You are interested in understanding the impact of Student Teacher Ratios (STR) on Test Scores (i.e., STR is your variable of interest and Test Scores are your outcome variable). Let’s pretend you have 2 models and you must only pick 1. The models along with mock results are in the table below. The coefficients are presented with standard errors in parenthesis. Further assume that the STR coefficient in Model 1 is less biased than the STR coefficient in Model 2. But as you can see, the STR coefficient in Model 2 is more precisely estimated (it’s statistically significant) than the coefficient in Model 1. Which model (Model 1 or Model 2) do you prefer and why. X1 and X2 are different control variables. You do not need to know what they are in order to answer this question – you only need to know that they are different. Y = Test Scores Model 1 Model 2 STR -1.4 (0.9) -3.7** (0.9) X1 5.6** (2.2) X2 4.6** (2.1) Constant 680*** (45) 690*** (55) Sample Size 1000 1000 R2 0.75 0.75
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
- You are interested in understanding the impact of Student Teacher Ratios (STR) on Test Scores (i.e., STR is your variable of interest and Test Scores are your outcome variable). Let’s pretend you have 2 models and you must only pick 1. The models along with mock results are in the table below. The coefficients are presented with standard errors in parenthesis.
Further assume that the STR coefficient in Model 1 is less biased than the STR coefficient in Model 2. But as you can see, the STR coefficient in Model 2 is more precisely estimated (it’s statistically significant) than the coefficient in Model 1. Which model (Model 1 or Model 2) do you prefer and why.
X1 and X2 are different control variables. You do not need to know what they are in order to answer this question – you only need to know that they are different.
|
Y = Test Scores |
Model 1 |
Model 2 |
|
STR |
-1.4 (0.9) |
-3.7** (0.9) |
|
X1 |
5.6** (2.2) |
|
|
X2 |
|
4.6** (2.1) |
|
Constant |
680*** (45) |
690*** (55) |
|
|
1000 |
1000 |
|
R2 |
0.75 |
0.75 |
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