Hypothesis Test t-test = sample size < 30, t distributionz-test = sample size > 30, z distribution For multi-level regression, t-test is different as needed to handle 2 level. ExampleModel 1 = grand-mean-centered IQ variable along with the group mean Model 2 = with-in group deviation variable Only Y01 is different between model Between group…

Example Regression Line given by Yij = 41.13 + 2.4801 IQij + 1.029 IQ (meanj) + Uoj + U1j IQij + RijStandard Deviation of random slope “Language Score” = √0.195 = 0.44Average slope = 2.480 Correlation between random slope and random intercept = -0.83/√(8.88×0.195) = -0.63The negative correlation means that classes with a higher performance…

Hierarchical Linear Model Advance from Random Intercept Model (simple case of hierarchical linear model) by introducing random slopes. RIM handle group difference with respect to average value of independent variable. Yij = β0j + β1j Xij + Rij become… Yij = γ00 + U0j + γ10 xij + U1j xij + Rij , note this…

Example Number of students is M = 3758Number of schools is N = 211Standard Deviation = 2.04 Using Y (Language Score) group by (School) Intraclass Correlation Coefficient (ρI) = 18.12/(18.12+62.85) = 0.22Standard Deviation of “Language Score” = √(18.12+62.85) = 9.00 Scale for effect that is independent of the measurement units = 2.04/9.0 = 0.57Each additional…

Random Intercept Model aka Ordinary Least Square (OLS) model Some brief introduction, before start. Fixed Effect (Taken only 1 group, level 1) Exception, when all group sample size nj are equal to one. The researcher need to have no qualied about using the model because nesting structure are not take place in this situation. The…

Disaggregation Disaggregation lead to “miraculous multiplication of the number of units” Suppose we want to understand “do new judges tend to give more harsh or more lenient sentences”? However taking observation base on (44) trials instead of (6) judges to estimate the relation is wrong. Sample size is exaggerated. From the perspective of between group…

Statistical Treatment of Clustered Data First step is to understand relationship between independent observation in a single classroom, or intraclass correlation. Second step is to perform aggregation to the observations such as simple statistics (mean, standard error of the mean, variance, correlation, reliability of aggregates). This is the treatment for two-stage sampling designs. Why this…

Variable Proposition In this case, interested effect of teacher efficacy (Z) on pupil motivation (y) controlling pupil aptitude (x). ps. Put it this way, by constant the x, how Z would affect y? This could be linear correlated, as Z does not influence x to influence y. Looking into this, simple random sample must not…

Data collected interpretation might have been wrong. One household is independent to other household; using simple random sampling. All single units in the population have the same chances of being selected into sample. The sampling was a two-stage one, and to pretend the secondary units were selected independently. Picking up household from the same housing…

Multilevel Analysis Word multi refer to many time aka stages. Multilevel analysis focus nested source and complex data. It has 2 components: Example School (look at classes(grade 1, grade 2, grade 3)) vs single class (look at pupils) [school funding, policies vs student performance] vs [teaching quality, classroom resources vs student performance] Firm (look at…