3_norm+theory

Practical Example
• Assume that there are 600 women and 400 men in the population, and we want to draw 10% as a sample (n=100). • 假设人群中有600名女性 和400名男性，我们要采 样10％（n＝100）
– test scores (predictor) -well-defined criteria – Scholastic aptitude test (predictor) – (criterion) Probabilistic preview statistical odds subsequent college grade point average expected outcome on a relevant task (criterion)
Stratified Random Sample
• Assume that the ratio of female to male is 3 to 2 (or 60% and 40%) in the population. We may use stratified random sampling to obtain a sample that contains the 3:2 ratio of females to males. • 假设女性和男性的比值为3：2 （或者60％：40％），我们可以 用分层随机取样的方法以女性和 男性3：2的比率进行采样
• Incidental Sampling (Convenience Sampling) • 常模的相对性
– Norms are not absolute, universal, or timeless
Simple Random Sampling 简单随机抽样
• Simple means that the sample is selected from an undivided population (usually more homogenous). • 简单是指样本从不划分的 简单是指样本从不划分的 是指样本从不划分 总人群（ 总人群（通常具有更多的 相似性） 相似性）中采集 • Random means that each unit in the population has equal chance of being selected. • 随机是指人群中每一单位 具有相同的概率被抽取到
Stratified Random Sample 分层随机抽样
• One way to reduce sampling errors is to draw a stratified sample. • 减少抽样误差的一个方 法是分层随机抽样法 • Usually, the more homogeneous (alike) the units of the population are, the fewer samples we need to draw to obtain representativeness. If the population is considered not homogeneous, stratified sampling is more appropriate to obtain a representative sample.
标准九 9 8 7 6 5 4 3 2 1
人数 21474 19444 32129 39398 34975 23699 11209 2139 904
20 57 56 54 50 44 38 33
30 57 55 52 48 43 37 28
40 57 54 50 47 41 31 28
50 54 52 48 42 34 24 21
60 54 52 46 37 30 22 19
Selecting a Norm Group (常模团体的选取)
• How to Select a Norm Group? • Age and Grade Norms • Local and Subgroup Norms • Expectancy Tables
Age and Grade norms
• Age Norm（年龄常模 / age-equivalent scores ）
– The level of test performance for each separate age group in the normative sample. – Problems with the comparison of “mental age”. Age span: a month ~ a decade or more
Stratified Random Sample
• To do this, we need to know the exact composition of the population. The population is divided into strata. • 首先，我们要知道人群的 确切组成，人群被分为不 同的层次 • The population can be divided subpopulation, e.g., male and female, white and non-white, young and old. We then draw the same percentage of sample from each stratum.
• Note:
– social conditions / institutional pol分数 75~79 70~74 65~69 60~64 55~59 50~54 45~49 40~44 35~39 30~34 100 100 100 100 100 96 85 100 94 87 72 46 100 100 88 83 61 40 15 100 94 85 63 45 24 20 H G F E D C 100 100 50 48 31 12 5 4 B 100 82 33 22 4 5 A 67 36 11 4
• Subgroup norms（小组常模）
– performance of identifiable subgroup ≠ more broadly defined standardization sample
Expectancy Tables （期望表）
• The established relationship
• Grade Norm（年级常模）
– Used to indicate the average test performance of test takers in a specific grade. – Based on a ten month scale, refers to grade and month (e.g., 7.3 is equivalent to seventh grade, third month).
Varieties of Norm
– – – – Percentile Ranks Age Equivalents（年龄当量） Grade Equivalents（年级当量） Standard Scores
以常模来解释测验分数 Percentile（百分位数）把测验分数转换为百分数
年龄 % 95 90 75 50 25 10 5
• Stratified sampling strategy divides the population into several more homogeneous subpopulations (strata or clusters) and draw sample with equal % from each sub-population. • 分层采样策略是将人群分为几 个同质亚群（层或群），然后 从每一层中抽取相同百分率的 样本
– A sample of examinees who are representative of the population for whom the test is intended.
•
Test Standardization (测验标准化)
– Its essential objective is to determine the distribution of raw scores in the norm group so that the test developer can publish derived scores known as norms.
• We can further increase our precision (which reduces sampling errors) by using multiple strata in selecting a given sample. • 我们可以用多层采样方法 来提高精度（减小抽样误 差）
How to Select a Norm Group?
• Simple Random Sampling (简单随机抽样) • Stratified Random Sampling (分层随机抽样) • Purposive Sampling
– Arbitrarily select some sample because we believe it to be representative of the population
• To maintain the same proportion of gender is important if we believe that gender may have impacts on the variables we are interested in. • 如果我们认为性别是影响变 量的因素的话，每一层采样 的性别比例就要一样