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Factors That AffectTransit Ridership in

Southern California

2005-2011

2012

A STATISTICAL STUDY OF EXTERNAL FACTORS, 2005-2011

SAMANTHA BEIER, ANDREW REKER, ELIZA YU, XINYU XU

UNIVERSITY OF CALIFORNIA, IRVINE PPD 204 QUANTITATIVE ANALYSIS FOR PLANNERS | Project

Submitted for Final Grade

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INTRODUCTION

For this project, we chose to explore public transportation in order to describe and better

understand the statistical relationship between the factors that may impact public transit ridership

in Southern California. The geographical scope of our study focuses on the Los Angeles

Combined Metropolitan Statistical Area (CMSA) including: Los Angeles, Orange, Riverside,

San Bernardino, and Ventura counties. We have chosen to explore transit ridership because the

maximized utilization of public transit is often considered to be a form of social welfare and may

be associated with positive change and well being at the community level.

We have analyzed multiple variables using monthly data from January 2005 until December

2011, such as, non-farm employment levels, average unleaded gasoline price, and precipitation.

We hypothesize that there is a relationship between public transit ridership and these variables.

In addition, we hypothesize that there is a difference in public transit ridership when comparing

the categories of school and non-school months. Due to limitations such as our regional scope,

the presence of a large number of transit agencies in this region, and the availability of applicable

data, we will not be analyzing internal factors of transit ridership such as fare rates or the

quantity or quality of public transit service.

Income is a contributing factor we believe can possibly explain transit riderships increase or

decrease in usage in the LACMSA region. We will be analyzing income qualitatively as opposed

to quantitatively due to lack of reliable monthly data available. Annual data, collected by the

U.S. Census Bureau, will allow us to better understand how income has changed throughout this

time period throughout the combined metropolitan areas in our area of interest.

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QUALITATIVE ANALYSIS

We have identified four time-series datasets to enable us to gain some insight into our

research topic. These datasets include: unlinked transit ridership in Southern California, monthly

total precipitation in inches at the downtown Los Angeles Civic Center weather station, average

monthly price of unleaded regular gasoline in the Los Angeles metropolitan area, and the Los

Angeles-Orange County-Inland Empire-Ventura County Combined Metropolitan Statistical Area

non-farm employment.

This paper is structured to examine the relationships between transit ridership and each

factor independently. The literature on factors that affect transit ridership generally divides these

factors into two categories: internal organizational factors and external economic or societal

factors (Taylor & Fink, 2003). We seek to examine the way in which factors external to transit

operators have an effect on transit ridership, generally, economic, climatological, and seasonal

factors.

The time period we have selected for examination spans from January 2005 to December

2011 and were recorded at monthly increments. We will examine the descriptive statistics for

each of the four variables in subsequent sub-sections. Afterward, we will examine the

correlation between transit ridership and precipitation, unleaded gasoline price, and non-farm

employment, respectively. This is followed by a seasonal comparison between ridership in

summer months, here described as non-school and school months using a t-test. Descriptive

statistics for each of the variables we will be discussing may be found in the table below (Table

1).

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TABLE 1GENERAL STATISTICS FOR DATA SETS

Unlinked

Transit

Ridership in

SouthernCalifornia

Group

Id.

Summer

versusNon-

Summer

Monthly

Total Precip

in Inches at

LA CivicCenter

Unleaded

Price LA-

OC

(USD)

LA-OC-IE-VC

Combined MSA

Non-Farm

Employment

N 84 84 84 84 84

Mean 59,876,176.93 1.25 1.2268 3.04165 6,882,615.48

Median 59,915,069.50 1.00 0.3100 3.03550 6,994,200.00

Mode 51,088,939a 1 .00 2.519a 7,202,300

Std. Deviation 3,364,748.747 .436 2.21565 .577614 288,170.031

Variance 11,321,534,130,019.254

.190 4.909 .334 83,041,966,866.036

Range 16,686,804 1 11.02 2.664 730,900

Minimum 51,088,939 1 .00 1.798 6,493,100

Maximum 67,775,743 2 11.02 4.462 7,224,000

Percentile 25 57,962,155.25 1.00 .0000 2.57475 6,551,825.00

50 59,915,069.50 1.00 .3100 3.03550 6,994,200.00

75 62,009,243.50 1.75 1.6250 3.33875 7,162,975.00

a. Multiple modes exist. The smallest value is shown

VARIABLE 1: Transit Ridership

To begin the qualitative portion of our research project, we started by describing transit

ridership with respect to the number of trips made using public transportation in the Southern

California area. The dataset we selected for transit ridership is from the US DOT National

Transit Database and is a sum of all unlinked rides served by transit operators in the Los

Angeles-Orange-Riverside-San Bernardino-Ventura County Combined Metropolitan Statistical

Area, calculated monthly. We collected monthly time-series data for January 2005 to December

2011, a total of 84 months. (United States Department of Transportation National Transit

Database, 2012). The list of operators for this CMSA can be found in Appendix A.

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When looking at this dataset, we found that the public transit ridership data shows a

relatively broad range in the measures of central tendency. The range of ridership over these 84

samples is somewhat broad at 16,686,804, with a minimum value of 51,088,939 and a maximum

value of 67,773,743 (Figure 1). The standard deviation for this data is 3,364,749. This shows us

that, even though the range is seemingly broad, with the standard deviation relatively small, the

majority of the data points are expected to be tightly distributed near the mean.

FIGURE 1:MONTHLY TRANSIT RIDERSHIP 2005-2011

The mean for the ridership data is 59,876,177. When comparing the range of this data to that

of the mean, this combination indicates that there are very few outliers. The median value of the

ridership data is 59,915,069. Also, the mean and median are particularly close in value; there is

only a difference of 38,993 between the two values. With the mean, the median, standard

50

52

54

56

58

60

62

64

66

68

70

PublicTransitRidership

Millions

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deviation, and range, we expect that the distribution of data to be close to normal and that there

would not be a significant positive or negative skew when graphing this data.

To test this conclusion, we use a histogram and can confirm that monthly ridership is

distributed closely to that of a normal distribution, centering near the mean of 59,976,177 (Figure

2). The histogram in our figure also shows a line that is fitted to a theoretical normal

distribution.

FIGURE 2HISTOGRAM OF MONTHLY RIDERSHIP WITH NORMAL DISTRIBUTION FITTED

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VARIABLE 2: Unleaded Gas PricesThe next factor is gas price. In this section we describe the set of data reflecting average gas

price within the Los Angeles-Orange-Riverside-San Bernardino-Ventura County Combined

Metropolitan Statistical Area from January 2005 to December 2011. We use the monthly average

unleaded gas price, as an independent variable to study and analyze the factors that affect transit

ridership. Based upon the data summarized below, we can gauge the progression of the average

gas prices over time in order to better describe possible patterns present in the data.

FIGURE 3MONTHLY UNLEADED GASOLINE PRICE 2005-2011

The mean of the gas price is $3.042, and the median is $3.036; they are almost the same.

The range is $2.664 and the interquartile range is just $0.764. From these descriptive statistics,

we conclude that gas prices in this time period are not distributed evenly. The box plot below

shows that the median is almost in the middle between the highest price and the lowest price, but

that it is slightly closer to Q3 than to Q1. (Figure 4) Because two of the data points are extreme

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outliers, they are not included in this figure, but they are the highest prices. To better understand

this distribution, we chose to display this information using a histogram and to draw a fitted line

on the graph; it shows that the distribution of gas price follows a normal distribution curve

(Figure 5).

FIGURE 4BOX PLOT OF MONTHLY UNLEADED GAS PRICE

FIGURE 5HISTOGRAM OF MONTHLY UNLEADED GAS PRICES,FITTED NORMAL

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VARIABLE 3: Total Non-Farm Employment

The second factor we want to analyze is the number of non-farm jobs. We choose to use the

total non-farm employment, which is representative of jobs in the Combined Metropolitan

Statistical Area. The mean of non-farm employment is 6,882,615.48 with a standard deviation of

288170.03. Looking at the month-to-month employment trends, from 2005 to 2007, employment

rose positively (Figure 6). But from 2008 to 2009, there is a decrease in non-farm jobs, which is

likely a result of the deep economic crisis. After that, the economy began a recovery with

increased non-farm employment, but had regular fluctuation.

FIGURE 6MONTHLY NON-FARM EMPLOYMENT LEVELS 2005-2011

When we examine the distribution of monthly non-farm data, we see that the distribution of

the non-farm employment is not normal (Figure 7). Using both a histogram and a stem-and-leaf

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plot, we see that there are two peaks in the data: the first one at approximately 6,500,000, and the

second one at approximately 7,100,000.

FIGURE 7HISTOGRAM AND STEM-AND-LEAF OF MONTHLY NON-FARM EMPLOYMENT

LEVELS

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VARIABLE 4: Precipitation

The third factor we want to discuss is weather. Anecdotally, we see that when it is raining in

this region, many people may postpone, alter, or cancel their travel plans. Therefore, we selected

the element of precipitation to represent the condition of inclement weather that may explain

possible reasons transit riders defer or cancel their travel plans. The value of precipitation rates

fluctuated dramatically from 2005 to 2011 (Figure 8). Since Southern California is a drier

climate and is semi-arid, the values of precipitation of many months are very close to zero.

FIGURE 8MONTHLY PRECIPITATION RECORDED AT LACIVIC CENTER 2005-2011

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TABLE 2DESCRIPTIVE STATISTICS FOR MONTHLY PRECIPITATION

The mean value of precipitation is 1.227 inches, with a significantly lower median of 0.310.

Given the significantly higher mean when compared to the median, we can conclude that the

distribution is positively skewed; we have also calculated the skewedness as having a value of

2.915, showing a very significant positive skew (Figure 9).

FIGURE 9HISTOGRAM OF MONTHLY PRECIPITATION

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VARIABLE 5: Household Income

Household income in the LACMSA region is shown below in a graph to better represent this

data (Table 3). Here we can see that there is a steady increase from 2005-2008 when it peaks and

then we can see there is a decline from 2008 to 2011 with a flattening out moving from 2010 to

2011 (Figure 10). From this information we can assess that the higher the household income, the

less likely residents within LACMSA service areas are to take public transportation. The lower

the income however, the greater likelihood that LACMSA residents will choose to take public

transportation.

TABLE 3ANNUAL HOUSEHOLD INCOME IN THE LACMSA

Year Household Income

2005 $52,069

2006 $55,678

2007 $58,648

2008 $60,141

2009 $58,005

2010 $56,542

2011 $56,231

FIGURE 10ANNUAL HOUSEHOLD INCOME IN THE LACMSA

$48,000

$50,000

$52,000

$54,000

$56,000

$58,000

$60,000

$62,000

2005 2006 2007 2008 2009 2010 2011

CSA Median Household Income 2005-2011

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QUANTITATIVE ANALYSIS

Now that we have described our data more generally, we will test our hypotheses (Table 4).

First, we will test the strength of transit ridership correlations to that of: employment level,

weather, and average unleaded gasoline price. Finally, we will test for seasonality in our data,

that is, we will look to show a significant difference in transit ridership based upon groupings of

school and non-school (summer) months.

TABLE 4:RESEARCH HYPOTHESES

Hypothesis 1: Employment level, weather, and average gasoline price correlate with transitridership.

Research Hypothesis There is a correlation between the three identified factors and transitridership.

Null Hypothesis There is no correlation.

Hypothesis 2: There is a seasonal trait in transit ridership based on school year.

Research Hypothesis There is a significant difference in transit ridership means betweenschool months and non-school (summer) months.

Null Hypothesis There is no significant difference.

CORRELATION: Transit Ridership and Total Non-Farm Employment

First, we examine the relationship between public transit ridership and non-farm

employment in order to better understand the relationship between these two variables. We

calculated a correlation coefficient of 0.431, which has significance at the 0.01 level. This

correlation value of 0.431 can be interpreted as a modest positive relationship. We found that as

the quantity of people employed in non-farm jobs increased, so did the quantity of passenger

trips in transit ridership (Figure 11). There is a clear, positive correlation between these two

variables when graphing these two variables for display. While this positive correlation does

show a relationship between public transit ridership and non-farm employment, we are unable to

determine a causal relationship from this form of analysis.

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FIGURE 11: CORRELATION OF TRANSIT RIDERSHIP AND NON-FARM EMPLOYMENT,2005-

2011

CORRELATION: Transit Ridership and Precipitation

In order to better understand the relationship between transit ridership and that of weather

patterns, we will be using precipitation (in inches) as a way of characterizing weather conditions

during any given month. For this analysis, we ran a correlation of these two variables in order to

better understand this relationship. When calculating the correlation of these two variables, we

found that there is a correlation of -0.589, which is significance at the 0.01 level and indicates a

moderate negative relationship. We found that as the average precipitation (in inches) increases,

the quantity of passenger trips in transit ridership tends to decrease (Figure 12). When graphed,

there is a relatively clear negative correlation between these two variables. While this negative

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correlation does show a relationship between public transit ridership and precipitation, we are

unable to determine a causal relationship from this form of analysis.

FIGURE 12: CORRELATION OF TRANSIT RIDERSHIP AND PRECIPITATION,2005-2011

CORRELATION: Transit Ridership & Gas Prices

We examined the influence of gas price on transit ridership by calculating a Pearsons

correlation statistic between ridership and the average price of unleaded gasoline within the

LACMSA. The correlation statistic for these two variables is 0.334 with a p-significance of

0.001. This correlation is meaningful as it is under the p-critical value of 0.05 (Table 5). The

correlation statistic also shows that there is a weak positive correlation between unleaded

gasoline price and transit ridership.

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TABLE 5TRANSIT RIDERSHIP &GAS PRICE CORRELATION TEST RESULT

Correlation p-significance n0.334 0.001 84

An alternative way of representing this relationship is to use a graph (Figure 13). A graph to

test for relationship between gasoline price and transit ridership would have gasoline price on the

x-axis and the transit ridership on the y-axis. Each point on the graph would represent one

particular month in our data set. The x-value would reflect the average gas price for a given

month while the y-value would reflect the transit ridership during that same month. The 84

points (n=84) would then be plotted and a line of best fit is plotted for reference. When rendered

for our data, the graph showed that there is a weak positive correlation between our two variables

indicating that as gas price increases, on average, so would public transit ridership.

FIGURE 13: CORRELATION OF TRANSIT RIDERSHIP AND PRECIPITATION,2005-2011

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T-TEST: Transit Ridership & School Status

For our next test, we sought to explain differences in transit ridership as it relates to school

status, here categorized as school and non-school months. We hypothesize that during the

academic school year there is an increase in transit ridership in the Los Angeles CMSA when

compared to non-school (summer) months. We have categorized school months to include

months September through May and non-school months to include months June through August

based on the public school academic calendar in the LA CMSA region.

To test this hypothesis, we used independent samples T-test in SPSS to help us analyze how

school and non-school status affect transit ridership (Figure 14). We assigned a group ID for

school and non-school categories for the purposes of this test. They were assigned the ID number

of 1 and 2, respectively.

FIGURE 14: SCHOOL SEASONALITY -INDEPENDENT SAMPLES T-TEST RESULTS

From the results of this T-test, we can conclude that there is no significant difference in

transit ridership between school and non-school months. This is seen in the p-value labeled as

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Sig (2-tailed) in our table, which has a value of greater than 0.05. This value means that the

variance in means of transit ridership between school and non-school months not statistically

different in both groups. Therefore, we fail to reject the null hypothesis, as there is no significant

difference between these two groups. Looking at the group-level descriptive statistics between

the two groups, both groups means are very close to each other as well as overlapping ranges.

This further reinforces the conclusion of the t-test (Table 6).

TABLE 6:SCHOOL AND NON-SCHOOL STATUS IN CORRELATION WITH TRANSIT RIDERSHIP

IN THE LA-CMSAREGION

Group 1 (School) Group 2 (Non-

school)

N Valid 63 21Mean 59,495,727.59 61,017,524.95Median 59,557,368.00 60,326,975.00Mode None NoneStd. Deviation 3,546,591.19 2,483,518.28Variance 12,578,309,076,811.90 6,167,863,065,431.20Range 16,686,804.00 9,077,955.00Minimum

51,088,939.00 57,898,818.00

Maximum 67,775,743.00 66,976,773.00

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Conclusions

Our statistical analysis found some interesting conclusion in the case of our selected factors.

We found significant correlations for all of our factors; however, they were only moderately

strong. With most of these calculated correlations, we can say that no single factor is strongly

correlated to transit ridership (Table 7). Further areas for research could involve time-series

analysis with regression. In addition, a model could be created to create generalized forecasts of

transit ridership in Southern California.

TABLE 7:SUMMARY TABLE OF CORRELATIONS AND T-TEST RESULTS

Transit Ridership and Correlation Relationship

Gasoline Prices 0.334 Weak Positive

Employment Levels 0.431 Weak Positive

Precipitation -0.589 Moderate Negative

Seasonality Seasonality Not Found

Several interesting points from our data include: the relative strength of the negative

correlation between precipitation and transit ridership, compared to the other two variables we

tested for correlation was surprising. One possible explanation for this is that December is a

month that often has increased precipitation in Southern California; it is also the month that

typically has fewer workdays due to a greater number of prominent holidays and an increase in

the use of vacation days at the years end. It is the multiple factors that impact transit ridership,

both internal and external, that make transit ridership such an interesting topic for research as no

single factor can exclusively predict change.

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REFERENCES

State of California Employment Development Department. (2012). MSA Seasonal Adjusted

Total Non-farm Employment. [Data File]. Retrieved from

http://www.calmis.ca.gov/file/indhist/msa$shws.xls

Taylor, Brian D., and Camille N. Y. Fink. The Factors Influencing Transit Ridership: A Review

and Analysis of the Ridership Literature. Fall 2003, p. 681

United States Census Bureau (2005-2011). American Fact Finder. Los Angeles-Long Beach-

Riverside, CA CSA

United States Department of Labor Bureau of Labor Statistics. (2012). Consumer Price Index -

Average Price Data Los Angeles-Riverside-Orange County, CA [Data file]. Retrieved from

http://data.bls.gov/timeseries/APUA42174714

United States Department of Transportation National Transit Database. (2012). Monthly Raw

Data. [Data File]. Retrieved from

http://www.ntdprogram.gov/ntdprogram/pubs/MonthlyData/MONTHLY_RAW_DATA_10

_03_2012.xls

Western Regional Climate Center. (2012). Monthly Precipitation Los Angeles Civic Center,

California. [Data File] Retrieved from http://www.wrcc.dri.edu/cgi-

bin/cliMONtpre.pl?ca5115

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APPENDIX A Transit Operators for LA - CMSA

Santa Monica's Big Blue BusAccess ServicesAnaheim Transportation NetworkAntelope Valley Transit AuthorityCity of Arcadia TransitCity of Commerce Municipal BuslinesCity of CoronaCity of Gardena Transportation DepartmentCity of La Mirada TransitCity of Los Angeles Department of TransportationCity of Redondo Beach - Beach Cities TransitCulver City Municipal Bus LinesDAVE Transportation Services, Inc.Foothill Transit

Gold Coast TransitLaguna Beach Municipal TransitLaidlaw Transit ServicesLong Beach TransitLos Angeles County Metropolitan Transportation Authority dba: MetroMontebello Bus LinesNorwalk Transit SystemOmnitransOrange County Transportation AuthorityRiverside Transit AgencyRyder/ATE

Santa Clarita TransitSimi Valley TransitSouthern California Regional Rail Authority dba: MetrolinkSunLine Transit AgencyThousand Oaks TransitTorrance Transit SystemVentura Intercity Service Transit AuthorityVictor Valley Transit Authority