Calculate the standard deviation of the binomial distribution related to Aarav's study. We proofread: The Scribbr Plagiarism Checker is powered by elements of Turnitins Similarity Checker, namely the plagiarism detection software and the Internet Archive and Premium Scholarly Publications content databases. Reduce measurement error by increasing the precision and accuracy of your measurement devices and procedures, Use a one-tailed test instead of a two-tailed test for, Does the number describe a whole, complete. 11.4 Find the standard error and 95% confidence interval for the slope, Womens, childrens & adolescents health, North Petherton Surgery: GP Opportunity (up to 8 sessions) - North Petherton Surgery, Meadows Surgery: GP Opportunity (up to 8 sessions) - The Meadows Surgery, Ilminster, Bruton Surgery: GP Opportunity (8 sessions) - Bruton Surgery, Government of Jersey: Staff Grade in Trauma & Orthopaedics. The symbol for Standard Deviation is (the Greek letter sigma). To project the line at either end to extrapolate is always risky because the relationship between x and y may change or some kind of cut off point may exist. You can use the qt() function to find the critical value of t in R. The function gives the critical value of t for the one-tailed test. Elementary statistics formulas | Statistics formulas such as mean median mode, variance, and standard deviation formulas are given here in accordance with the number of observations There is a significant difference between the observed and expected genotypic frequencies (p < .05). where the tstatistic from has 13 degrees of freedom, and is equal to 2.160. l.033 2.160 x 0.18055 to l.033 + 2.160 x 0.18055 = 0.643 to 1.422. The Pearson correlation coefficient (r) is the most common way of measuring a linear correlation. Testing the effects of feed type (type A, B, or C) and barn crowding (not crowded, somewhat crowded, very crowded) on the final weight of chickens in a commercial farming operation. The word correlation is used in everyday life to denote some form of association. Standard deviation and Mean both the term used in statistics. If you are only testing for a difference between two groups, use a t-test instead. Missing data are important because, depending on the type, they can sometimes bias your results. Using the sample we got: Sample Mean = 6.5, Sample Standard Deviation = 3.619 Our Sample Mean was wrong by 7%, and our Sample Standard Deviation was wrong by 21%. Random Integer Generator. If your variables are in columns A and B, then click any blank cell and type PEARSON(A:A,B:B). In the formula above (the greek letter "mu") is the mean of all our values 9+2+5+4+12+7+8+11+9+3+7+4+12+5+4+10+9+6+9+4 Together with the mean, standard deviation can tell us a lot about the data, and the units can also help us to understand the data. The Akaike information criterion is calculated from the maximum log-likelihood of the model and the number of parameters (K) used to reach that likelihood. If the bars roughly follow a symmetrical bell or hill shape, like the example below, then the distribution is approximately normally distributed. Russell MAH, Cole PY, Idle MS, Adams L. Carbon monoxide yields of cigarettes and their relation to nicotine yield and type of filter. Follow Email Archive . Standard deviation is calculated based on the mean. A paired t-test is used to compare a single population before and after some experimental intervention or at two different points in time (for example, measuring student performance on a test before and after being taught the material). Now you know all about the units for standard deviation and how they relate to the units for mean, variance, range, and the data values themselves. 5 . The handy Sigma Notation says to sum up as many terms as we want: We want to add up all the values from 1 to N, where N=20 in our case because there are 20 values: Which means: Sum all values from (x1-7)2 to (xN-7)2. The t-score is the test statistic used in t-tests and regression tests. Norsk konomi preges av lav arbeidsledighet, hy konsumprisvekst, fallende boligpriser og kende renter. What does it mean if my confidence interval includes zero? The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship. Real gross domestic product (GDP) increased at an annual rate of 2.9 percent in the third quarter of 2022, in contrast to a decrease of 0.6 percent in the second quarter. Variance has units that are the square of the units for standard deviation. Most values cluster around a central region, with values tapering off as they go further away from the center. The test should not be used for comparing two methods of measuring the same quantity, such as two methods of measuring peak expiratory flow rate. where d is the difference in the ranks of the two variables for a given individual. Statistical significance is arbitrary it depends on the threshold, or alpha value, chosen by the researcher. Then for each number: subtract the Mean and square the result. The geometric mean is often reported for financial indices and population growth rates. The units can be linear (such as for lengths), squared (such as for areas), or cubed (such as for volumes). Standard deviation is a measure of volatility of the fund's performance over a period of time. NFL Week 13 December 05, 3:41 pm ET 1. 2022 - EDUCBA. However, in statistical terms we use correlation to denote association between two quantitative variables. Other outliers are problematic and should be removed because they represent measurement errors, data entry or processing errors, or poor sampling. If you converted all of the data values to miles per hour (multiply meters per second by 2.237 to get miles per hour), then the variance would be given in terms of miles squared per hour squared (miles2/hour2). Relative Standard deviation is derived by multiplying Standard Deviation by 100 and dividing the result by a groups average. The first of these is its distance above the baseline; the second is its slope. What are the main assumptions of statistical tests? 3 . What is the difference between a one-sample t-test and a paired t-test? This means that your results only have a 5% chance of occurring, or less, if the null hypothesis is actually true. If your dependent variable is in column A and your independent variable is in column B, then click any blank cell and type RSQ(A:A,B:B). A p-value, or probability value, is a number describing how likely it is that your data would have occurred under the null hypothesis of your statistical test. The symbols also change to reflect that we are working on a sample instead of the whole population: But they do not affect the calculations. Why is the t distribution also called Students t distribution? The 3 main types of descriptive statistics concern the frequency distribution, central tendency, and variability of a dataset. The data are given in table 11.1 and the scatter diagram shown in figure 11.2 Each dot represents one child, and it is placed at the point corresponding to the measurement of the height (horizontal axis) and the dead space (vertical axis). THE CERTIFICATION NAMES ARE THE TRADEMARKS OF THEIR RESPECTIVE OWNERS. What is the difference between skewness and kurtosis? You can use the PEARSON() function to calculate the Pearson correlation coefficient in Excel. You can use the CHISQ.TEST() function to perform a chi-square test of independence in Excel. In a well-designed study, the statistical hypotheses correspond logically to the research hypothesis. A statistically powerful test is more likely to reject a false negative (a Type II error). The relationship can be represented by a simple equation called the regression equation. Your choice of t-test depends on whether you are studying one group or two groups, and whether you care about the direction of the difference in group means. By signing up, you agree to our Terms of Use and Privacy Policy. ), the calculated standard deviation will have units. Cale Clinton. That the relationship between the two variables is linear. A chi-square distribution is a continuous probability distribution. I hope you found this article helpful. Whats the difference between a point estimate and an interval estimate? 3 These principles are set out in the ILO fundamental Conventions, No. The standard deviation reflects variability within a sample, while the standard error estimates the variability across samples of a population. If it truly had a Z-score of 103.333, it would be 103 standard deviations above the mean which is remarkably far out in the tail of the distribution! Both measures reflect variability in a distribution, but their units differ: Although the units of variance are harder to intuitively understand, variance is important in statistical tests. The AIC function is 2K 2(log-likelihood). Standard deviation vs mean both the tool used for statistical valuation of the stock price, both have their own importance in the field of finance. Both variables should be quantitative. If you converted all of the data values to square feet (multiply square yards by 32 = 9 to get square feet), then the variance would be given in terms of feet4. P-values are calculated from the null distribution of the test statistic. The formula for standard deviation below suggests how the squared and square root (radical) cancel each other out. To calculate standard deviation from variance, take the square root. The line representing the equation is shown superimposed on the scatter diagram of the data in figure 11.2. How to Calculate Variance from Standard Deviation? How do I find a chi-square critical value in Excel? For measuring the volatility of the fund. Want to contact us directly? A one-sample t-test is used to compare a single population to a standard value (for example, to determine whether the average lifespan of a specific town is different from the country average). The most common effect sizes are Cohens d and Pearsons r. Cohens d measures the size of the difference between two groups while Pearsons r measures the strength of the relationship between two variables. We have taken examples and guidelines from Ablebits.com We already have to hand all of the terms in this expression. Whats the difference between statistical and practical significance? What does it mean? If you know or have estimates for any three of these, you can calculate the fourth component. You can use the QUARTILE() function to find quartiles in Excel. There are two steps to calculating the geometric mean: Before calculating the geometric mean, note that: The arithmetic mean is the most commonly used type of mean and is often referred to simply as the mean. While the arithmetic mean is based on adding and dividing values, the geometric mean multiplies and finds the root of values. A histogram is an effective way to tell if a frequency distribution appears to have a normal distribution. In this context regression (the term is a historical anomaly) simply means that the average value of y is a function of x, that is, it changes with x. Its often simply called the mean or the average. Statistical methods for assessing agreement between two methods of clinical measurement. Figure 11.3 Regression line drawn on scatter diagram relating height and pulmonaiy anatomical dead space in 15 children. Find a distribution that matches the shape of your data and use that distribution to calculate the confidence interval. It takes two arguments, CHISQ.TEST(observed_range, expected_range), and returns the p value. Different test statistics are used in different statistical tests. Correlation coefficients always range between -1 and 1. From the formula it should be clear that with even with a very weak relationship (say r = 0.1) we would get a significant result with a large enough sample (say n over 1000). KPI-JAE steg 5,7 prosent samme periode. Here is the probability of success and the function denotes the discrete probability distribution of the number of successes in a sequence of independent experiments, and is the "floor" under , i.e. ALL RIGHTS RESERVED. is the residual standard deviation, given by: This can be shown to be algebraically equal to. In any dataset, theres usually some missing data. The primary difference between std deviation and variance is that standard deviation is expressed in the same units as the mean of data, whereas the variance is expressed in squared units.. What is Variance and Standard Deviation? Lets take an example to understand the calculation of Relative Standard Deviation in a better manner. For example, = 0.748 floods per year. Applying equation 11.1, we have: Entering table B at 15 2 = 13 degrees of freedom we find that at t = 5.72, P < 0.001 so the correlation coefficient may be regarded as highly significant. 6 . Its use in this way appears to be a common mistake, with a significant result being interpreted as meaning that one method is equivalent to the other. Standard deviation is used to measure the volatility of a stock. The direction in which the line slopes depends on whether the correlation is positive or negative. Se pressekonferanse for Konjunkturtendensene. Some variables have fixed levels. To find the sample standard deviation, take the following steps: To find the population standard deviation, the process is very similar to the one we used for finding samples standard deviation. For example, the probability of a coin landing on heads is .5, meaning that if you flip the coin an infinite number of times, it will land on heads half the time. While interval and ratio data can both be categorized, ranked, and have equal spacing between adjacent values, only ratio scales have a true zero. In this article, well talk about the units for standard deviation and how they are determined. Within each category, there are many types of probability distributions. Whats the difference between relative frequency and probability? No matter what quantity we are measuring in our data (height, weight, length, width, time, day length, etc. a mean or a proportion) and on the distribution of your data. In the Kelvin scale, a ratio scale, zero represents a total lack of thermal energy. If you want the critical value of t for a two-tailed test, divide the significance level by two. The standard deviation is the average amount of variability in your data set. As a further example, a plot of monthly deaths from heart disease against monthly sales of ice cream would show a negative association. There are various analytics and statistics that prevails in the world of investment followed by a return from a specific fund managed by different fund houses. The 2 value is greater than the critical value, so we reject the null hypothesis that the population of offspring have an equal probability of inheriting all possible genotypic combinations. This is the part of the formula that says: So what is xi ? 55.8. The alpha value, or the threshold for statistical significance, is arbitrary which value you use depends on your field of study. Because the range formula subtracts the lowest number from the highest number, the range is always zero or a positive number. What is the definition of the Pearson correlation coefficient? Missing at random (MAR) data are not randomly distributed but they are accounted for by other observed variables. For small populations, data can be collected from the whole population and summarized in parameters. To calculate standard deviation of a data set, first calculate the variance and then the square root of that. This means your results may not be generalizable outside of your study because your data come from an unrepresentative sample. In statistics, a Type I error means rejecting the null hypothesis when its actually true, while a Type II error means failing to reject the null hypothesis when its actually false. (3,4 )This is the most versatile of statistical methods and can be used in many situations. The mode is the only measure you can use for nominal or categorical data that cant be ordered. You may also have a look at the following articles to learn more. Complete absence of correlation is represented by 0. A t-test is a statistical test that compares the means of two samples. It is the simplest measure of variability. Having obtained the regression equation, calculate the residuals. 7 . Variance and standard deviation in mathematics can be determined by employing the mean of a group of numbers in question. If you converted all of the data values to miles per hour squared (multiply meters per second squared by 8053 to get miles per hour squared), then the variance would be given in terms of miles squared per hour to the fourth (miles2/hour4). To find the slope of the line, youll need to perform a regression analysis. Significance is usually denoted by a p-value, or probability value. Calculate the Relative Standard Deviation for the following set of numbers: 8, 20, 40 and 60 where the standard deviation is 5. If you converted all of the data values to gallons (multiply cubic feet by 7.48 to get gallons), then the variance would be given in terms of gallons3. It is a number between 1 and 1 that measures the strength and direction of the relationship between two variables. Correlation describes the strength of an association between two variables, and is completely symmetrical, the correlation between A and B is the same as the correlation between B and A. For example: m = matrix(data = c(89, 84, 86, 9, 8, 24), nrow = 3, ncol = 2). The yield of the one does not seem to be dependent on the other in the sense that, on average, the height of a child depends on his age. So, does standard deviation have units? If your confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups. What properties does the chi-square distribution have? How do you reduce the risk of making a Type I error? Se pressekonferansen her. The calculation of the correlation coefficient on the data in table 11.2 gave the following: Applying these figures to the formulae for the regression coefficients, we have: Therefore, in this case, the equation for the regression of y on x becomes, This means that, on average, for every increase in height of 1 cm the increase in anatomical dead space is 1.033 ml. Step 1: Find the standard deviation of your sample. The more standard deviations away from the predicted mean your estimate is, the less likely it is that the estimate could have occurred under the null hypothesis. If any value in the data set is zero, the geometric mean is zero. Some vehicles waive the initial charge and apply an exit charge instead. Even though the geometric mean is a less common measure of central tendency, its more accurate than the arithmetic mean for percentage change and positively skewed data. Together, they give you a complete picture of your data. However, if the intention is to make inferences about one variable from the other, the observations from which the inferences are to be made are usually put on the baseline. Then you simply need to identify the most frequently occurring value. For example, income is a variable that can be recorded on an ordinal or a ratio scale: If you have a choice, the ratio level is always preferable because you can analyze data in more ways. Both chi-square tests and t tests can test for differences between two groups. The regression coefficient is often positive, indicating that blood pressure increases with age. The absolute value of a number is equal to the number without its sign. Healthcare practitioners and technical occupations had employment of 8.8 million in May 2021, representing 6.2 percent of national employment. You can use the chisq.test() function to perform a chi-square goodness of fit test in R. Give the observed values in the x argument, give the expected values in the p argument, and set rescale.p to true. These are the assumptions your data must meet if you want to use Pearsons r: A correlation coefficient is a single number that describes the strength and direction of the relationship between your variables. Thus, RSD eliminates the results which are too far in comparison with the actual RSD. For a test of significance at = .05 and df = 3, the 2 critical value is 7.82. In statistics, power refers to the likelihood of a hypothesis test detecting a true effect if there is one. The standard deviation used for measuring the volatility of a stock. One common application is to check if two genes are linked (i.e., if the assortment is independent). Calculate the Relative Standard Deviation for the following set of numbers: 48, 52, 56, 60 where the standard deviation is 2.48. What type of documents does Scribbr proofread? However, a correlation is used when you have two quantitative variables and a chi-square test of independence is used when you have two categorical variables. The empirical rule, or the 68-95-99.7 rule, tells you where most of the values lie in a normal distribution: The empirical rule is a quick way to get an overview of your data and check for any outliers or extreme values that dont follow this pattern. Example: Standard deviation in a normal distribution You administer a memory recall test to a group of students. There are 4 levels of measurement, which can be ranked from low to high: No. To test whether the association is merely apparent, and might have arisen by chance use the. London: BMJ Publishing Group, 1993. In the case of the reverse situation i.e. Only N-1 instead of N changes the calculations. There are two formulas you can use to calculate the coefficient of determination (R) of a simple linear regression. The independent variable, such as time or height or some other observed classification, is measured along the horizontal axis, or baseline. You can use the CHISQ.TEST() function to perform a chi-square goodness of fit test in Excel. To find the quartiles of a probability distribution, you can use the distributions quantile function. This has been a guide to the top difference between Standard Deviation vs Mean. Cale Clinton. Figure 11.2 Scatter diagram of relation in 15 children between height and pulmonary anatomical dead space. We have to calculate the mean with the help of standard deviation. When should I use the interquartile range? Medical Statistics on Personal Computers , 2nd edn. Chi-square goodness of fit tests are often used in genetics. The 3 most common measures of central tendency are the mean, median and mode. Using descriptive and inferential statistics, you can make two types of estimates about the population: point estimates and interval estimates. Around 68% of scores are within 1 standard deviation of the mean, Around 95% of scores are within 2 standard deviations of the mean, Around 99.7% of scores are within 3 standard deviations of the mean. What do the sign and value of the correlation coefficient tell you? For example, gender and ethnicity are always nominal level data because they cannot be ranked. You can test a model using a statistical test. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy, Explore 1000+ varieties of Mock tests View more, Special Offer - All in One Financial Analyst Bundle (250+ Courses, 40+ Projects) Learn More, You can download this Relative Standard Deviation Template here , 250+ Online Courses | 40+ Projects | 1000+ Hours | Verifiable Certificates | Lifetime Access, All in One Financial Analyst Bundle- 250+ Courses, 40+ Projects, Investment Banking Course (123 Courses, 25+ Projects), Financial Modeling Course (7 Courses, 14 Projects), All in One Financial Analyst Bundle (250+ Courses, 40+ Projects), Examples of Relative Standard Deviation Formula (With Excel Template), Relative Standard Deviation Formula Calculator, How to Calculate Sharpe Ratio Using Formula, Relative Standard Deviation = (2.48 * 100) / 54, Relative Standard Deviation = (10 * 100) / 30, Relative Standard Deviation = (5 * 100) / 32. There are different types for calculation of mean, including the arithmetic mean method, which uses sums of all numbers in the series, and the geometric mean method. It is two-thirds of a standard deviation above the mean. Whats the difference between the range and interquartile range? As increases, the asymmetry decreases. The table below gives some examples of how the units for variance compare to the units for standard deviation. The formula depends on the type of estimate (e.g. The standard deviation used in for measuring volatility, so it is used for short-term analysis purposes. In this way, the t-distribution is more conservative than the standard normal distribution: to reach the same level of confidence or statistical significance, you will need to include a wider range of the data. If your data does not meet these assumptions you might still be able to use a nonparametric statistical test, which have fewer requirements but also make weaker inferences. If so, please share it with someone who can use the information. If the particular product appears to have a higher relative standard deviation, that means the numbers are very widely spread from its mean. How do you know whether a number is a parameter or a statistic? The data supports the alternative hypothesis that the offspring do not have an equal probability of inheriting all possible genotypic combinations, which suggests that the genes are linked. These scores are used in statistical tests to show how far from the mean of the predicted distribution your statistical estimate is. That the scatter of points about the line is approximately constant we would not wish the variability of the dependent variable to be growing as the independent variable increases. 90%, 95%, 99%). The coefficient of determination (R) is a number between 0 and 1 that measures how well a statistical model predicts an outcome. Because its based on values that come from the middle half of the distribution, its unlikely to be influenced by outliers. MSE is calculated by: Linear regression fits a line to the data by finding the regression coefficient that results in the smallest MSE. In this way we get the same picture, but in numerical form, as appears in the scatter diagram. Standard deviation is often used in creating for trading and investing because it helps to measure the volatility of stock prices and predict the future trend. In most cases, researchers use an alpha of 0.05, which means that there is a less than 5% chance that the data being tested could have occurred under the null hypothesis. For the numerator multiply each value of x by the corresponding value of y, add these values together and store them. Here we have discussed how to calculate Relative Standard Deviation and practical examples. When we use statistics to analyze data, we often use mean (to find center) and standard deviation (to find spread). It penalizes models which use more independent variables (parameters) as a way to avoid over-fitting. There may be a third variable, a confounding variable that is related to both of them. Complete correlation between two variables is expressed by either + 1 or -1. Standard deviation measures the volatility of the stock over a certain period of time. When should I use the Pearson correlation coefficient? I help with some common (and also some not-so-common) math questions so that you can solve your problems quickly! Thus to simplify the requirements, RSD helps to detect the actual results from different possibilities. If you have a set of data points that measure the acceleration of an object (like a car) in meters per second squared (meters/second2), then the standard deviation would also be given in terms of meters per second squared (meters/second2). By signing up, you agree to our Terms of Use and Privacy Policy. If it is categorical, sort the values by group, in any order. You can use the summary() function to view the Rof a linear model in R. You will see the R-squared near the bottom of the output. What happens to the shape of Students t distribution as the degrees of freedom increase? is the square root of . The interquartile range is the best measure of variability for skewed distributions or data sets with outliers. How do I decide which level of measurement to use? A one-way ANOVA has one independent variable, while a two-way ANOVA has two. We already calculated (x1-7)2=4 etc. The point estimate you are constructing the confidence interval for. You can choose from four main ways to detect outliers: Outliers can have a big impact on your statistical analyses and skew the results of any hypothesis test if they are inaccurate. Can I use a t-test to measure the difference among several groups? Download Relative Standard Deviation Template. The distance of the centre from the hospital of each area was measured in miles. Thus, the situations and the outcomes are led by huge uncertainties and probabilities. The t-distribution is a way of describing a set of observations where most observations fall close to the mean, and the rest of the observations make up the tails on either side. Calculate the Relative Standard Deviation for the following set of numbers: 10, 20, 30, 40, and 50 where the standard deviation is 10. Sample variance calculator. If your measurements, in pounds, were {25, 27, 33, 34, 40, 40, 41, 42, 50, 100}, then the range would be 100 25 = 75 pounds. Testing the combined effects of vaccination (vaccinated or not vaccinated) and health status (healthy or pre-existing condition) on the rate of flu infection in a population. The only difference between one-way and two-way ANOVA is the number of independent variables. But that isn't the mean yet, we need to divide by how many, which is done by multiplying by 1/N (the same as dividing by N): Mean of squared differences = (1/20) 178 = 8.9, (Note: this value is called the "Variance"). For each of these methods, youll need different procedures for finding the median, Q1 and Q3 depending on whether your sample size is even- or odd-numbered. In statistics, a model is the collection of one or more independent variables and their predicted interactions that researchers use to try to explain variation in their dependent variable. If you have a set of data points that measure the speed of an object (like a car) in meters per second, then the variance would also be given in terms of meters squared per second squared (meters2/second2). Tip: To convert a percentage to a decimal divide by 100! Nominal level data can only be classified, while ordinal level data can be classified and ordered. Homoscedasticity, or homogeneity of variances, is an assumption of equal or similar variances in different groups being compared. 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