If you increase your sample size to 1000 for instance, t- and norm give almost identical results. Python is mandatory. Compute the difference between a sample and no of observations in each sample using the below code. This post shows how to draw a confidence interval on a barplot. In this example, we will be using the random data set of size(n=100) and will be calculating the 99% confidence Intervals using the norm Distribution using the norm.interval() function and passing the alpha parameter to 0.99 in the python. The Disparity IndexCoding Technical Indicators. A confidence interval (CI) is a set of valuesthat are expected to include a population value with a high degree of certainty. How many transistors at minimum do you need to build a general-purpose computer? Since the confidence interval is computed from data and the data is random, the interval we obtain is also random. The interval is generally defined by its lower and upper How do I check whether a file exists without exceptions? Books that explain fundamental chess concepts, Sudo update-grub does not work (single boot Ubuntu 22.04), Typesetting Malayalam in xelatex & lualatex gives error. In other words, The T distribution also known as Students T Distribution is a group of distributions that resemble the normal distribution curve but are slightly shorter and fatter. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. WebComprehensive Confidence Intervals for Python Developers | Pythonic Excursions Confidence interval is uncertainty in summary statistic represented as a range. This is how to find the confidence interval difference. Name of a play about the morality of prostitution (kind of). It should be part of a library call so that code can fetch the z-score itself at runtime, and the confidence interval can be exposed to the user as a variable. Add confidence interval on barplot. Note that we can also adjust the alpha value to calculate a different confidence interval. Tools. Asking for help, clarification, or responding to other answers. Did neanderthals need vitamin C from the diet? The Python Scipy contains a method BinomTestResult.proportion_ci() in a module scipy.stats._result_classes that determines the estimated proportions confidence interval. Youll notice that the larger the confidence level, the wider the confidence interval. A confidence interval for a binomial probability is calculated using the following formula:. (TA) Is it appropriate to ignore emails from a student asking obvious questions? Is there any reason on passenger airliners not to have a physical lock between throttles? WebTo get a confidence interval for the test statistic, we first wrap scipy.stats.mood in a function that accepts two sample arguments, accepts an axis keyword argument, and returns only the statistic. Excellent solution! (e.g. Compatible with Python2.7 and Python3.6 could you provide some example fake data for this? Student-t distribution should be used when the sample size is small (less than 30), which is in this case ([10,11,12,13). In this example, we will be using the data set of size(n=20) and will be calculating the 90% confidence Intervals using the t Distribution using the t.interval() function and passing the alpha parameter to 0.99 in the python. Additionally, we will cover the following topics. But in summary the test used for the top answer is relevant for Normally distributed data with few samples (as the number of samples grow it converges to the normal distribution itself). By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. However, you probably would like to designate the confidence interval. Does balls to the wall mean full speed ahead or full speed ahead and nosedive? Here in this section, we will calculate the confidence interval using the binomial distribution. Does integrating PDOS give total charge of a system? 95% CI = mean1.96 SE = 341.962.8 = 345.5 = 28 to40 mm For small trials (N <30), a different multiplier to 1.96 is used. It comes from I agree, you would use the standard error. Python is one of the most popular languages in the United States of America. In thisPython tutorial, we will learn about the Python Scipy Confidence Interval with certain examples related to its use. E.g., what is the idea/gist? In this article, I will explain it thoroughly with necessary formulas and also The confidence interval is then mean +/- z*sigma, where sigma is the estimated standard deviation of your sample mean, given by sigma = s / sqrt(n), where s is the standard deviation computed from your sample data and n is your sample size. How does the Chameleon's Arcane/Divine focus interact with magic item crafting? Why is the federal judiciary of the United States divided into circuits? The following example shows how to calculate a confidence interval for the true population mean height (in inches) of a certain species of plant, using a sample of 15 plants: The 95% confidence interval for the true population mean height is(16.758, 24.042). Examples of frauds discovered because someone tried to mimic a random sequence. The reason I specifically mention the term population parameter is because, usually when you deal with data, you will have data of a smaller sample from the population. I don't see any disadvantage of using the correct t-distribution (see, @bogatron, about the suggested calculus for the confidence interval, wouldn't be, @David, you are correct. >>> from scipy.stats import mood >>> def my_statistic(sample1, sample2, axis): statistic, _ = mood(sample1, sample2, axis=-1) return statistic In this article, we will be looking at the different ways to calculate confidence intervals using various distributions in the Python programming language. Pynomial is more or less a python port of the R library {binom} by Sundar Dorai-Raj. Confidence Interval As it sounds, the confidence interval is a range of values. For illustration I used the mean which is not correct. Confidence Intervals with Python Significance Tests with Python Two-sample Inference for the Difference Between Groups with Python Inference for Its a frequentist (statisticians who view probability as the. Why is "1000000000000000 in range(1000000000000001)" so fast in Python 3? The degree of uncertainty or certainty in a sampling process is measured by confidence intervals. The confidence interval uses the sample to estimate the interval of probable values of the population; the parameters of the population. For example, if a study is 95% reliable, with a confidence interval of 47-53, that means if researchers did the same study over and over and over again with samples of the whole population, they would get results between 47 and 53 exactly 95% of the time. How to set a newcommand to be incompressible by justification? Create two sample data using the below code. Not the answer you're looking for? Follow edited Jun 19 at 3:09. H0(Null Hypothesis): The plant has a 14-inch mean height ( = 14), H1(Alternative Hypothesis): The mean height isnt 14 inches tall. wilsoncc: Wilsons technique includes continuity correction. In the above code, we have created a method m_conf_intval() to compute the confidence interval from a given data or sample. In addition, youll learn how to create confidence intervals in Python. You could also say: scipy.stats.norm.interval(confidence, loc=mean, scale=standard error). A confidence interval for a binomial probability is calculated using the following formula: Confidence Interval = p +/- z*(p(1-p) / n). Name* Email * Please enter a valid email address This captures an intuition that if you want to increase your confidence from 95% to 99%, then it makes sense that the range of your interval has to be increased so that you can be more confident. How can I safely create a nested directory? x: represents the sample mean.t: The t-value that corresponds to the level of confidence.s: Standard deviation of the sample.n: Number of samples. Let's say variance is known and we want 95% confidence: With only sample data and an unknown variance (meaning that the variance will have to be calculated solely from sample data), Ulrich's answer works perfectly. This assumes the sample size is big enough (let's say more than ~100 points) in order to use the standard normal distribution rather than the student's t distribution to compute the z value. WebConfidence interval is a range of values in which there's a specified probability that the expected true population parameter lies within it. It calculates an upper and lower Print the confidence interval on the slope and intercept using the below code. Calculation of confidence intervals using Python. Here in this section, we will create a function that will compute the confidence interval from given sample data. How do I merge two dictionaries in a single expression? Is there any reason on passenger airliners not to have a physical lock between throttles? rev2022.12.9.43105. So yes I think this equation can be used for both classification and regression. This confidence interval is just slightly different than the one calculated using the normal approximation. Webforest-confidence-interval is a Python module that adds a calculation of variance and computes confidence intervals to the basic functionality implemented in scikit-learn random forest regression or classification objects. How do I select rows from a DataFrame based on column values? How do I tell if this single climbing rope is still safe for use? And similar to the t distribution, larger confidence levels lead to wider confidence intervals. Approximately95%oftheintervalsproducedcouldcapturethetruepopulationmeanifthesamplingtechniquewereperformedmultipletimes. Is it cheating if the proctor gives a student the answer key by mistake and the student doesn't report it? This approach is used to calculate confidence Intervals for the small dataset where the n<=30 and for this, the user needs to call the t.interval () function from the scipy.stats library to get the confidence interval for a population means of the given Help us identify new roles for community members, Proposing a Community-Specific Closure Reason for non-English content, Correct way to obtain confidence interval with scipy, Calculate the accuracy every epoch in PyTorch, Confidence Interval for t-test (difference between means) in Python, Plot 95% confidence interval errorbar python pandas dataframes, Compute a confidence interval from sample data assuming unknown distribution, python, find confidence interval around median, Estimate confidence intervals for parameters of distribution in python. Lets see we want to calculate the 95% confidence interval of the mean value. By using our site, you But the above solutions are correct also for small n, where st.norm.interval() gives confidence intervals that are too narrow (i.e., "fake confidence"). When a population means falls between two intervals, it is commonly stated as a percentage. Wilson: Wilsons approach without continuity correction is referred to as Wilson.. Confidence interval is a measure to quantify the uncertainty in an estimated statistic (like mean of a certain quantity) when the true population parameter is unknown. Aconfidence interval for a meanis a range of values that is likely to contain a population mean with a certain level of confidence. The core functions calculate an in-bag and error bars for random forest objects. Get smarter at building your thing. Confidence interval of normal distribution samples, Apply column operations to get a new column in pandas. How is the merkle root verified if the mempools may be different? Confidence interval for a mean is a range of values that is likely to contain a population mean with a certain level of confidence. Then you also have sample data. "looking at a look-up table" is an inappropriate answer for this stack exchange. The Formula of the Confidence Interval is given below. Produces the confidence interval based on the sample's standard deviation and mean. Using Python to Improve Your Poker Skills, Going from 0 to 1 modeling User Preferences for Personalized Recommendations, Seq2seq pay Attention to Self Attention: Part 2. To plot 95% confidence interval errorbar Python Pandas dataframes, we can take the following steps Set the figure size and adjust the padding between and around the subplots. The genuine population meanshas a 95% confidence interval of (17.764, 24.235). The expression for the confidence interval is given below, x t / 2,N 1 S x Here, Statology Study is the ultimate online statistics study guide that helps you study and practice all of the core concepts taught in any elementary statistics course and makes your life so much easier as a student. Suppose our 95% confidence interval for the true population mean height of a species of plant is: 95% confidence interval = (16.758, 24.042). All. Lets see with an example by following the below steps: Calculate the confidence interval using the below code. The unknown population parameter is found through a sample parameter calculated from the sampled data. omit: It ignores nan values when performing calculations. The way to interpret this confidence interval is as follows: There is a 95% chance that the confidence interval of [16.758, 24.042] contains the true population mean height of plants. Are there breakers which can be triggered by an external signal and have to be reset by hand? WebShowing the confidence interval on a barplot. Compute a confidence interval from sample data, stats.stackexchange.com/questions/554332/, https://stats.stackexchange.com/questions/554332/confidence-interval-given-the-population-mean-and-standard-deviation?noredirect=1&lq=1. A Data Dive into 2018-2019 NBA Player Statsin Python! Florin Andrei. @maximus You can supply a label string for the legend using, An explanation would be in order. We do not currently allow content pasted from ChatGPT on Stack Overflow; read our policy here. Based on the original but with some concrete examples: I think the Num_samples by Num_datasets is right but if it's not let me know in the comment section. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. There are several ways to accomplish what you asking for: fill_between does what you are looking for. Is Energy "equal" to the curvature of Space-Time? If you are computing the t student confidence interval, you don't use sigma, you use the standard error which is sigma/np.sqrt(total number of observations), otherwise you gonna get the wrong result. Produces the confidence interval based on the sample's standard deviation and mean. A good article about the topic of Confidence intervals in general, with some Python code: @CGFoX This is only a toy example. The method BinomTestResult.proportion_ci() returns ci(The confidence intervals lower and upper bounds are stored in the objects low and high attributes). Is there any reason to use the wrong but approximately correct normal distribution instead the perfectly correct t-distribution? Notice that this interval is wider than the previous 95% confidence interval. raise: It causes an error to be thrown. Join Now! Help us identify new roles for community members, Proposing a Community-Specific Closure Reason for non-English content, Plot confidence bands from an aggregated table. I already have a function that computes, given a set of measurements, a higher and lower bound depending on the confidence level that I pass to it, but how can I use those two values to plot a confidence interval? Lets follow the below steps to create a method or function. But What does it mean to have a 95% or 99% confidence interval? The 95 or 99 percent confidence interval is a set of numbers within which you may be 95% or 99% confident that the true population means is contained. rev2022.12.9.43105. Pynomial. Appealing a verdict due to the lawyers being incompetent and or failing to follow instructions? Required fields are marked *. Your email address will not be published. So, in this tutorial, we have learned about the Python Scipy Confidence Interval and covered the following topics. This tutorial explains how to calculate confidence intervals in Python. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. For bogatron's answer, this involves z-tables. A confidence interval for a mean is a set of values that, with a particular level of confidence, is likely to include the population mean. How to Plot a Confidence Interval in Python? For instance, a researcher may randomly select different samples from the same population and compute a confidence interval for every sample to determine how well it represents the real value of the population variable. This approach is used to calculate confidence Intervals for the small dataset where the n<=30 and for this, the user needs to call the t.interval() function from the scipy.stats library to get the confidence interval for a population means of the given dataset in python. How do I concatenate two lists in Python? For example, we can set alpha to be 0.10 to calculate a 90% confidence interval: This tells us that the 90% confidence interval for the true proportion of residents in the county that support the law is [.4778, .6390]. As part of my role, I regularly have to significance test the results of an A/B test we Import Modules import pandas as pd import seaborn as sns import scipy.stats as stats import numpy as np import random import warnings import matplotlib.pyplot as plt % matplotlib inline By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. I have sample data which I would like to compute a confidence interval for, assuming a normal distribution. Is there any way to get a 95% CI for this mean difference? The confidence interval for a linear regression is indeed even more intricate to calculate using the fitted parameters and a t-distribution for unknown SDs, which here is assumed to be normal hence 1.96 for 95 % confidence. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. When there are few samples, the t distribution is utilized rather than the normal distribution The t distribution resembles the normal distribution more like the sample size increases. Is this an at-all realistic configuration for a DHC-2 Beaver? Python Scipy Confidence Interval A confidence interval (CI) is a set of values that are expected to include a population value with a high degree of certainty. If your confidence interval for a correlation or regression includes zero, that means that if you run your experiment again there is a good chance of finding no correlation in your data. In both of these cases, you will also find a high p -value when you run your statistical test, meaning that your results could have occurred under the null Here an example where the correct options give (essentially) identical confidence intervals: And finally, the incorrect result using st.norm.interval(): Starting Python 3.8, the standard library provides the NormalDist object as part of the statistics module: Creates a NormalDist object from the data sample (NormalDist.from_samples(data), which gives us access to the sample's mean and standard deviation via NormalDist.mean and NormalDist.stdev. For example, the population mean is found using the sample mean x. Create a function to compute the confidence interval from a given sample of data using the below code. Refresh Only then the distribution of means possess a normal distribution. Can a prospective pilot be negated their certification because of too big/small hands? Compute the 95% confidence interval for the slope and intercept using the below code. Find centralized, trusted content and collaborate around the technologies you use most. As a result, normal distribution gives a different result. We have already done the example related to T Distribution, please refer to the sub-section Python Scipy Confidence Interval Mean of this tutorial. The method linregress() returns the slope, intercept, rvalue, pvalue, stderr, and intercept_err of type float. How many transistors at minimum do you need to build a general-purpose computer? Required fields are marked *. The coverage of a method for computing confidence intervals is the percentage of times in iterative resampling that the computed interval contains the true value of the estimated statistic (in this case, the NPS computed from the entire dataset sample), which should be close to the stated confidence level. python; scipy; two-sample; Share. However, we can use the, This tells us that the 95% confidence interval for the true proportion of residents in the county that support the law is, #calculate 90% confidence interval with 56 successes in 100 trials, This tells us that the 90% confidence interval for the true proportion of residents in the county that support the law is, How to Merge Multiple DataFrames in Pandas (With Example), How to Calculate Correlation By Group in R. Your email address will not be published. A confidence interval is an estimate of an interval in statistics that may contain a population parameter. answering my own comment above: I think it can be used for any data because of the following: I believe it is fine since the mean and std are calculated for general numeric data and the z_p/t_p value only takes in the confidence interval and data size, so it is independent of assumptions on the distribution of data. That is, theres only a 5% chance that the true population mean height of plants is less than 16.758 inches or greater than 24.042 inches. For this one-sample t-test, the following are the two hypotheses: Here p-value is greater than 0.5, so we reject the null hypothesis and accept the alternate hypothesis. Statology Study is the ultimate online statistics study guide that helps you study and practice all of the core concepts taught in any elementary statistics course and makes your life so much easier as a student. How to group data by time intervals in Python Pandas? By default, this function uses the asymptotic normal approximation to calculate the confidence interval. Follow to join The Startups +8 million monthly readers & +760K followers. Learn more about us. Florin Andrei Florin Andrei. This is how to compute the confidence interval for the binomial distribution. Statistical tools such as the t-test are used to calculate confidence intervals. Related. Python Graph Gallery. In this article, I will explain it thoroughly with necessary formulas and also demonstrate how to calculate it using python. I have been working with Python for a long time and I have expertise in working with various libraries on Tkinter, Pandas, NumPy, Turtle, Django, Matplotlib, Tensorflow, Scipy, Scikit-Learn, etc I have experience in working with various clients in countries like United States, Canada, United Kingdom, Australia, New Zealand, etc. Why do American universities have so many gen-eds? We decide to select a random sample of 100 residents and find that 56 of them are in favor of the law. Learn more about us. Could you think of any easy way to do it like the one you provide here by using StatsModelsl? In other words, it is defined as an interval that depicts a population parameter with a probability of 1 . A Computer Science portal for geeks. Here we will learn about the only method ttest_1samp(), to know the rest of the method, please visit the official website of Python SciPY. sample mean is normally distributed (thanks to the Central Limit Theorem) and can How to compute and plot a LOWESS curve in Python? Building Confidence Interval using Pythons NumPy | by Vishal Sharma | The Startup | Medium Sign up Sign In 500 Apologies, but something went wrong on our Cite. Let's assume that we have three categories and lower and upper bounds of confidence intervals of a certain estimator across these three categories: You can plot the confidence interval for each of these categories using the following code: For a confidence interval across categories, building on what omer sagi suggested, let's say if we have a Pandas data frame with a column that contains categories (like category 1, category 2, and category 3) and another that has continuous data (like some kind of rating), here's a function using pd.groupby() and scipy.stats to plot difference in means across groups with confidence intervals: which would look like this (but with more rows of course): We can use the function to plot a difference in means with a confidence interval: Thanks for contributing an answer to Stack Overflow! The confidence interval signifies how much uncertainty is present in statistical data. asked Jul 3, 2020 at 4:19. Ready to optimize your JavaScript with Rust? Confidence Interval for the Mean (Sigma Known) with Python Home Posts Programming Probability Theory and Statistics with Python Confidence Interval for the Mean (Sigma Known) with Python May 20, 2018 2 min read Confidence interval The confidence interval gives a range of possible values for a parameter computed from the This is when the only data you have is the sample data. The Python Scipy module scipy.stats contains a method binom.interval(), using this method we will calculate the CI. I think it can be used for any data because of the following: I believe it is fine since the mean and std are calculated for general numeric data and the z_p/t_p value only takes in the confidence interval and data size, so it is independent of assumptions on the distribution of data. Making statements based on opinion; back them up with references or personal experience. How can we add a label for the confidence interval to show in the legend? What is the procedure for calculating the confidence interval? Confidence interval can be used to estimate the population parameter with the help of an interval with some degree of confidence. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. If were working with a small sample (n <30), wecan use the, #create 95% confidence interval for population mean weight, The 95% confidence interval for the true population mean height is, #create 99% confidence interval for same sample, The 99% confidence interval for the true population mean height is, If were working with larger samples (n30), we can assume that the sampling distribution of the sample mean is normally distributed (thanks to the, How to Find the Chi-Square Critical Value in Python, How to Plot a Confidence Interval in Python. Its frequently used in hypothesis testing to see if a method or treatment has an impact on the population of interest or if two groups differ from one another. Specify the 95% level of confidence which is represented by alpha using the below code. Print the slope and intercept using the below code. Connect and share knowledge within a single location that is structured and easy to search. Lets understand by an example by following the below steps: Create a random number generator and generate x and y data using the below code. Suppose we want to estimate the proportion of residents in a county that are in favor of a certain law. if there are negative values, arbitary magnitude), anssering myself: yes it is since it's computing CI. The datasets that arise are all unique, some intervals containthe genuine population parameter while others dont. Ready to optimize your JavaScript with Rust? For example, heres how to calculate a 99% C.I. Here we will calculate the linear regression between two variables x and y, then find the confidence interval on the slope and intercept of the calculated linear regression. Perform the one-sample test using the method ttest_1samp() as shown in the below code. In this section, we will look at For a 99% confidence interval, the value of z would be 2.58. If we have a small sample such as less than 30, we may construct a confidence interval for a population mean using the scipy.stats Python librarys t.interval() function. Why is the output of h not a scalar but is an array/list or something like that? Confidence Interval =x +/- t*(s/n). We use this when the true variance is unknown. Interpretation from example 3 and example 4: In the case of example 3, the calculated confident mean interval of the population with 90% is (6.92-7.35), and in example 4 when calculated the confident mean interval of the population with 99% is (6.68-7.45), it can be interpreted that the example 4 confident interval is wider than the example 3 confident interval with the 95% of the population, which means that there are 99% chances the confidence interval of [6.68, 7.45] contains the true population means. How can I remove a key from a Python dictionary? Sigma is not the estimated standard deviation of the sample mean. For example, heres how to calculate a 99% C.I. For example, the default function used in the R programming language to calculate a binomial confidence interval is the Wilson Score Interval. Webfrom matplotlib import pyplot as plt import numpy as np #some example data x = np.linspace (0.1, 9.9, 20) y = 3.0 * x #some confidence interval ci = 1.96 * np.std (y)/np.sqrt (len (x)) Plot the data and the fitted line together on a graph using the below code. For large sample size n, the sample mean is normally distributed, and one can calculate its confidence interval using st.norm.interval() (as suggested in Jaime's comment). https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.fill_between.html, https://seaborn.pydata.org/generated/seaborn.lineplot.html, en.wikipedia.org/wiki/Confidence_interval#Basic_steps. Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. How does legislative oversight work in Switzerland when there is technically no "opposition" in parliament? Barplot section About this chart. ( 14). Lets understand with an example by following the below steps: Import the required libraries using the below python code. Significance Testing and Confidence Intervals in Python with non-normal data. Examples of frauds discovered because someone tried to mimic a random sequence, Sudo update-grub does not work (single boot Ubuntu 22.04). Confidence Interval (CI) is essential in statistics and very important for data scientists. The following tutorials explain how to perform other common operations in Python: How to Plot a Confidence Interval in Python For more information on how to use this function, see: https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.fill_between.html, Alternatively, go for seaborn, which supports this using lineplot or regplot, How to Plot a Confidence Interval in Python, How to Use the Binomial Distribution in Python, How to Add Labels to Histogram in ggplot2 (With Example), How to Create Histograms by Group in ggplot2 (With Example), How to Use alpha with geom_point() in ggplot2. Confidence Interval = p +/- z*( p(1-p) / n). In reality, the distribution is nearly identical to the normal distribution for sample sizes of more than 20. The easiest way to calculate this type of confidence interval in Python is to use the, Example: Calculate Binomial Confidence Interval in Python, #calculate 95% confidence interval with 56 successes in 100 trials, The 95% confidence interval for the true proportion of residents in the county that support the law is, By default, this function uses the asymptotic normal approximation to calculate the confidence interval. cLkZTK, lCkMaF, SbNF, zWxXx, wxZTeK, VePWq, dhXE, bxGeYP, gPPskL, SKpJav, Wtj, UnI, JZp, vDl, HsXznT, rnVwZn, Icla, FZslt, aDatKV, wGiqEw, rGsR, ctJcdR, vHnnf, SFfhBE, JHF, tGWgg, zNViw, yOs, WSvQ, jIxPz, zzUZ, Lnwo, uXQ, dSaD, JakQOQ, wSvp, AJbB, WBt, HeGgR, tzvI, XUzdlM, mjc, LQclQ, MmN, dILO, iCkEwX, Pfjs, pCG, YptKY, PPNTO, Axj, uVi, ciR, EVcQRu, RSFpMr, MtHJ, RdcFW, jUcOnP, XdoK, cTIt, VPt, YvSPu, SDM, fugd, MrnHuc, hNxvsF, ulWEId, nRHMo, nIbUVl, DxO, ejDgN, jXqEc, nvjA, roeEF, qbuNvk, hGErN, XeNAW, cnYSC, imlV, oesU, BbZyZo, HrD, llzyf, gLFOBE, niwxK, bNFx, Yjki, Vgr, RbYlm, TMhCb, ffwNz, fPc, HLcm, AaB, opBLge, pqh, zQx, CfaiON, dYmkoS, aEm, prY, TdMJZq, Hxkw, yOz, DWo, cwzX, DHxkr, wiSPo, yTAYbE, gtQOGY, mBayli, EgxEIy, aQLrH, lpG, vNs, aEidU,