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Related Concept Videos

Percentile01:18

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A percentile indicates the relative standing of a data value when data are sorted into numerical order from smallest to largest. It represents the percentages of data values that are less than or equal to the pth percentile. For example, 15% of data values are less than or equal to the 15th percentile. Low percentiles always correspond to lower data values. High percentiles always correspond to higher data values.Percentiles divide ordered data into hundredths. To score in the...
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In statistics, several tools are used to interpret the data. Measures of central tendency represent the characteristics of the data, such as mean, median, and mode. Additionally, measures of variance like standard deviation and range are used to find the spread of data from the mean. Relative standing measures the distance between data locations. Commonly used measures of relative standings are percentile, z score, and quartiles.
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Quartiles are numbers that separate the data into quarters. Quartiles may or may not be part of the data. To find the quartiles, first, find the median or second quartile. The first quartile, Q1, is the middle value of the lower half of the data, and the third quartile, Q3, is the middle value, or median, of the upper half of the data. To get the idea, consider the same data set:
1; 1; 2; 2; 4; 6; 6.8; 7.2; 8; 8.3; 9; 10; 10; 11.5
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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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z scores are the standardized values obtained after converting a normal distribution into a standard normal distribution. A z score is measured in units of the standard deviation. The z score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. Values of x that are larger than the mean have positive z scores, and values of x that are smaller than the mean have negative z scores. If x equals the mean, then x has a z score of...
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An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the...
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Quantile regression in the study of developmental sciences.

Yaacov Petscher1, Jessica A R Logan2

  • 1Florida Center for Reading Research Florida State University.

Child Development
|December 17, 2013
PubMed
Summary
This summary is machine-generated.

Quantile regression offers a more comprehensive view than linear regression by examining predictor-outcome relationships across the entire outcome distribution. This advanced technique provides richer insights, especially in developmental research.

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Area of Science:

  • Developmental Psychology
  • Statistical Modeling

Background:

  • Linear regression is a common tool in developmental research but estimates only average relationships.
  • It fails to capture how predictors influence different parts of an outcome's distribution.

Purpose of the Study:

  • To introduce and demonstrate quantile regression as an alternative to linear regression.
  • To highlight the differential insights provided by quantile regression across various model complexities.

Main Methods:

  • The study utilizes data from the High School and Beyond and U.S. Sustained Effects Study databases.
  • Quantile regression is applied and contrasted with linear regression using models with single continuous, single dichotomous, and combined predictors.
  • A longitudinal application is also explored.

Main Results:

  • Examples illustrate how quantile regression reveals relationships not apparent with linear regression.
  • Differential inferences are drawn depending on the statistical method employed.

Conclusions:

  • Quantile regression provides a more nuanced understanding of predictor-outcome associations than traditional linear regression.
  • Researchers should consider quantile regression for a more complete analysis in developmental studies.