Program Analysis and Identification System (PAIS)
The Program Analysis and Identification System (PAIS) is designed to evaluate the effectiveness of various exercise programs and generate a unique identifier for each program based on its performance metrics. This system ensures that each program can be uniquely identified, similar to a fingerprint, based on its analysis results.
Steps in the Analysis Process
1. Data Loading
```python
data = pd.read_csv('exercise_program_data.csv')
```
The data is loaded from a CSV file into a pandas DataFrame. The data should include columns for `ParticipantID`, `PreTestScore`, `PostTestScore`, and `Program`.
2. Function to Calculate Effectiveness and Generate a Unique Identifier
```python
def analyze_program_effectiveness(data, program_name):
...
```
This function takes the data and the name of a specific program as input and returns a dictionary of results, including a unique identifier.
3. Filtering Data
```python
program_data = data[data['Program'] == program_name]
```
The data is filtered to include only the records for the specified program.
4. Calculating Improvement Scores
```python
program_data['Improvement'] = program_data['PostTestScore'] - program_data['PreTestScore']
```
The improvement score for each participant is calculated as the difference between their post-test and pre-test scores.
5. Calculating Mean and Standard Deviation
```python
mean_improvement = program_data['Improvement'].mean()
std_improvement = program_data['Improvement'].std()
```
The mean and standard deviation of the improvement scores are calculated. These metrics provide insight into the average improvement and the variability of the improvements, respectively.
6. Paired T-Test
```python
t_statistic, p_value = stats.ttest_rel(program_data['PreTestScore'], program_data['PostTestScore'])
```
A paired t-test is performed to determine if the improvement is statistically significant. The t-statistic and p-value are obtained from this test. A low p-value (typically < 0.05) indicates that the improvement is statistically significant.
7. Composite Score
```python
composite_score = (mean_improvement / std_improvement) (1 / p_value if p_value > 0 else 1)
```
A composite score is calculated to quantify the overall effectiveness of the program. The formula used here takes into account the mean improvement, standard deviation, and p-value. Specifically:
- `mean_improvement / std_improvement`: This ratio provides a measure of the effect size relative to the variability.
- `1 / p_value`: This term gives more weight to programs with statistically significant results.
- `if p_value > 0 else 1`: This ensures that the denominator is not zero, which would cause a division error.
8. Normalization
```python
normalized_score = str(int(composite_score 10000))
```
The composite score is multiplied by 10,000 and converted to an integer string. This normalization step scales the score to a consistent range, making it easier to handle in the next step.
9. Generating a Unique Identifier
```python
unique_identifier = hashlib.sha256(normalized_score.encode()).hexdigest()
```
A SHA-256 hash function is used to generate a unique identifier from the normalized composite score. This identifier serves as a unique "fingerprint" for the program, ensuring that even small differences in effectiveness are captured uniquely.
10. Results Compilation
```python
results = {
'Program': program_name,
'Mean Improvement': mean_improvement,
'Standard Deviation': std_improvement,
'T-Statistic': t_statistic,
'P-Value': p_value,
'Composite Score': composite_score,
'Unique Identifier': unique_identifier
}
return results
```
The results, including the unique identifier, are compiled into a dictionary. This dictionary is returned by the function.
11. Analyzing All Programs
```python
programs = data['Program'].unique()
results = [analyze_program_effectiveness(data, program) for program in programs]
```
The function is applied to each unique program in the dataset, and the results are collected in a list.
12. Converting Results to DataFrame
```python
results_df = pd.DataFrame(results)
```
The list of results is converted to a pandas DataFrame for easy viewing and further analysis.
13. Displaying Results
```python
print(results_df)
```
The results DataFrame is printed, showing the effectiveness metrics and unique identifiers for each program.
Here is the Complete Code for anyone to use as a template for their business.
```python
import pandas as pd
import numpy as np
from scipy import stats
import hashlib
Load the dataset
data = pd.read_csv('exercise_program_data.csv')
Function to calculate the effectiveness and generate a unique identifier
def analyze_program_effectiveness(data, program_name):
Filter data for the specific program
program_data = data[data['Program'] == program_name]
Calculate the improvement scores
program_data['Improvement'] = program_data['PostTestScore'] - program_data['PreTestScore']
Calculate the mean and standard deviation of the improvements
mean_improvement = program_data['Improvement'].mean()
std_improvement = program_data['Improvement'].std()
Perform a paired t-test to determine if the improvement is statistically significant
t_statistic, p_value = stats.ttest_rel(program_data['PreTestScore'], program_data['PostTestScore'])
Create a composite score based on mean improvement, standard deviation, and p-value
composite_score = (mean_improvement / std_improvement) (1 / p_value if p_value > 0 else 1)
Normalize composite score to a fixed range and convert to a string
normalized_score = str(int(composite_score 10000))
Generate a unique identifier using a hash function
unique_identifier = hashlib.sha256(normalized_score.encode()).hexdigest()
Results
results = {
'Program': program_name,
'Mean Improvement': mean_improvement,
'Standard Deviation': std_improvement,
'T-Statistic': t_statistic,
'P-Value': p_value,
'Composite Score': composite_score,
'Unique Identifier': unique_identifier
}
return results
Analyze all programs
programs = data['Program'].unique()
results = [analyze_program_effectiveness(data, program) for program in programs]
Convert results to DataFrame for easy viewing
results_df = pd.DataFrame(results)
Display results
print(results_df)
```
Steps in the Analysis Process
1. Data Loading
```python
data = pd.read_csv('exercise_program_data.csv')
```
The data is loaded from a CSV file into a pandas DataFrame. The data should include columns for `ParticipantID`, `PreTestScore`, `PostTestScore`, and `Program`.
2. Function to Calculate Effectiveness and Generate a Unique Identifier
```python
def analyze_program_effectiveness(data, program_name):
...
```
This function takes the data and the name of a specific program as input and returns a dictionary of results, including a unique identifier.
3. Filtering Data
```python
program_data = data[data['Program'] == program_name]
```
The data is filtered to include only the records for the specified program.
4. Calculating Improvement Scores
```python
program_data['Improvement'] = program_data['PostTestScore'] - program_data['PreTestScore']
```
The improvement score for each participant is calculated as the difference between their post-test and pre-test scores.
5. Calculating Mean and Standard Deviation
```python
mean_improvement = program_data['Improvement'].mean()
std_improvement = program_data['Improvement'].std()
```
The mean and standard deviation of the improvement scores are calculated. These metrics provide insight into the average improvement and the variability of the improvements, respectively.
6. Paired T-Test
```python
t_statistic, p_value = stats.ttest_rel(program_data['PreTestScore'], program_data['PostTestScore'])
```
A paired t-test is performed to determine if the improvement is statistically significant. The t-statistic and p-value are obtained from this test. A low p-value (typically < 0.05) indicates that the improvement is statistically significant.
7. Composite Score
```python
composite_score = (mean_improvement / std_improvement) (1 / p_value if p_value > 0 else 1)
```
A composite score is calculated to quantify the overall effectiveness of the program. The formula used here takes into account the mean improvement, standard deviation, and p-value. Specifically:
- `mean_improvement / std_improvement`: This ratio provides a measure of the effect size relative to the variability.
- `1 / p_value`: This term gives more weight to programs with statistically significant results.
- `if p_value > 0 else 1`: This ensures that the denominator is not zero, which would cause a division error.
8. Normalization
```python
normalized_score = str(int(composite_score 10000))
```
The composite score is multiplied by 10,000 and converted to an integer string. This normalization step scales the score to a consistent range, making it easier to handle in the next step.
9. Generating a Unique Identifier
```python
unique_identifier = hashlib.sha256(normalized_score.encode()).hexdigest()
```
A SHA-256 hash function is used to generate a unique identifier from the normalized composite score. This identifier serves as a unique "fingerprint" for the program, ensuring that even small differences in effectiveness are captured uniquely.
10. Results Compilation
```python
results = {
'Program': program_name,
'Mean Improvement': mean_improvement,
'Standard Deviation': std_improvement,
'T-Statistic': t_statistic,
'P-Value': p_value,
'Composite Score': composite_score,
'Unique Identifier': unique_identifier
}
return results
```
The results, including the unique identifier, are compiled into a dictionary. This dictionary is returned by the function.
11. Analyzing All Programs
```python
programs = data['Program'].unique()
results = [analyze_program_effectiveness(data, program) for program in programs]
```
The function is applied to each unique program in the dataset, and the results are collected in a list.
12. Converting Results to DataFrame
```python
results_df = pd.DataFrame(results)
```
The list of results is converted to a pandas DataFrame for easy viewing and further analysis.
13. Displaying Results
```python
print(results_df)
```
The results DataFrame is printed, showing the effectiveness metrics and unique identifiers for each program.
Here is the Complete Code for anyone to use as a template for their business.
```python
import pandas as pd
import numpy as np
from scipy import stats
import hashlib
Load the dataset
data = pd.read_csv('exercise_program_data.csv')
Function to calculate the effectiveness and generate a unique identifier
def analyze_program_effectiveness(data, program_name):
Filter data for the specific program
program_data = data[data['Program'] == program_name]
Calculate the improvement scores
program_data['Improvement'] = program_data['PostTestScore'] - program_data['PreTestScore']
Calculate the mean and standard deviation of the improvements
mean_improvement = program_data['Improvement'].mean()
std_improvement = program_data['Improvement'].std()
Perform a paired t-test to determine if the improvement is statistically significant
t_statistic, p_value = stats.ttest_rel(program_data['PreTestScore'], program_data['PostTestScore'])
Create a composite score based on mean improvement, standard deviation, and p-value
composite_score = (mean_improvement / std_improvement) (1 / p_value if p_value > 0 else 1)
Normalize composite score to a fixed range and convert to a string
normalized_score = str(int(composite_score 10000))
Generate a unique identifier using a hash function
unique_identifier = hashlib.sha256(normalized_score.encode()).hexdigest()
Results
results = {
'Program': program_name,
'Mean Improvement': mean_improvement,
'Standard Deviation': std_improvement,
'T-Statistic': t_statistic,
'P-Value': p_value,
'Composite Score': composite_score,
'Unique Identifier': unique_identifier
}
return results
Analyze all programs
programs = data['Program'].unique()
results = [analyze_program_effectiveness(data, program) for program in programs]
Convert results to DataFrame for easy viewing
results_df = pd.DataFrame(results)
Display results
print(results_df)
```
