Introduction
Gueorguieva Ralitza in Statistical Methods in Psychiatry and Related Fields, 2017
Variability of observations around the mean from a simple random sample is described by the variance or standard deviation of the observations (see Section 1.7). The sample standard deviation is often preferable as it provides a measure of variability that is evaluated in the same units as the mean. In repeated measures situations with longitudinal data, often the variability of the response at one particular time point differs from the variability at another, in which case it makes sense to estimate separate variances in order to assess data spread at individual time points. However, in some situations it may be reasonable to assume that the variances on all repeated occasions are the same. In this case, a better statistical estimate of the common variance can be obtained by pooling information from all occasions. Examples of both scenarios are considered in Chapter 2.
Common Statistical Issues in Ophthalmic Research
Ching-Yu Cheng, Tien Yin Wong in Ophthalmic Epidemiology, 2022
A measure of variability that is frequently used when describing data is the standard deviation. This is typically abbreviated to sd. Standard deviations are often used because continuous data often follow a normal distribution and if this is the case then statistical theory can be used to demonstrate that 95% of the data will lie between the mean – 1.96*sd and the mean + 1.96*sd. A value which sounds similar to the sd is the standard error, which may be abbreviated to se. The standard error is not the same as the standard deviation. The standard error is used to reflect the uncertainty about a population parameter (such as the mean) and its dependency on the sample size whilst the standard deviation informs us about the spread of data. One of the reasons that the standard error might be chosen is that it is always smaller than the standard deviation – its use might therefore suggest less variability amongst measurements. If previous researchers have reported the se then adopting the sd for your paper might suggest to reviewers who are unware of the misuse of standard errors that your data have more variability and hence are less robust. A particular challenge is faced when researchers have inadvertently labeled standard errors standard deviations because they simply assume that error is another term for deviation and that the two are identical. This is an example of the challenges presented when terms have a special meaning within statistics that they may not have outside of statistics.
Numerical Summary Measures
Marcello Pagano, Kimberlee Gauvreau in Principles of Biostatistics, 2018
In practice, the standard deviation is used more frequently than the variance. This is primarily because the standard deviation has the same units of measurement as the mean, rather than squared units. In a comparison of two groups of data, the group with the smaller standard deviation has the more homogeneous observations; the group with the larger standard deviation exhibits a greater amount of variability. The actual magnitude of the standard deviation depends on the values in the data set—what is large for one group of data may be small for another. In addition, because the standard deviation has units of measurement, it is meaningless to compare standard deviations for two unrelated quantities. Together, the mean and the standard deviation of a set of data can be used to summarize the characteristics of the entire distribution of values. We shall see how this works in Section 3.4.
Selection of preferred thermal environment and cold-avoidance responses in rats rely on signals transduced by the dorsal portion of the lateral funiculus of the spinal cord
Published in Temperature, 2023
Robson C.L. Vizin, Maria C. Almeida, Renato N. Soriano, Andrej A. Romanovsky
The effects of bilateral DLF transection on the spontaneous innate behavior of selecting Tpr were studied in the thermogradient apparatus over a 24-h period. While the Tpr and Tc dynamics in funiculotomized rats were similar to those in sham-operated rats (Figure 2, Table 1), there was a notable difference. The fluctuations of Tpr were markedly greater in funiculotomized rats than in sham-operated controls, especially during the light (inactive) phase of the diurnal cycle (Figure 2, Table 1). Furthermore, in funiculotomized rats, the changes at the effector level (greater fluctuations in Tpr) translated into the greater amplitude of Tc fluctuations and greater Tc variability (as measured by standard deviation) during the light phase (Table 1). Standard deviation is a measure of data dispersion, or variability, and is often used as such in the thermophysiological literature (see, e.g., Ref. [34]). The wider fluctuations in both Tpr and Tc suggest that funiculotomized rats were less sensitive to environmental thermal changes, and that their behavioral thermoregulation was less precise.
Efficacy of non-surgical treatments for androgenetic alopecia in men and women: a systematic review with network meta-analyses, and an assessment of evidence quality
Published in Journal of Dermatological Treatment, 2022
Aditya K. Gupta, Mary A. Bamimore, Kelly A. Foley
Our point estimate of interest was mean change in hair count from baseline, in units of hairs per square centimeter (hairs/cm2), and our measure of variability was the standard deviation (±SD). For studies that did not directly provide this point estimate (nor its standard deviation), we used various techniques to estimate them. When the mean difference was not directly provided, baseline and follow-up values of mean hair count, sample size and standard deviation were used to compute the mean change in hair count from baseline (±SD); the difference was estimated with a two-sample t-test in the NCSS statistical software (15). When the standard deviation was not directly provided, it was estimated using the range rule which states that the value of the standard deviation is approximately equivalent to: the quotient of the absolute difference, between the minimum and maximum, divided by 4 (16). When standard error of the mean was provided, the standard deviation was computed by multiplying the square root of sample size with the standard error. When the 95% confidence interval of the mean was provided, the standard deviation was estimated by applying the following equation (17):
Identification of technical analysis patterns with smoothing splines for bitcoin prices
Published in Journal of Applied Statistics, 2019
Nikolay Miller, Yiming Yang, Bruce Sun, Guoyi Zhang
Assuming that we enter trades immediately after identifying a pattern, the closing price is therefore also used as the price to enter a trade. This is a reasonable assumption because of high liquidity and market activity on cryptocurrency exchanges. If a pattern is identified by 35 min data in a particular window, we simulate entering a trade with different holding period, say 1, 2, 3, 4, 5, 10, 15, 20, 25 and 30 min. Our goal is to identify the best holding period for the particular pattern. If a pattern is not identified in a window, we will move to another window fitting. For each pattern identified with different holding period, mean return and sample standard deviation are computed. For example, HS pattern has been identified in 3269 windows (refer to Table 1). Consider a holding period of 20 min, mean return is calculated by the average of these 3269 returns after entering a trade and hold for 20 min. Similarly, sample standard deviation is calculated by standard deviation of these 3269 returns.
Related Knowledge Centers
- Margin of Error
- Statistical Dispersion
- Expected Value
- Sampling
- Margin of Error
- Statistical Significance
- Average
- Height
- Sample Mean & Covariance
- Unbiased Estimation of Standard Deviation
- Accuracy & Precision