. Young ◽  
Alex R. Martin
Keyword(s):  
Negative Binomial ◽  
Sequential Sampling ◽  
Mean Value ◽  
Sampling Plan ◽  
Seedling Density ◽  
Probability Of Error ◽  
Sample Mean ◽  
Average Value ◽  
The Mean ◽  
The Difference

An intensive survey of two farmer-managed corn and soybean fields in eastern Nebraska was conducted to investigate parametric sequential sampling of weed seedling populations using a multistage procedure to estimatek, of the negative binomial distribution.kis a nonspatial aggregation parameter related to the variance at a given mean value. Mean weed seedling density ranged from 0.18 to 3.11 plants 0.38 m−2(linear meter of crop row) based on 806 sampling locations. The average value ofk, derived from 200 multistage estimation procedures, ranged from 0.17 to 0.32. A sequential sampling plan was developed with the goal of estimating the mean with a coefficient of variation (CV) of 10, 20, 30, and 40% of the sample mean. A sampling plan was also constructed to estimate the mean within a specified distance H of the true mean (H(x̄)= 0.10, 0.50 and 1.0 plants 0.38 m−2) with 80, 85, and 90% confidence. Estimating mean weed seedling density within a specified CV of the true mean CV(x̄) using parametric sequential sampling techniques was superior to estimating the mean within a specified distance (H(x̄)) of the true mean when considering the frequency of sampling and probability of error, especially at intermediatekvalues. At ak: value of 0.32 and 0.25, the difference between the actual CV(x̄) obtained from sampling and the CV(x̄) specified by the sampler was minimal. However, the accuracy of weed seedling density estimates was reduced with decreasingkvalues below 0.25, especially as the specified CV(x̄) increased.

SOCIOECONOMIC STATUS AND BLACK AND WHITE INTELLIGENCE REVISITED

1980 ◽  
Vol 8 (2) ◽  
pp. 233-237 ◽  
Author(s):  
Douglas Tate ◽  
Gail Gibson
Keyword(s):  
Standard Deviation ◽  
Middle Class ◽  
Youth Development ◽  
Black Youth ◽  
Lower Class ◽  
Black Middle Class ◽  
Sample Mean ◽  
Black And White ◽  
Blacks And Whites ◽  
The Difference

The mean average difference previously recorded between blacks and whites on intelligence may be an artifact based upon the differences in education and socioeconomic position of blacks and whites in this country. Previous studies in this area, with a few exceptions, have been comparing lower class blacks with second-third through tenth generation middle class whites. Only recently in this country has a true black middle class emerged that has had access to both education and income. Even though black income nationally is still only 61% of white income, the black middle class income has approached 75% of white income. This increase in disposable income is being invested in youth development. Second generation black youth of middle class status will show many attributes of the American achievement syndrome. The black youth in this study exceeded the white sample mean on the Stanford-Binet and the WISCR. The black mean was 128.63 with a standard deviation of 14.44, while the white mean was 115.75 with a standard deviation of 13.37. The difference was significant at the 0.001 level.

scholarly journals COMPARACION DEL PROMEDIO Y LA MEDIANA COMO ESTIMADORES DE LA MEDIA PARA MUESTRAS NORMALES DEPENDIENDO DEL TAMAÑO DE MUESTRA

2017 ◽  
Vol 23 (2) ◽  
pp. 33
Author(s):  
José W. Camero Jiménez ◽  
Jahaziel G. Ponce Sánchez
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Normal Distribution ◽  
Confidence Intervals ◽  
Hypothesis Tests ◽  
Sample Mean ◽  
Palabras Clave ◽  
The Mean ◽  
The Difference

Actualmente los métodos para estimar la media son los basados en el intervalo de confianza del promedio o media muestral. Este trabajo pretende ayudar a escoger el estimador (promedio o mediana) a usar dependiendo del tamaño de muestra. Para esto se han generado, vía simulación en excel, muestras con distribución normal y sus intervalos de confianza para ambos estimadores, y mediante pruebas de hipótesis para la diferencia de proporciones se demostrará que método es mejor dependiendo del tamaño de muestra. Palabras clave.-Tamaño de muestra, Intervalo de confianza, Promedio, Mediana. ABSTRACTCurrently the methods for estimating the mean are those based on the confidence interval of the average or sample mean. This paper aims to help you choose the estimator (average or median) to use depending on the sample size. For this we have generated, via simulation in EXCEL, samples with normal distribution and confidence intervals for both estimators, and by hypothesis tests for the difference of proportions show that method is better depending on the sample size. Keywords.-Sampling size, Confidence interval, Average, Median.

scholarly journals Assessing balance in outcome regressions

2017 ◽  
Author(s):  
Frank Popham ◽  
Alastair Leyland
Keyword(s):  
Matrix Representation ◽  
Causal Effect ◽  
Inverse Probability Weighting ◽  
Probability Weighting ◽  
Sample Mean ◽  
Inverse Probability ◽  
Inverse Probability Weight ◽  
Probability Weight ◽  
The Difference ◽  
Confounder Adjustment

An outcome regression controlling for observed confounders remains a popular way to assess the causal effect of an exposure in epidemiology, despite more modern causal techniques for adjusting for observed confounders, such as inverse probability weighting. A feature of inverse probability weighting is that checking balance of confounders in the control and exposure groups after confounder adjustment is simple. However, researchers using outcome regressions commonly do not check confounder balance after controlling for confounders. Although outcome regressions will balance any confounder specified in the model, the confounder value the model balances at is not transparent. We show that a matrix representation of an outcome regression reveals that an outcome regression includes a weight similar to an inverse probability weight. We also show that outcome regressions may not be balancing at the sample mean of the confounders particularly if interactions are not included with the exposure, which is typically the case in outcome regressions. Finally, we show that the coefficient of the exposure in an outcome regression is simply the difference between two weighted counterfactuals. Thus, there is an important connection between traditional outcome regression and modern causal techniques.

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