From a205334f81f851bcd69bbba087083edcc17d57c8 Mon Sep 17 00:00:00 2001 From: ErdemOzgen Date: Tue, 5 Dec 2023 10:04:46 +0300 Subject: [PATCH] Add statistics section 1 --- .../Intro Statistics in Python.md | 386 ++++++++++++++++++ .../Screenshot from 2023-12-05 08-43-58.png | Bin 0 -> 72262 bytes .../Screenshot from 2023-12-05 08-45-14.png | Bin 0 -> 36188 bytes .../Screenshot from 2023-12-05 08-45-36.png | Bin 0 -> 42840 bytes 4 files changed, 386 insertions(+) create mode 100644 content/AI&DATA/Data Science/Intro Statistics in Python.md create mode 100644 content/imgs/Screenshot from 2023-12-05 08-43-58.png create mode 100644 content/imgs/Screenshot from 2023-12-05 08-45-14.png create mode 100644 content/imgs/Screenshot from 2023-12-05 08-45-36.png diff --git a/content/AI&DATA/Data Science/Intro Statistics in Python.md b/content/AI&DATA/Data Science/Intro Statistics in Python.md new file mode 100644 index 000000000..8badfa2dd --- /dev/null +++ b/content/AI&DATA/Data Science/Intro Statistics in Python.md @@ -0,0 +1,386 @@ +--- +tags: + - python + - datascience + - statistics + - "#math" + - numpy + - pandas +--- +#statistics +#numpy +#pandas +# What is statistics? +The field of statistics - the practice and study of collecting and analyzing data A summary statistic - a fact about or summary of some data + +# Types of statistics + +* Descriptive statistics +Describe and summarize data +50% of friends drive to work +* Inferential statistics +Use a sample of data to make inferences about a larger population +What percent of people drive to work? + +# Types of data + +| Types of Data | Nature | Examples | +|--------------------------|-------------------|-------------------------------------------| +| Numeric (Quantitative) | Continuous (Measured) | Airplane speed (e.g., 600 mph) | +| | | Time spent waiting in line (e.g., 20 minutes)| +|--------------------------|-------------------|-------------------------------------------| +| | Discrete (Counted)| Number of pets (e.g., 2 dogs) | +| | | Number of packages shipped (e.g., 10 packages)| +|--------------------------|-------------------|-------------------------------------------| +| Categorical (Qualitative)| Nominal (Unordered)| Marital status (e.g., Married/Unmarried) | +| | | Country of residence (e.g., USA, Canada) | +|--------------------------|-------------------|-------------------------------------------| +| | Ordinal (Ordered) | Educational level (e.g., Bachelor's Degree)| +| | | Socioeconomic status (e.g., Middle Class)| +| | | Customer satisfaction rating (e.g., 4 out of 5)| +| | | Likert Scale (e.g., Agree) | + +Categorical data can be represented as numbers + +**Nominal (Unordered)** Married/unmarried ( 1 / 0 ) +**Ordinal (Ordered)** Strongly disagree ( 1 ) Somewhat disagree ( 2 ) Neither agree nor disagree ( 3 ) Somewhat agree ( 4 ) Strongly agree ( 5 ) + +# Why data type matter ? + +Data type matters in various aspects of data analysis and decision-making for several reasons: + +1. **Data Representation**: Different data types require different methods of representation. Understanding the data type helps in choosing the appropriate data structures for storage and analysis. For example, numeric data may be stored as floating-point numbers, while categorical data may be stored as strings or integers. + +2. **Data Analysis Techniques**: The type of data determines which statistical or analytical techniques are suitable for analysis. For instance, you would use different methods to analyze numeric data compared to categorical data. Using the wrong analysis method can lead to incorrect results and conclusions. + +3. **Data Visualization**: Data type influences how data is visualized. Scatter plots and histograms are useful for numeric data, while bar charts and pie charts are often used for categorical data. Understanding the data type helps in creating effective data visualizations. + +4. **Data Preprocessing**: Data type affects data preprocessing steps. For example, missing values may need to be handled differently for numeric and categorical data. Data transformation techniques, such as one-hot encoding for categorical data, are specific to data types. + +5. **Modeling and Machine Learning**: In machine learning, the data type of features and the target variable is crucial. Algorithms have specific requirements and assumptions about data types. For example, linear regression typically works with numeric data, while decision trees can handle both numeric and categorical data. + +6. **Interpretation**: The interpretation of results depends on data type. For example, when interpreting correlation coefficients between two numeric variables, you can make statements about the strength and direction of the relationship. Interpreting results from logistic regression for categorical data involves odds ratios and probabilities. + +7. **Data Quality and Validation**: Understanding data type is essential for data validation and data quality checks. It helps in identifying inconsistencies or errors in the data. For instance, if a numeric field contains non-numeric values, it could be a data quality issue. + +8. **Data Integration**: When combining data from multiple sources, understanding data types helps in data integration. Mismatched data types can lead to integration challenges and data transformation requirements. + +9. **Decision-Making**: Ultimately, the correct interpretation of data and informed decision-making rely on understanding data types. Making decisions based on misinterpreted or mishandled data can have significant consequences. + +In summary, data type matters because it affects how data is treated, analyzed, and interpreted. A clear understanding of data types is fundamental for effective data analysis and informed decision-making in various domains, including business, science, and technology. + +```python +import pandas as pd +import numpy as np +data = { + "Species": [ + "African Elephant", "Giraffe", "Lion", "Hippopotamus", "Gorilla", + "Cheetah", "Kangaroo", "Koala", "Brown Bat", "Dolphin", + "Human", "Hedgehog", "Sloth", "Raccoon", "Dog", "Cat", "Mouse" + ], + "Class": ["Mammal"] * 17, + "Hours of Sleep per Day": [ + 3.5, 4.6, 13.5, 4.5, 9.9, + 12.1, 4.8, 18.0, 19.9, 4.0, + 7.0, 10.0, 14.4, 12.5, 12.0, 12.0, 12.5 + ] +} + +# Create a pandas DataFrame from the dictionary +mammal_sleep_df = pd.DataFrame(data) + +# Print the DataFrame +print(mammal_sleep_df) + +# print mean of data +print(np.mean(mammal_sleep_df['Hours of Sleep per Day'])) + +``` + +#histogram + +The histogram is a popular graphing tool. It is used to summarize discrete or continuous data that are measured on an interval scale. It is often used to illustrate the major features of the distribution of the data in a convenient form. It is also useful when dealing with large data sets (greater than 100 observations). It can help detect any unusual observations (outliers) or any gaps in the data. + +See also Canadian statistics website [link](https://www150.statcan.gc.ca/n1/edu/power-pouvoir/toc-tdm/5214718-eng.htm) + +#mod +#median +#mean + +You would use measures of central tendency (mean, median, and mode) in various situations in data analysis and statistics to summarize and understand the characteristics of a dataset. Here are some common scenarios when each measure is useful: + +1. **Mean**: + - Use the mean when you want to find the average value of a dataset. + - It's appropriate for data that is approximately normally distributed or symmetric, where the values are relatively evenly distributed around a central value. + - Be cautious when using the mean with data that has outliers, as outliers can significantly affect the mean. + + Example: Calculating the average test score in a class. + +2. **Median**: + - Use the median when you want to find the middle value of a dataset. + - It's robust to outliers and resistant to extreme values, making it suitable for data with outliers or skewed distributions. + - Useful when you want to understand the central value that divides the data into equal halves. + + Example: Determining the median income in a population. + +3. **Mode**: + - Use the mode when you want to find the most frequently occurring value(s) in a dataset. + - It's suitable for categorical data or discrete data with distinct categories. + - Can help identify the most common categories or values in a dataset. + + Example: Identifying the most popular flavor of ice cream in a survey. + +In practice, the choice of which measure to use depends on the nature of your data and the specific questions you want to answer: + +- If your data is roughly symmetric and free from outliers, the mean is often a good choice. +- If your data is skewed or contains outliers, the median may provide a more representative central value. +- For categorical or discrete data, the mode helps identify the most frequent category or value. + +It's also common to use a combination of these measures to gain a more comprehensive understanding of your data. Additionally, visualizations such as histograms, box plots, and scatter plots can provide valuable insights into the distribution and central tendency of your data. + +```python +import numpy as np +data = [10, 15, 20, 25, 30] +mean_value = np.mean(data) +print("Mean:", mean_value) + + +# FOR MEDIAN YOU NEED TO SORTED DATA +median_value = np.median(data) +sorted_data = sorted(data) +print("Median:", sorted_data) + +from statistics import mode + +data = [10, 15, 20, 25, 20, 30] +mode_value = mode(data) +print("Mode:", mode_value) +# when you using in dataframe +#msleep['vore'].value_counts() +# statistics.mode(msleep['vore']) + +``` + +#skew +#leftskewed +#rightskewed + +![[Screenshot from 2023-12-05 08-43-58.png]] + + +![[Screenshot from 2023-12-05 08-45-14.png]] + +![[Screenshot from 2023-12-05 08-45-36.png]] + +When dealing with skewed data, whether positively skewed (right-skewed) or negatively skewed (left-skewed), the choice between using the mean or the median as a measure of central tendency depends on the specific characteristics of the data and the goals of your analysis. Here are some guidelines: + +1. **Positively Skewed Data (Right-Skewed)**: + - In a positively skewed distribution, the tail of the data points extends to the right, meaning that there are relatively few extremely high values pulling the mean to the right. + - Use the median when you want a measure of central tendency that is less affected by extreme outliers or when you want to describe the typical value for the majority of the data. + - The mean can be significantly higher than the median in positively skewed data because it is influenced by the long tail of high values. If you use the mean, be aware that it may not accurately represent the central tendency for the majority of the data. + +2. **Negatively Skewed Data (Left-Skewed)**: + - In a negatively skewed distribution, the tail of the data points extends to the left, meaning that there are relatively few extremely low values pulling the mean to the left. + - Use the median when you want a measure of central tendency that is less affected by extreme outliers or when you want to describe the typical value for the majority of the data. + - Similar to positively skewed data, the mean can be significantly lower than the median in negatively skewed data because it is influenced by the long tail of low values. If you use the mean, it may not accurately represent the central tendency for the majority of the data. + +In summary, for skewed data, it's often a good practice to report both the mean and the median, along with other summary statistics, to provide a more complete picture of the data's distribution. Additionally, visualizations like histograms or box plots can help you assess the skewness and understand the shape of the distribution, aiding in the choice of the appropriate measure of central tendency. + +#variance +# Variance +Average distance from each data point to the data's mean + +```python +import pandas as pd + +# Sample DataFrame +data = { + 'A': [10, 15, 12, 8, 14], + 'B': [25, 30, 22, 18, 27], + 'C': [7, 11, 9, 5, 10] +} + +df = pd.DataFrame(data) + +# Calculate the variance using .var() method +variance_df = df['C'].var() + +# Calculate the mean of column 'C' +mean_c = df['C'].mean() + +# Calculate the squared differences from the mean +squared_diff = (df['C'] - mean_c) ** 2 + +# Calculate the variance manually +variance_manual = squared_diff.mean() + +print("Variance for column 'C' using .var() method:", variance_df) +print("Variance for column 'C' (calculated manually):", variance_manual) + +# Compare the results +if variance_df == variance_manual: + print("The results match.") +else: + print("The results do not match.") + +``` + +# What is ddof ? +In the expression `np.var(msleep['sleep_total'], ddof=1)`, `ddof` stands for "Delta Degrees of Freedom." It is a parameter used to specify the degrees of freedom correction when calculating the variance. + +Degrees of freedom (DF) represent the number of values in the final calculation of a statistic that are free to vary. In the context of calculating the variance, degrees of freedom refer to the number of independent pieces of information used in the calculation. The concept is relevant when you are calculating sample variance, as opposed to population variance. + +Here's how `ddof` works in the context of variance calculation: + +1. **Population Variance (ddof=0)**: When you want to calculate the variance of an entire population (all available data points), you set `ddof` to 0. This is because you are using all the data points, and there are no degrees of freedom being "lost" due to estimation. + + Example: + ```python + population_var = np.var(data, ddof=0) # Calculate population variance + ``` + +2. **Sample Variance (ddof=1)**: When you are dealing with a sample (a subset of the population) and you want to estimate the variance of the entire population based on that sample, you set `ddof` to 1. This correction accounts for the loss of one degree of freedom when estimating the population variance from a sample. + + Example: + ```python + sample_var = np.var(sample_data, ddof=1) # Calculate sample variance + ``` + +In most cases, when working with sample data, you'll want to use `ddof=1` to calculate the sample variance because it provides an unbiased estimate of the population variance. It accounts for the fact that you are estimating the population variance based on a sample and adjusts the calculation accordingly. However, if you're working with a full population dataset, you can use `ddof=0` to calculate the population variance directly. + +#Standard-deviation +# Standard deviation + +Formula + +![\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}](https://www.gstatic.com/education/formulas2/553212783/en/population_standard_deviation.svg) + +| | | | +|---|---|---| +|![\sigma](https://www.gstatic.com/education/formulas2/553212783/en/population_standard_deviation_sigma.svg)|=|population standard deviation| +|![N](https://www.gstatic.com/education/formulas2/553212783/en/population_standard_deviation_N.svg)|=|the size of the population| +|![x_i](https://www.gstatic.com/education/formulas2/553212783/en/population_standard_deviation_xi.svg)|=|each value from the population| +|![\mu](https://www.gstatic.com/education/formulas2/553212783/en/population_standard_deviation_mu.svg)|=|[the population mean](https://www.google.com/search?sca_esv=587928711&q=Mean&stick=H4sIAAAAAAAAAOPgE-LQz9U3MCs3MlICs0zKCky0tLKTrfRTU0qTE0sy8_P00_KLcktzEq2gtEJmbmJ6qkJiXnF5atEjRmNugZc_7glLaU1ac_IaowoXV3BGfrlrXklmSaWQGBcblMUjxcUFt4BnESuLb2piHgBE6iKyfwAAAA&sa=X&ved=2ahUKEwjRxODGzfeCAxXTRaQEHVsSDKoQ24YFegQIHxAC)| + +#quantiles + +Quantiles are values that divide a dataset into equal-sized subsets or intervals. They help us understand the distribution of data and identify specific data points that represent certain percentiles or proportions of the data. + +Here are some common quantiles: + +- **Quartiles** divide the data into four equal parts, with three quartile values: Q1 (25th percentile), Q2 (50th percentile, or median), and Q3 (75th percentile). + +- **Percentiles** divide the data into 100 equal parts. The median is the 50th percentile (P50), and other percentiles like the 25th percentile (P25) and 75th percentile (P75) are commonly used. + +- **Deciles** divide the data into 10 equal parts, with values like the 10th decile (D10), 20th decile (D20), and so on. + +- **Quintiles** divide the data into 5 equal parts, with values like the 20th quintile (Q20), 40th quintile (Q40), and so on. + +To calculate quantiles in Python, you can use libraries like NumPy or pandas. Here's an example using NumPy: + +```python +import numpy as np + +# Sample dataset +data = [12, 15, 18, 22, 25, 30, 32, 35, 40, 45, 50] + +# Calculate quartiles (Q1, Q2, Q3) +q1 = np.percentile(data, 25) +q2 = np.percentile(data, 50) +q3 = np.percentile(data, 75) + +print("Q1 (25th percentile):", q1) +print("Q2 (50th percentile, median):", q2) +print("Q3 (75th percentile):", q3) + +# Calculate other percentiles (e.g., 10th and 90th percentiles) +p10 = np.percentile(data, 10) +p90 = np.percentile(data, 90) + +print("P10 (10th percentile):", p10) +print("P90 (90th percentile):", p90) +``` + +In this code: + +- We have a sample dataset `data` containing 11 values. + +- We use `np.percentile()` from NumPy to calculate various quantiles and percentiles of the data. You specify the desired percentile as the second argument to the function. + +- We calculate quartiles (Q1, Q2, Q3) and percentiles (P10 and P90) in this example. You can adjust the percentiles according to your needs. + +Running this code will display the calculated quantiles and percentiles for the given dataset. Quantiles are valuable for summarizing and understanding the distribution of data, especially in statistics and data analysis. + +#outliners + +Outliers Outlier: data point that is substantially different from the others How do we know what a substantial difference is? +A data point is an outlier if: data < Q1 − 1.5 × IQR or data > Q3 + 1.5 × IQR + +In statistics, outliers are data points that are significantly different from the majority of the data in a dataset. They can be unusually high or low values compared to the rest of the data and can potentially skew statistical analyses or model results if not properly identified and handled. + +One common method for identifying outliers is using the Interquartile Range (IQR) method, which you mentioned. The IQR is a measure of the spread or variability of the middle 50% of the data. Here's how it works: + +1. **Calculate the IQR**: + - Calculate the first quartile (Q1) and the third quartile (Q3) of the dataset. + - The IQR is defined as: \[ IQR = Q3 - Q1 \] + +2. **Identify Outliers**: + - Any data point that falls below \[ Q1 - 1.5 \times IQR \] or above \[ Q3 + 1.5 \times IQR \] is considered an outlier. + +In other words, data points are considered outliers if they are more than 1.5 times the IQR away from either the lower quartile (Q1) or the upper quartile (Q3). + +Here's some Python code to identify outliers using the IQR method: + +```python +import numpy as np + +# Sample dataset (replace with your own data) +data = [12, 15, 18, 22, 25, 30, 32, 35, 40, 45, 200] + +# Calculate quartiles (Q1 and Q3) +q1 = np.percentile(data, 25) +q3 = np.percentile(data, 75) + +# Calculate IQR +iqr = q3 - q1 + +# Define lower and upper bounds for identifying outliers +lower_bound = q1 - 1.5 * iqr +upper_bound = q3 + 1.5 * iqr + +# Identify outliers +outliers = [x for x in data if x < lower_bound or x > upper_bound] + +print("Outliers:", outliers) +``` + +In this code: + +- We calculate the first quartile (Q1) and third quartile (Q3) using `np.percentile()`. + +- We calculate the IQR as the difference between Q3 and Q1. + +- We define the lower and upper bounds for identifying outliers as per the IQR method. + +- We identify outliers by iterating through the data and checking if each data point falls outside the defined bounds. + +Running this code will identify and print the outliers in the given dataset. Outliers are important to be aware of because they can have a significant impact on statistical analyses and may require special treatment in data analysis and modeling processes. + +``` +pandas dataframe +In [1]: + +food_consumption.head() + +Out[1]: + +Unnamed: 0 country food_category consumption co2_emission 0 1 Argentina pork 10.51 37.20 1 2 Argentina poultry 38.66 41.53 2 3 Argentina beef 55.48 1712.00 3 4 Argentina lamb_goat 1.56 54.63 4 5 Argentina fish 4.36 6.96 +``` +```python +# Calculate the quartiles of co2_emission + +print(np.quantile(food_consumption['co2_emission'], [0, 0.25, 0.5, 0.75, 1])) + + +``` + diff --git a/content/imgs/Screenshot from 2023-12-05 08-43-58.png b/content/imgs/Screenshot from 2023-12-05 08-43-58.png new file mode 100644 index 0000000000000000000000000000000000000000..77dea177bf12428cebd878dc5e13673a9fcee837 GIT binary patch literal 72262 zcmd?RWmH>T)HRArp}3YpC|(>|+)4?hNRi_1?(S0DDWw657fNvp#oZ}d+zIX$+_@*u z`+ej7zT?WDn-NAxa?UtyamLZU^I 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