No abstract available.
Normal Distribution*

No abstract available.
Normal Distribution*

Most parametric tests start with the basic assumption on the distribution of populations. The conditions required to conduct the t-test include the measured values in ratio scale or interval scale, simple random extraction, normal distribution of data, appropriate sample size, and homogeneity of variance. The normality test is a kind of hypothesis test which has Type I and II errors, similar to the other hypothesis tests. It means that the sample size must influence the power of the normality test and its reliability. It is hard to find an established sample size for satisfying the power of the normality test. In the current article, the relationships between normality, power, and sample size were discussed. As the sample size decreased in the normality test, sufficient power was not guaranteed even with the same significance level. In the independent t-test, the change in power according to sample size and sample size ratio between groups was observed. When the sample size of one group was fixed and that of another group increased, power increased to some extent. However, it was not more efficient than increasing the sample sizes of both groups equally. To ensure the power in the normality test, sufficient sample size is required. The power is maximized when the sample size ratio between two groups is 1 : 1.
Biostatistics ; Normal Distribution ; Sample Size

According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ², distribute normally with mean, µ, and variance, σ²/n. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding.
Mathematical Concepts ; Normal Distribution ; Statistical Distributions

Humans ; Noise, Occupational ; Normal Distribution ; Textiles

In data analysis, given that various statistical methods assume that the distribution of the population data is normal distribution, it is essential to check and test whether or not the data satisfy the normality requirement. Although the analytical methods vary depending on whether or not the normality is satisfied, inconsistent results might be obtained depending on the analysis method used. In many clinical research papers, the results are presented and interpreted without checking or testing normality. According to the central limit theorem, the distribution of the sample mean satisfies the normal distribution when the number of samples is above 30. However, in many clinical studies, due to cost and time restrictions during data collection, the number of samples is frequently lower than 30. In this case, a proper statistical analysis method is required to determine whether or not the normality is satisfied by performing a normality test. In this regard, this paper discusses the normality check, several methods of normality test, and several statistical analysis methods with or without normality checks.
Data Collection ; Methods ; Normal Distribution ; Statistics as Topic

BACKGROUND: Our aim was to set reference intervals of healthy adults using Beckman Coulter LH 750 by gender and age. METHODS: The specimens were obtained from a total of 705 healthy adults (male 484, female 221), who took part in annual health-check at Chungnam National University Hospital, analyzed in total 22 parameters and compared using SPSS V10.0 program. RESULTS: Totally 16 parameters showed the Gaussian distribution with 12 in parametric method and 4 in logarithmically transformed parametric method. All acquired reference intervals were showed in Table 3, 4, 5 and 6. There were statistical significances between genders in RBC, Hgb, Hct, MCV, MCH, WBC, EO%, LY#, MO#, EO#, MPV, PDW (P<0.001), BA% (P=0.001), NE% (P=0.016), BA# (P=0.019), MO% (P=0.021) and NE# (P=0.039), between age decades in RBC, Hgb, Hct, MCV, MCH, NE%, LY% (P<0.001), LY# (P=0.002), EO%, NE# (P=0.003) and Pct (P=0.033) as well as between genders and age decades in RBC, Hct (P=0.001), Hgb (P=0.004), LY# (P=0.005), Plt (P=0.014) and MO% (P=0.017). CONCLUSIONS: This study suggested that the reference intervals of RBC and Hgb ought to be set by both genders and age decades, WBC by gender and the others by total study populations. Moreover, it need to be set the reference intervals by each laboratory for itself and to be monitored with periodic review.
Adult* ; Cell Count* ; Chungcheongnam-do ; Female ; Humans ; Normal Distribution

In statistic tests, the probability distribution of the statistics is important. When samples are drawn from population N (micro, sigma2) with a sample size of n, the distribution of the sample mean X should be a normal distribution N (micro, sigma2/n). Under the null hypothesis micro = micro0, the distribution of statistics z=X-micro0/sigma/radical(n) should be standardized as a normal distribution. When the variance of the population is not known, replacement with the sample variance s2 is possible. In this case, the statistics X-micro0/s/radical(n) follows a t distribution (n-1 degrees of freedom). An independent-group t test can be carried out for a comparison of means between two independent groups, with a paired t test for paired data. As the t test is a parametric test, samples should meet certain preconditions, such as normality, equal variances and independence.
Biostatistics ; Matched-Pair Analysis ; Normal Distribution ; Sample Size

BACKGROUND: The reference values of laboratory should review regularly to maintain good quality of practice. This is the second report of studies on reference values of Korea Association of Health Promotion (KAHP). The first one was reported in 2002 in Journal of Laboratory Medicine and Quality Assurance in Korea. The aim of this study is to know the changes of reference values for the past five years. METHODS: The way to analyze the data this time was essentially the same as the previous one (Indirect Method). The data from January to December, 2007 were collected. They totalled 5,133,327 test results from approximately 140 thousands individuals who visited for health checkup. The data were statistically analyzed with Minitab version 15.1.20.0 for Gaussian distribution using Anderson-Darling test. The trimming process repeated for the outliers, the results lying outside of +/-3SD, and as much as four times in certain test items, though, none of the tests showed Gaussian distribution. Subsequently, the reference values of most tests were defined in the ranges from the point of lowest 2.5% to the point of highest 97.5% and others were those, below 95 percentiles according to CLSI C28-A3 guideline. RESULTS: The reference ranges of 56 test items were either set as before or adjusted with new values, and compared. CONCLUSIONS: Comparing to the previous reference values (2002), the tests for liver function showed the lower upper values and the tests for diabetes and lipids showed higher upper values. Others were changed minimally with no significance.
Deception ; Health Promotion ; Korea ; Liver ; Normal Distribution ; Reference Values

Heart sound segmentation is a key step before heart sound classification. It refers to the processing of the acquired heart sound signal that separates the cardiac cycle into systolic and diastolic, etc. To solve the accuracy limitation of heart sound segmentation without relying on electrocardiogram, an algorithm based on the duration hidden Markov model (DHMM) was proposed. Firstly, the heart sound samples were positionally labeled. Then autocorrelation estimation method was used to estimate cardiac cycle duration, and Gaussian mixture distribution was used to model the duration of sample-state. Next, the hidden Markov model (HMM) was optimized in the training set and the DHMM was established. Finally, the Viterbi algorithm was used to track back the state of heart sounds to obtain S
Algorithms ; Electrocardiography ; Heart Sounds ; Markov Chains ; Normal Distribution