This document is a pedagogical introduction to statistics for particle physics. Emphasis is placed on the terminology, concepts, and methods being used at the Large Hadron Collider. The document addresses both the statistical tests applied to a model of the data and the modeling itself. The doucment lives on GitHub and authorea; the initial arxiv version is 1503.07622.

Abstract / Executive SummaryUrban bicycle usage has gained in importance across many cities with progressive transportation policies. According to \cite{hu_more_2017}, as of this paper's publication,  "there are more than 450,000 daily bike trips in New York City, up from 170,000 in 2005, an increase that has outpaced population and employment growth".  About one in five bike trips is by a commuter. Biking serves as an important transportation option to many around the world and we argue that the need for effective bicycle lane maintenance should be a top concern for municipalities.Conventionally, street maintenance is an expensive, often inaccurate, and time intensive process that either uses subjective data prone to error or uses very precise data that is very expensive to collect citywide. There exists a clear need for cities to adopt a cost-effective and data intensive maintenance practice that can scale to the entire city and be performed frequently. These needs have been explored through the Street Quality Identification also known as the SQUID project \cite{adibhatla_digitizing_2016} to develop standardized methods for digital street inspection. This work extends the SQUID project and repurposes it for citywide bike lane measurements.In this paper, we describe the development of a data and analytics framework to measure bicycle lane quality using street imagery and accelerometer data obtained from an open source smartphone application, OpenStreetCam (OSC)  \cite{telenav_openstreetmap_nodate} . This framework can be used in crowdsourced or situated settings with the overall purpose being the standardized measurement of citywide bike lane quality.IntroductionIn recent years, bike based mobility in cities around the world has been growing rapidly. Compared to cars, bikes are cheaper, safer, more sustainable, allow for higher traffic flows, and require far less space for parking. Many city governments have invested in a permanent bike-sharing infrastructure and programs in an effort to improve transit conditions within the urban core.

ABSTRACT In this analysis, we explore whether if there is a difference between the number of CitiBike rides during the rush hours of New York City and during non-rush hours. We define the rush hours of New York City to be the hours between 7 to 9 A.M. and 4 to 9 P.M during business days. We state our hypothesis and test it using a two-sided t-test. The test indicates that there is indeed a difference.

Ozgur L. Akkas

ABOUT THIS DOCUMENT In this document I outline my ideas and goals for a handful of projects to work on over the summer (2013). The purpose is to maintain ordered thoughts and to be constructive/directed about tackling problems. I HAVE ABANDONED THESE QUESTIONS (AT LEAST FOR THE MEANTIME) TO PURSUE SOME MORE “USEFUL” WORK.

Let θ₁, θ₂…θN ∈ [0, 2π) the preferred orientations of a network of N neurons with circular Normal tuning curves and Poisson firing rates. Model input is a target orientation (θt, ct) superimposed on a mask orientation (θm, cm), where a pair (θ, c) represents an orientation θ at contrast c. Tuning response of ith neuron to a set of orientations (θj, cj): $$\lambda_i := \sum_j g \cdot c_j e^{2\kappa \cos(\theta_j)},$$ where g is the gain of the network. The Poisson response is a random sample from the Poisson distribution with λ as the mean firing rate: $$r_i \sim (\lambda_i)$$ The Poisson response acts as the input drive to divisive normalization, so we can normalized response: $$R_i^{(t)} = {\sigma^2 + \rfloor^2}}$$ Then the weights are updated based on the Hebbian learning rule: $$^{(t)} = ^{(t-1)} + \alpha (^T - )$$ where α is the Hebbian learning rate, C is the Hebbian learning homeostatis target. This feedforward network runs until tsat such that network responses are stable. We initialize the network with initial weights W(0) and a homeostatis target C. The initial weights W(0) is a uniform matrix scaled by the network’s mean tuning response to gratings that are at full contrast and each neuron’s preferred orientation. That is equivalent to the tuning response of a single neuron to a full-contrast grating at this neuron’s preferred orientation. Thus: $$^{(0)} := _{NN}}{\lambda_i(\theta = \theta_i, c=1)}$$ The homeostatis target is set to the network’s mean response product over some period t₀ to tmax to a set of orientations θ₁, θ₂…θk equally spaced within [0, 2π), normalized by the size of the network: $$ := }(\theta_1, \theta_2 \ldots \theta_k) }(\theta_1, \theta_2 \ldots \theta_k)^T / N,$$ $$} := (\theta_j) = ^{t_{max}} R_i(\theta_j)}{t_{max}},$$ where Ri(θj) is the normalized (but not Hebbian weight learned) response of ith neuron to the orientation θj from the set of equally spaced orientations. Furthermore, since the input to the time average of the normalized responses is Poisson process, the time average asymptotes to the Poisson rate λ. Thus, we could replace the time average by the asymptote for better precision and computational efficiency. That is: $$R_{ij} := \to +\infty}} = \to +\infty}(\theta_j) = \to +\infty} ^{t_{max}} R_i(\theta_j)}{t_{max}} = \to +\infty} ^{t_{max}} {\sigma^2 + )} \rfloor^2}}}{t_{max}} = {\sigma^2 + )} \rfloor^2}}$$ Here is a simple model readout that takes the normalized response of the neuron whose preferred orientation θi (pre-learning) matches target orientation θt: $$d := R_i, \theta_i = \theta_t$$ Alternatively, we could normalize that w.r.t. the total network response: $$d := {\sum }, \theta_i = \theta_t$$ Or we can weight the network response with their pre-learning sensitivity to the target: $$d := w , $$ $$ w_i := \lambda_i(\theta_t, c = 1)$$

AbstractThis study was designed to investigate the idea about Customers riders being more frequent users of citibikes on weekends proportionally to Subscribers riders. If proved so, this finding can be useful to Citibike operations team to make the user experience better and to provide better infrastructure to the riders due to a particular operation during weekends. The study was made investigating Usertype and Date data from March, 2015 and measured through z-test.

ABSTRACT New York City keeps records of Citi Bike services, including demographics of users and statistics on bike use. Here, we performed a statistical analysis to determine the relationship between biker age and trip duration, testing the alternative hypothesis that Citi Bike users under age 35 are more likely to bike for longer durations than the average user. Through a simple Z-test, we were able to reject our null hypothesis, concluding that trip duration of bikers under 35 is significantly greater than the average user. DATA For this project, our research question was: _Are Citi Bike users under 35 years of age significantly more likely bike for longer durations compared to the average user?_ For this analysis, we formed the following hypotheses: _Null Hypothesis:_ The mean trip duration of Citi Bike users under the age of 35 is the same or less than the mean trip duration of an average user, significance level = 0.05. _Alternative Hypothesis:_ The mean trip duration of Citi Bike users under the age of 35 is more than the mean trip duration of an average user, significance level = 0.05 To test these hypotheses, we chose Citi Bike data from December 2015. The information downloaded from the data facility contained more variables than needed to compare age and trip duration. Additionally, it was not organized in columns, which could led to errors, such as interpreting variable names as observations. As such, we first organized our data into columns, then dropped 13 of the 15 categories. We were left with “birth year” as our independent variable, and “trip duration” in seconds as our dependent variable. After plotting both variables, we identified several outliers of impossibly old users, i.e., those born before 1910. Plot 1 shows a scatter plot of the raw data, plotting birth year against trip duration. Histogram 1 shows the raw distribution of age across the data set. In Histogram 3, the distributions of trip duration for the entire data set (in blue) and for the group of those 35 and under (in green) are compared. ANALYSIS Our peer reviews suggested we perform a Z-test to compare the information of users under 35 and the total population. This test is possible because we know the population parameters (since dataset itself represents the entire population of Citi Bike users). Given the size of our sample, and the fact that we know the mean and standard deviation for both both groups, we chose to test our hypothesis with a Z-test. As such, we first had to calculate the mean and standard trip duration for the two groups. These values were plugged into the Z-test formula. RESULTS From our Z-test, we obtained a Z-statistic of 17.79. From the Z-Table, this gave an area of over 0.9998. Thus, our p-value is (1 - 0.9998), or 0.0002, meaning there is a 0.02% probability that the difference observed between the two groups is due to chance alone. Specifically, this p-value is much smaller than our alpha level of 0.05, meaning we can reject our null hypothesis, and can conclude that trip duration times of Citi Bike users are longer for those under age 35 compared the average user. LINK TO ORIGINAL NOTEBOOK https://github.com/jc7344/PUI2016_jc7344/blob/master/HW6_jc7344/HW6_Assignment2.ipynb

Do men take longer CitiBike trips than women?The goal of this project was to test whether men take longer CitiBike trips than women. The null hypothesis: The number of women taking longer trips on Citi Bike is the same or higher than the number of men taking Citi Bike trips.The significance level was set at 0.05.The null and alternative hypotheses could be represented with the following formulas:H0 = W(time of the trip) > = M(time of the trip)H1 = W(time of the trip) < M(time of the trip)

Co-Authors (Team)Anastasia ShegayPriyanshi SinghAaron D'SouzaVishwajeet ShelarAkshay PenmatchaAchilles Saxby

AbstractThis report aims to find whether mean trip duration of young people is longer than middle-aged people. Z-test is performed to determine whether this hypothesis is true. After performed the test, it's very likely that young people ride longer than middle-aged people.DataThe data source is citibikedata, which contains the information of people using citibikes. Columns of birth years and trip durations of the data are used. To classify young and middle-agedpeople, people whose age is between 21 to 40 are defined as young and whose age is between 40 and 59 are defined as elder.AnalysisNull hypothesis test was performed. The null hypothesis is: Total trip duration of people who are in the age of (20,40] is equal or shorter than those in the age of (40,60] in the year 2015 in NYC. (with 5% significance) The normalized total trip duration of 5 different age range is shown below. It shows each certain age range's total trip duration divided by all age ranges' total trip duration.

INTRODUCTION Our project is aimed at children growing up in NYC, by investigating the information of recreation facilities like playgrounds around zip codes zones and residential neighborhoods. Through this project we want to supply information of the playgrounds within walking distance in neighborhood units, the amounts for average children living in communities, the crime rates around the playgrounds, the transportation situation, the restaurants and schools around the playgrounds for parents to consider that when they plan to take children out.

Abstract This project intends to examine if there is any difference between male bikers and female bikers in the day and night time. More specifically, my initial hypothesis is that men are more likely to bike than women in the night time due to safety concerns. Women are more sensitive to the potential safety risks when traveling at night than men do. Data I use the information of bikers in February, 2015 as the sample for my study. The time they started biking will be the determinant of the time they biked. I divided my sample into two groups, men and women based on the gender information. The day and night times are categorized as the followings: - Day time: from 7am - 7pm - Night time: from 7pm - 7 am Based on the available data, I calculated the normalized ratios of bikers in the day and night times for each gender for illustrative graphs and statistical analysis. Analysis Data Overview The graphs below show that there may be some differences between men and women in terms of the hours they are most likely to bike. In figure 1, the fractions of men riding bike after 6pm and before 8am are higher than those of women riding bike. In figure 2, which illustrates the fraction of each gender at day and night, the fraction of female riders is higher than that of male riders at day and lower at night.

PUI2016 Citibike Project Summary ABSTRACT: In this project we looked at whether on average older individuals (over 40 years old) used Citibikes for shorter trips than younger individuals(less than 40 years old). Using information on trip duration and rider age for the month of February 2015, we ran a Z-test test for the proportions grouped by trip duration, yielding at statistic of 26.09. In this case we will reject the null hypothesis and conclude that older individuals are more willing to take shorter trips. DATA: We used the zip file on the Citibike's website corresponding to the month of February 2015. The data can be downloaded here: https://s3.amazonaws.com/tripdata/201502-citibike-tripdata.zip The corresponding .csv file contained entries for the start and stop station location, trip duration, customer type, birth year and gender of each rider during the month. We extracted age by subtracting the birth year of subscribers from the then current year 2015, and dropping all entries except trip duration and age. We split the pandas dataframe into those over and under 40 to create 2 samples. Then we divided the trip duration into two categories as short trip(less than 10 mins) and long trip(more than 10 mins) (see Figure 1). At last we normalized the distribution(see Figure 2).

Note: Throughout this paper, ‘taxis’ include green and yellow taxis and ‘other FHVs’ include all the for hire vehicles other than Uber vehicles and taxis.Abstract: For Hire Vehicles have played an important role in New York City’s transportation. With the increasing number of platforms providing these services, the number of actors in the city’s transportation network have increased, raising a wide range of concerns, including their role played in the city’s traffic congestion.   This project was chosen in light of the debate between Uber and Mayor de Blasio. For my analysis, I used the ‘Aggregate FHV Data’ which was available on FiveThirtyEight’s Github account who have been analyzing the data for the same purposes. This data contains information in the number of pick ups per day by yellow and green taxis, Uber, Lyft and the other ‘For Hire Vehicles’ in Midtown Manhattan. For my analysis of the research question – Does Uber have an impact on the Traffic congestion of the city, I performed a test of means – Z test to compare the mean of daily pick ups made by Uber vehicles to the mean of daily pick ups made by the other FHVs in Midtown Manhattan. With the calculated Z statistic, I rejected the Null Hypothesis, which proved that Uber vehicles did not lead to traffic congestion in the city (at a significance level of 0.05).  Introduction: According to an article published in the blog ‘Hot Air’ in August 2016, when Uber was launched in New York City in the year 2011, the taxi business in the city was booming, increasing the number of medallion licenses being issued. This led to an increase in the number of vehicles on the streets, resulting in traffic congestion.  In Summer 2015, New York City Mayor Bill de Blasio raised his concerns about the increase in traffic congestion due to the increasing number of ride hailing apps, most popular of them being Uber. Mayor de Blasio decided to cap the number of Uber vehicles on the streets in the city implying that the uncapped number of vehicles along with the number of taxis on the streets of the city may lead to ‘urban gridlock’ (FiveThirtyEight, October 2015).  As a result, to study this further, in January 2016, de Blasio administration released the ‘For-Hire Vehicle Transportation Study’ which highlighted that even though the number of Uber vehicles have increased in the city, they are not responsible for the increasing traffic congestion because they are replacing the yellow cabs. Similarly, a study done by FiveThirtyEight (a website involved in a number of poll analysis in the fields of politics, economics, sports etc.) performed a similar statistical test and came up with the same conclusion as the report by the Mayor’s administration.  Based on the above mentioned studies, I have attempted to answer the following research question:Does Uber have an impact on the traffic patterns in New York City? Null Hypothesis:The average number of Uber pick ups in a day on the streets in Midtown Manhattan is more than the average number of ‘For Hire Vehicles’ and taxi pick ups in a day on the streets in Midtown Manhattan.Alternate Hypothesis: The average number of Uber pick ups in a day on the streets in Midtown Manhattan is less than or equal to the average number of ‘For Hire Vehicles’ and taxi trips in a day on the streets in Midtown Manhattan. The significance level for this analysis is 0.05. To answer this question, I first specified my null and alternate hypothesis, followed by specifying the significance level. I decided to perform a Z test to answer this research question. The Z test compares the standard deviation of the expected distribution and the observed result. It tells us how many standard deviations from the mean an observation is, under the assumption of normality. The logic behind using this test will be detailed out further in the next section.  Data: To answer my research question, I needed the following information:1.     Number of Uber pick ups2.     Number of Taxi pick ups 3.     Number of other For Hire Vehicles pick upsSince Midtown Manhattan is one of the Central Business Districts of New York City, I realized that it would be a good area to analyze traffic in. I received data for the months of July, August and September 2014. I got all this information from FiveThirtyEight’s github account which had this information apart from other numbers such as:·      Average trips per Hour and day of week (Uber, Lyft and the other FHVs)·      Uber, Lyft pick ups per day within Manhattan core, LaGuardia airport and JFK (2014)·      Taxi pick ups per day within Manhattan core, LaGuardia airport and JFK (2013 and 2014)·      Change in daily Uber and Lyft trips in Manhattan Core (Sept 2014)·      Change in daily yellow taxi trips in Manhattan Core (September 2013 compared with September 2014)However, I did not need this information to answer my research question, so I dropped these columns while data wrangling. Since the document had a lot of unfilled columns and rows, I dropped them all so that I could get a clean dataframe which was good for processing the data quickly.  Methodology: To make the dataframe easy to understand, I made a new column in the dataframe which added the total number of FHVs (excluding Uber vehicles, yellow and green taxis) on the streets. Similarly, I combined both the green and yellow taxis. I also grouped the information given in groups of three (using groupby) – for the months of July, August and September – this gave me a clear look at the traffic patterns through the three months in summer 2014.I also plotted the total daily trips made by Uber, Taxis and other For Hire Vehicles everyday from July 1, 2014 to September 30, 2014 to look at the trends. 

AbstractThis report is based on my PUI Assignment 2 on Homework3 about a Citibike analysis with the python tool. The goal is to explore the Citibike trip duration difference between one-time customers and subscribers in terms of the MTP (Mean Trip Duration). The idea is that to prove that the average trip duration of single time customers is more than that of the subscribers, and further concludes that a single time customer would make better maximize the utilization than a subscriber. A hypothesis is established below. As the samples are not equal,  a further Two-sided T-test is implemented, the results support the hypothesis.Keywords: CitiBike Data, Data Wrangling, Null Hypothesis, Alternative Hypothesis, Statistical Significance Level, Two-sided t-testHypothesis Null HypothesisH0: T(customer) <= T(subscriber)The mean trip duration of single time customers over a week is less than or equal to the mean trip duration of the subscribers over a week Alternative HypothesisH1: T(customer) > T(subscriber)The mean trip duration of single time customers over a week is more than the mean trip duration of the subscribers over a week. Statistical Significance LevelSignificance level: α = 0.05A significance level alpha(α) is chosen here  to reflect how significant the hypothesis testing will be at the end of the  test. Data AnalysisThe data was collected from the CitiBike_Data_Website for the trip duration from both one-time customer and subscriber. Later, this data was used to clean, organize, select, analyze, plot and visualize. First, the Null and Alternative hypothesis were established with a statistical significance level at 0.05, and then the data was collected, tabulated, cleaned, and reshaped.The analysis is conducted by applying Pandas and DataFrames to the Python to get the mean trip duration for Customers(one-time user) and Subscribers respectively. The figures are plotted by using Matplotlib accordingly. Meanwhile, as t-test applies for testing the difference between the samples when the variances of two normal distributions are unknown, which fit in the situation,  the distribution of data is subjected to a two-sided t-test.

QUESTION Federal US circuit courts often make rulings in areas that are socially relevant to the American public, such as capital punishment, affirmative action, or racial discrimination. In this project, we seek to measure how these rulings may affect Americans' social and political attitudes. Our goal is to determine whether court rulings tend to move attitudes in the direction "intended" by the ruling or whether rulings tend to move attitudes in the opposite direction or polarize attitudes. We will focus on rulings about gender discrimination and their impact on on attitudes about gender roles. DATASETS To address this question we used two datasets. First, we used the US General Social Survey (GSS), which is a long running (1972–) survey on social attitudes and behaviors of US American citizens . In addition to social attitudes, the GSS provides demographic and life-course data about respondents. Each row represents one respondent. Second, we used a database of federal appeals court cases that were decided at the level of circuit courts . The cases were separated by issue (e.g. affirmative action, gender discrimination, racial discrimination). The federal court system is divided into 12 circuits, each of which establishes legal precedent for a group of several states. A circuit court case is decided by a randomly assigned panel of three judges chosen from the pool of judges appointed to that circuit. The dataset provides information about the outcome of each case, which is coded as the number of judges who voted in favor the outcome that can be considered to be more "progressive" (for example, pro-affirmative action, and against racial or gender discrimination). Another dataset was used to assign judge characteristics to each case . This included, for instance, the number of panel judges who were female, or who were appointed by a Democratic president. It also included the average number of female judges (and other characteristics) in the pool of judges for that circuit at the time of the ruling. For our analyses reported below, we focused of the issue of gender discrimination, and restricted ourselves to court case data pertaining to that issue. In total, we used 100 cases (one case per row) that were decided between 1995 and 2004. We chose this subset of cases because it was the subset that had the longest period of intersection with several relevant questions on the GSS.

The notion of a digital divide has been increasingly addressed by policy makers for the last two decades. In the year 2013 the Census Bureau included questions regarding internet access for the first time in the federal agency’s history. The results of the survey highlighted the situation of hundreds of thousands of low-income Americans with no computer ownership and deficient access broadband. For New York City, the American Community Survey (ACS) stressed estimates for its most vulnerable segments of the population located in all five boroughs. According to the Comptroller’s Office’ analysis of ACS results, 20% of the city’s youth and 45% of its senior population lacked broadband at home. The deficient access was concentrated in the Bronx and Brooklyn with 34% and 30% of residents lacking internet access, respectively. Aiming to address this increasing divide, Mayor Bill de Blasio announced LinkNYC program, a municipal Wi-Fi network that will eventually replace more than 7,000 phone booths with as many as 10,000 interactive kiosks with the capacity to provide New Yorkers with free high-speed internet within a 150-foot radius from each device. This project evaluates the spatial relationship between the current disposition of the self-funded LinkNYC kiosks (Links) and the areas of New York City hosting population living below poverty. Specifically, this study was designed to examine whether or not, low-income members of the community were more likely to be located in long-proximity to Links, compared to high-income segments of the population. The study was done by utilizing American Community Survey population and internet use estimates for 2015 and 2014, respectively and the LinkNYC locator provided by New York City’s open data portal. Among the findings of this project, a strong presence of Links was identified in the borough of Manhattan, with 90% of total free Wi-Fi devices installed within community districts of higher median household income and the greatest number internet subscriptions. Conversely, Brooklyn was the borough with lower median income households, the least number of internet subscriptions and had, at the time of the analysis, only two installed LinkNYC kiosks (representing less than 1% of the total installed Links). Findings indicated that population below poverty was more likely to be located at longer-distance from their nearest LinkNYC kios than their higher-income neighbors. The limitations of the linear nature measurements and results’ implications within New York City’s digital divide, however, will be explored in depth throughout the sections below.