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PISA Data Analysis Manual: SPSS and SAS, Second Edition
Malaysian education blueprint — preschool to postsecondary education. Putrajaya: MOE. Mullis, I. TIMSS international results in mathematics.
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Personality and Individual Differences, 55 7 , — Steele, F. Module 5 concepts : Introduction to multilevel modelling. Centre for Multilevel Modelling. Bristol, England: University of Bristol. Spiegelhalter, D. The problems with PISA statistical methods. Tabachnick, B. Using multivatiate statistics , 6th ed. Boston, MA: Pearson Education. Taylor, G. A self-determination theory approach to predicting school achievement over time: The unique role of intrinsic motivation.
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Contemporary Educational Psychology, 39, — Willms, J. Student engagement at school: A sense of belonging and participation. All rights reserved.
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User Username Password Remember me. Font Size. Keywords bahan ajar berpikir kritis kemampuan berpikir kritis kemampuan komunikasi matematis kemampuan pemecahan masalah learning achievement motivasi belajar pembelajaran berbasis masalah pemecahan masalah penalaran matematis pendekatan problem posing pendekatan saintifik penemuan terbimbing pengembangan perangkat pembelajaran prestasi belajar problem-based learning self-confidence self-efficacy self-regulated learning task commitment.
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How to cite item. Email this article Login required. Email the author Login required. Notifications View Subscribe. Kartianom Kartianom, Oscar Ndayizeye. This chapter has briey described: i what a weight is and how to compute it; ii what the PISA sampling design is and why such a design is considered as the most appropriate; iii why the PISA weights show some variability; and iv the impact of the weights on population estimates. All statistical analyses or procedures on the PISA data should be weighted.
Unweighted analyses will provide biased population parameter estimates. Notes 1. N usually represents the size of the population and n the size of the sample. In PISA , the student weight adjustment for student non response might also differ in a particular school. Replicate Weights Introduction In most cases, as mentioned in Chapter 2, national or international surveys collect data from a sample instead of conducting a full a census.
However, for a particular population, there are thousands, even millions of possible samples, and each of them does not necessarily yield the same estimates of population statistics. Every generalisation made from a sample, i. The sampling variance corresponds to the measure of this uncertainty due to sampling. This chapter explains the statistical procedures used for computing the sampling variance and its square root, the standard error.
More specically, this chapter discusses how to estimate sampling variances for population estimates derived from a complex sample design using replicate weights. First, the concept of sampling variance will be examined through a ctitious example for simple random sampling. Second, the computation of the standard error will be investigated for two-stage sampling. Third, replication methods for estimating sampling variances will be introduced for simple random samples and for two-stage samples respectively.
Suppose that a teacher decides to implement the mastery learning approach in his or her classroom. This methodology requires that each lesson be followed by a student assessment. In the example given, the teachers class has 36 students. The teacher quickly realises that it would be too time consuming to grade all assessments and therefore decides to select a sample of quizzes to nd out whether the material taught has been assimilated Bloom, However, the random sampling of a few quizzes can result in the selection of high achievers or low achievers only, which would introduce an important error in the class mean performance estimate.
These situations are extreme examples, but drawing a random sample will always generate some uncertainty. In the same example, before selecting some quizzes, the teacher grades all of them and analyzes the results for the rst lesson. Figure 3. One student gets a grade 5, two students get a grade 6, and so on. The distribution of the student grades corresponds to a normal distribution. The population mean and the population variance are respectively equal to:.
The teacher then decides to randomly select a sample of two students after the next lesson to save on grading time. The number of possible samples of 2 students out of a population of 36 students is equal to:. There are possible samples of 2 students out of a population of 36 students. Table 3. For instance, there are two possible samples which provide a mean estimate of 5. These two samples are: i the student with a grade 5 and the rst student with a grade 6; and ii the student with a 5 and the second student with a 6. Similarly, there are two ways of selecting a sample that would produce a mean grade of 6: i the two sampled students both receive a grade 6; or ii one student receives a 5 and the second student receives a 7.
As only two students obtained a grade 6 Figure 3.
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Since Figure 3. As shown in Table 3.
Svyset command for a two-stage sampling survey dataset - PISA - Statalist
As for all distributions, this distribution of the means of all possible samples can be summarized by central tendency indices and dispersion indices, such as the mean and the variance or its square root, i. The mean of all possible sample means is equal to the student population mean, i. This result is not a coincidence, but a fundamental property of the mean of a simple random sample, i.
In more formal language, the sample mean is an unbiased estimate of the population mean. Stated differently, the expected value of the sample mean is equal to the population mean.