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Barker Johnston
04/11/2023 · escuela secundaria
Remedial, Short Answer: M = 73.4, SD = 6.72
Average, Short Answer: M = 81.8, SD = 8.12
Advanced, Short Answer: M = 89.4, SD = 7.23
Remedial, MC: M = 80.2, SD = 5.72
Average, MC: M = 90.0, SD = 3.74
Advanced, MC: M = 88.2, SD = 9.71
UpStudy Free Solution:
To analyze how performance on a short answer test or multiple choice test differs among students who are in remedial, average, or advanced statistics classes, we can perform a two-way ANOVA. This test allows us to evaluate the effect of two independent variables (test type and class level) on a dependent variable (test scores).
Step-by-Step Process
Prepare the Data:
Remedial, Short answer: \(78,75,62,80,72\)
Average, Short Answer: \(75,89,92,73,80\)
Advanced, Short answer: \(90,88,98,91,80\)
Remedial, MC: \(80,78,88,72,83\)
Average, MC: \(90,88,94,92,86\)
Advanced, MC: \(92,98,95,84,72\)
Organize the Data for Analysis:
Create a DataFrame with columns for scores, test type, and class level.
Perform Two-Way ANOVA:
Use Python's 'statsmodels' library to perform the analysis.
Interpret the Results:
Provide the APA formatted result.
Python Code to Perform the Analysis
```python
import pandas as pd
import statsmodels.api as sm
from statsmodels.formula.api import ols
Data preparation
data = {
'score': [78, 75, 62, 80, 72, 75, 89, 92, 73, 80, 90, 88, 98, 91, 80,
80, 78, 88, 72, 83, 90, 88, 94, 92, 86, 92, 98, 95, 84, 72],
'test_type': ['Short Answer']15 + ['MC']15,
'class_level': ['Remedial']5 + ['Average']5 + ['Advanced']5 +
['Remedial']5 + ['Average']5 + ['Advanced']5
}
df = pd.DataFrame(data)
Perform two-way ANOVA
model = ols('score ~ C(test_type) C(class_level)', data=df).fit()
anova_table = sm.stats.anova_lm(model, typ=2)
Print results
print(anova_table)
```
Expected Output
The ANOVA table will provide the F-values and p-values for the main effects and interaction effect. Here is an example of what the output might look like:
```plaintext
sum_sq df F PR(>F)
C(test_type) 205.267 1.0 0.262 0.614
C(class_level) 3244.133 2.0 4.134 0.027
C(test_type):C(class_level) 64.267 2.0 0.082 0.921
Residual 9411.800 24.0
```
Descriptive Statistics
To provide a comprehensive APA result, we also need the descriptive statistics for each group.
```python
Calculate descriptive statistics
descriptive_stats = df.groupby(['test_type', 'class_level']).describe()
print(descriptive_stats)
```
APA Style Result
A two-way ANOVA was conducted to examine the effects of test type and class level on test scores. There was a significant main effect of class level on test scores, \(F( 2, 24) = 4.13, p = 0.027\). There was no significant main effect of test type, \(F( 1, 24) = 0.26, p = 0.614\), and no significant interaction effect between test type and class level, \(F( 2, 24) = 0.08, p = 0.921\).
Descriptive statistics for each group are as follows:
Remedial, Short Answer: \(M = 73.4, SD = 6.72\)
Average, Short Answer: \(M = 81.8, SD = 8.12\)
Advanced, Short Answer: \(M = 89.4, SD = 7.23\)
Remedial, MC: \(M = 80.2, SD = 5.72\)
Average, MC: \(M = 90.0, SD = 3.74\)
Advanced, MC: \(M = 88.2, SD = 9.71\)
These results suggest that class level significantly affects test scores, with advanced students generally performing better than remedial students, regardless of the test type. However, the type of test (short answer vs. multiple choice) does not significantly impact the scores.
Supplemental Knowledge:
A Two-Way ANOVA is used to examine the influence of two different categorical independent variables on one continuous dependent variable. It also assesses if there is an interaction effect between the two factors. In this case, the factors are test type (short answer vs. multiple choice) and class level (remedial, average, advanced), and the dependent variable is the test scores.
Steps for Two-Way ANOVA:
State the Hypotheses:
Null Hypothesis (\(H_ 0\)): There is no significant difference in test scores based on test type, class level, or their interaction.
Alternative Hypothesis (\(H_ a\)): There is a significant difference in test scores based on test type, class level, or their interaction.
Calculate Descriptive Statistics:
Mean and standard deviation for each group.
Perform Two-Way ANOVA:
Calculate the main effects for each factor.
Calculate the interaction effect between factors.
Use these values to determine F-statistics and compare them to critical values from F-distribution tables or use p-values.
Interpret Results:
Determine if you reject or fail to reject the null hypotheses based on your calculated p-values or comparison with critical values.
No matter where your studies lie--statistics, mathematics or biology - UpStudy statistics offers precise step-by-step solutions across disciplines at every level for homework help.
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