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.

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