Inferential statistics
Louis Cohen, Lawrence Manion, Keith Morrison in Research Methods in Education, 2017
To calculate the z-score we subtract the mean from the raw score and divide that answer by the standard deviation. The formula is thus: For example, if the raw (unadjusted) score is 15, the mean is 10 and the standard deviation is 4, then the standardized score is (15–10)/4 = (5 ÷ 4) = 1.25. Here the z-score tells us that the person’s score is +1.25 standard deviations above the mean. However, we do not know whether this is a good score, a bad score, or, indeed, what it means. We need to see how this compares with other scores on the same distribution. Figure 42.5 plots the standardized scores on the normal curve of distribution, with the mean score of 0 (zero) and the standard deviation of 1, and marks the score of +1.25 on that diagram.
COVID-19 Spatiotemporal Hotspots and Prediction Based on Wavelet and Neural Network
Abbas Rajabifard, Greg Foliente, Daniel Paez in COVID-19 Pandemic, Geospatial Information, and Community Resilience, 2021
Network Common Data Form (NetCDF) is a file format to store multi-dimensional scientific data such as temperature, humidity, disease, and crime. The NetCDF cube is generated using the COVID-19 x, y, and time data as x, y, and z axes. It summarizes a collection of points into a NetCDF by aggregating them into space-time bins. The Mann-Kendall p-values and z-scores show the statistical significance of the trend in a hot spot (spatial clusters of high values) or cold spot (spatial clusters of low values) at a location. A positive or negative z-score indicates an upward or downward trend respectively [9, 27]. Then, the pattern in the spatiotemporal data was identified with Getis-Ord Gi* statistic based on neighborhood distance and neighborhood time step. The Getis-Ord Gi* statistic is calculated for each bin as follows [28, 29]:
Statistics for Genomics
Altuna Akalin in Computational Genomics with R, 2020
Oftentimes, we do not need the exact probability of a value, but we need the probability of observing a value larger or smaller than a critical value or reference point. For example, we might want to know the probability of X being smaller than or equal to -2 for a normal distribution with mean 0 and standard deviation 2: . In this case, what we want is the area under the curve shaded in dark blue. To be able to do that, we need to integrate the probability density function but we will usually let software do that. Traditionally, one calculates a Z-score which is simply , and corresponds to how many standard deviations you are away from the mean. This is also called “standardization”, the corresponding value is distributed in “standard normal distribution” where . After calculating the Z-score, we can look up the area under the curve for the left and right sides of the Z-score in a table, but again, we use software for that. The tables are outdated when you can use a computer.
Feedback to support examiners’ understanding of the standard-setting process and the performance of students: AMEE Guide No. 145
Published in Medical Teacher, 2022
Mohsen Tavakol, Brigitte E. Scammell, Angela P. Wetzel
A simple feedback approach employs bar charts to demonstrate examiner performance. In this approach, examiners are compared with each other using a statistic called a standard score or z score. The z score indicates how many standard deviations the score is from the mean of a particular distribution. If examiners’ scores are converted to z score, we can compare them with each other and see which examiner rated ‘dovish’ or ‘hawkish’ across all stations. The higher the z score, the more extreme the score relative to others. Therefore, a z score of 0.5, being close to the mean, indicates that the assessor was not particularly ‘dovish’ or ‘hawkish’. Suppose a standard score is −2 on the whole distribution. In that case, this indicates the examiner scored −2 standard deviations below the mean and is likely to be harsh or ‘hawkish’ compared to the average examiner. If a standard score is larger than 2 this shows the examiner is lenient or ‘dovish’. Setting a standard score larger than 2 or less than −2 as the threshold is an arbitrary approach. However, it should be noted, when the scores are normally distributed, it is exceptional to get a standard score greater than +3 or less than −3. When we convert the examiners’ scores to z scores, we can draw bar charts for the z scores. As shown in Figure 9, examiner 10’s scores appear below the −2 z score, but no scores appeared above the +2 z score. Using two standard deviations above or below the mean as the threshold may suggest little ‘dove or hawk’ effect on students’ scores. For more information on z scores, readers can refer elsewhere (Tavakol and Pinner 2018).
Investigation of the validity and reliability of the L test in children with cerebral palsy
Published in Physiotherapy Theory and Practice, 2022
Sebahat Yaprak Cetin, Suat Erel
Standard error measure (SEM) was applied to evaluate changes in individual scores in repeated measurements. SEM was also used to determine the variability around the mean measurement and to calculate a confidence interval. The confidence interval of 95% is frequently used in health-related studies (Glantz, 2012). The z score is used in SEM and confidence interval calculations. The z-score reflects the location of a data point as the number of standard deviations from the mean. At a 95% confidence interval, the z score was 1.96 (Altman and Bland, 2005). The MDC value was used in the interpretation of the results to determine whether a change between repeated tests was a random change or a real change in performance. In practical terms, MDC values make it easier for researchers and clinicians to determine when a person actually changes their physiological gait performance in situations such as experimental conditions, natural changes (aging), surgery, or rehabilitation interventions (Haley and Fragala-Pinkham, 2006). SEM was calculated according to the formula below (1) (Weir, 2005) and then minimal detectable change at 95% confidence interval was calculated (2): standard error of measurement = [standard deviation at first assessment] x sqrt (1- intra-class correlation coefficient)minimal detectable change = [standard error of measurement] x 1.96x sqrt
Association of dietary inflammatory index and leukocyte telomere length with mild cognitive impairment in Chinese older adults
Published in Nutritional Neuroscience, 2023
Qian Liu, Dongtao Zhou, Huilian Duan, Yun Zhu, Yue Du, Changqing Sun, Hongyan Lin, Mengdi Jin, Jingzhu Fu, Yuxia Gao, Fei Ma, Yongjie Chen, Meilin Zhang, Guowei Huang
The details of the DII were available elsewhere [9]. Briefly, the dietary data for each study participant was first linked to the regionally representative global database of dietary surveys from 11 countries for each of the 45 parameters (i.e. foods, nutrients, and other food constituents). This global database provided a robust estimate of a mean and standard deviation for each of the food parameters considered [9]. A z-score was derived by subtracting the ‘standard global mean’ from the amount reported and then dividing this value by the standard deviation. This value was then converted to a centered percentile score, which was then multiplied by the respective food parameter inflammatory effect score (derived from a literature review and scoring of 1943 ‘qualified’ articles) to obtain the subject’s food parameter-specific DII score. All of the food parameter-specific DII scores were then summed to create an overall DII score for each participant in our study. In the current study, we calculated the DII score based on 22 available food parameters, which were as follow: carbohydrate; protein; total fat; saturated fatty acids; mono-unsaturated fatty acids; polyunsaturated fatty acids; fiber; cholesterol; niacin; thiamine; riboflavin; folate; vitamin A; β-Carotene; vitamin C; vitamin E; iron; magnesium; selenium; zinc; isoflavones and anthocyanidins. To adjust for total energy intake, we calculated the energy-adjusted version of the DII per 1000 calories of food consumed.
Related Knowledge Centers
- Standard Deviation
- Normalization
- Sampling
- T-Statistic
- Expected Value
- Sample Mean & Covariance
- Studentized Residual