Association and Causation
Statistics is the science pertaining to the collection and analysis of data. It is the refinement of the ambiguous, the distilling of truth from the crudest of resources. For this reason, it is necessary to discern the simplest path from Point A to Point B, disregarding any unnecessary data that may lie in the path. This, however, is easier in theory than in practice, and statisticians have developed various techniques to help differentiate between causation, a variable directly related to phenomena, and association, a variable who's changes occur concurrently with the phenomena, and could be causal or non-causal.

Every morning around sunrise, the rooster crows. Does the rooster cause the sun to rise? Not likely. But, if we were to track and plot the sunrises and rooster crows every morning for a year, it would be evident that they occur concurrently. This is an association. So, then, does the sunrise cause the rooster to crow? Not necessarily. A spurious association is an association between two variables that can be better explained by a third lurking, or hidden variable. In this case, the lurking variable is territorial advertising. "Roosters crow every hour, on the hour saying, This is my coop, get the heck out of my way, don't mess with my women.' If a truck goes by, the rooster interprets the noise as that of an intrusion by another rooster. If most of the crowing takes place in early morning, it is because that is when there is the most activity." (Feldman, 1990, pp. 51-52). As you can see, association can be easily confused with causation.

Several methods have been developed to determine and analyze association. Just as the rooster and the sunset can be charted, so can other variables. When analyzing the linear relationship of these variables, the strength of their similarities is called correlation. Basically, if two variables exhibit simultaneous movement on the chart, a correlation exists. A high degree of correlation...

...techniques.
Firstly we look at data analysis. This approach starts with data that are manipulated or processed
into information that is valuable to decision making. The processing and manipulation of raw
data into meaningful information are the heart of data analysis. Data analysis includes data
description, data inference, the search for relationships in data and dealing with uncertainty
which in turn includes measuring uncertainty and modelling uncertainty explicitly.
In addition to data analysis, other decision making techniques are discussed. These techniques
include decision analysis, project scheduling and network models.
Chapter 1 illustrates a number of ways to summarise the information in data sets, also known as
descriptive statistics. It includes graphical and tabular summaries, as well as summary measures
such as means, medians and standard deviations.
Uncertainty is a key aspect of most business problems. To deal with uncertainty, we need a basic
understanding of probability. Chapter 2 covers basic rules of probability and in Chapter 3 we
discuss the important concept of probability distributions in some generality.
In Chapter 4 we discuss statistical inference (estimation), where the basic problem is to estimate
one or more characteristics of a population. Since it is too expensive to obtain the population
information, we instead select a sample from the population and then use the information in the
sample to infer the...

...Trajico, Maria Liticia D.
BSEd III-A2
REFLECTION
The first thing that puffs in my mind when I heard the word STATISTIC is that it was a very hard subject because it is another branch of mathematics that will make my head or brain bleed of thinking of how I will handle it. I have learned that statistic is a branch of mathematics concerned with the study of information that is expressed in numbers, for example information about the number of times something happens. As I examined on what the statement says, the phrase “number of times something happens” really caught my attention because my subconscious says “here we go again the non-stop solving, analyzing of problems” and I was right. This course of basic statistic has provided me with the analytical skills to crunch numerical data and to make inference from it. At first I thought that I will be alright all along with this subject but it seems that just some part of it maybe it is because I don’t pay much of my attention to it but I have learned many things. I have learned my lesson.
During our every session in this subject before having our midterm examination I really had hard and bad times in coping up with this subject. When we have our very first quiz I thought that I would fail it but it did not happen but after that, my next quizzes I have taken I failed. I was always feeling down when in every quiz I failed because even though I don’t like this...

...of 1000 flights and proportions of three routes in the sample. He divides them into different sub-groups such as satisfaction, refreshments and departure time and then selects proportionally to highlight specific subgroup within the population. The reasons why Mr Kwok used this sampling method are that the cost per observation in the survey may be reduced and it also enables to increase the accuracy at a given cost.
TABLE 1: Data Summaries of Three Routes
Route 1
Route 2
Route 3
Normal(88.532,5.07943)
Normal(97.1033,5.04488)
Normal(107.15,5.15367)
Summary Statistics
Mean
88.532
Std Dev
5.0794269
Std Err Mean
0.2271589
Upper 95% Mean
88.978306
Lower 95% Mean
88.085694
N
500
Sum
44266
Summary Statistics
Mean
97.103333
Std Dev
5.0448811
Std Err Mean
0.2912663
Upper 95% Mean
97.676525
Lower 95% Mean
96.530142
N
300
Sum
29131
Summary Statistics
Mean
107.15
Std Dev
5.1536687
Std Err Mean
0.3644194
Upper 95% Mean
107.86862
Lower 95% Mean
106.43138
N
200
Sum
21430
From the table above, the total number of passengers for route 1 is 44,266, route 2 is 29,131 and route 3 is 21,430 and the total numbers of passengers for 3 routes are 94,827.
Although route 1 has the highest number of passengers and flights but it has the lowest means of passengers among the 3 routes. From...

...compliments the regular mathematics and therefore both are tested in primary schools. Mathematics is the written application of operation. It teaches students to think clearly, reason well and strategize effectively. Mental Mathematics is the ability to utilise mathematical skills to solve problems mentally. The marks scored by pupils generate statistics which are used by teachers to analyse a student’s performance and development of theories to explain the differences in performance.
The Standard 3 class is where the transition from junior to senior level occurs where teachers expect the transference of concrete to abstract thinking would have occurred.
A common theory by many primary school teachers is ‘Students perform better in Mathematics than Mental math. Mental math is something that has to be developed and involves critical thinking. Mental math requires quick thinking and the student must solve the problem in their minds whereas in regular mathematics, the problem can be solved visually. Therefore, teachers should take these factors into consideration while testing and marking students in these areas.’
In this study, the statistics of 30 students of a standard 3 class of San Fernando Boys’ Government School will be analysed to determine the truth of this theory.
DATA COLLECTION METHODS
Mathematics and mental mathematics marks of term 1 of the class of 2013 were obtained from a Standard 3 teacher of San Fernando Boys’...

...ENMA 420/520
Statistical Processes
Mid-Term
Take Home
Due 17 March 2007
Name: Student#
You may use your course textbooks, notes and appropriate computer software (e.g., Excel) in solving the problems in this take home quiz. However, all work is to be done independently with no consultation with anyone else or with anyone else’s notes. The Old Dominion University honor system is to be strictly adhered to in the preparation of the responses to this quiz. By signing this test, I pledge that I have adhered to the Old Dominion University honor system and the requirements of this quiz.
Student signature
You have two weeks to complete this quiz: it is due prior to class on March 17th. You must email me your test response as ONE Excel file attachment to mcochran@odu.edu.
Please be sure to show all work in order to facilitate partial credit. You may use software in the process of determining the answer. However, if you do so please do not simply provide “the answer”. For example, if you use Excel, be sure all appropriate formula calculations are visible. Note that all graphs, tables and other work must be labeled to a level of professional quality. All work is to be done independently. This quiz contains 7 questions in 4 pages.
1. (13 Points) The time in days between breakdowns of two machines is exponentially distributed with a mean time between failure of 5 for machine A and 6 for machine B.
a. What is the...

...Organization of Terms
Experimental Design
Descriptive
Inferential
Population
Parameter
Sample
Random
Bias
Statistic
Types of
Variables
Graphs
Measurement scales
Nominal
Ordinal
Interval
Ratio
Qualitative
Quantitative
Independent
Dependent
Bar Graph
Histogram
Box plot
Scatterplot
Measures of
Center
Spread
Shape
Mean
Median
Mode
Range
Variance
Standard deviation
Skewness
Kurtosis
Tests of
Association
Inference
Correlation
Regression
Slope
y-intercept
Central Limit Theorem
Chi-Square
t-test
Independent samples
Correlated samples
Analysis-of-Variance
Glossary of Terms
Statistics - a set of concepts, rules, and procedures that help us to:
organize numerical information in the form of tables, graphs, and charts;
understand statistical techniques underlying decisions that affect our lives and well-being; and
make informed decisions.
Data - facts, observations, and information that come from investigations.
Measurement data sometimes called quantitative data -- the result of using some instrument to measure something (e.g., test score, weight);
Categorical data also referred to as frequency or qualitative data. Things are grouped according to some common property(ies) and the number of members of the group are recorded (e.g., males/females, vehicle type).
Variable - property of an object or event that can take on different values. For example,...

...
PRINCIPLE OF CAUSATION
Every criminal action can be divided into actus reus, mens rea and causation. Actus reus compacts with the ‘guilty act’, mens rea with the ‘guilty mind’ and the causation compacts with the consequences of the actus. In crimes, which require consequence like murder, causation is a essential and imperative element. The absence of causation between the actus and the consequence may render a verdict untenable in spite of the existence of the necessary mens rea and actus reus.
The doctrine of causation is based on the simple principle that ‘a man can only be held liable for the consequence of his own actions’. The entire doctrine is effectively based on the interpretation of a single word: ‘consequence’. A liberal definition of the word consequence extends not to only direct acts of a person but also to the acts done through innocent agents like cases of duress, or use of infants or insane people to commit crime. In the Suryanarayan Murthy case1 the court stated that IPC in itself at three instances supported transfer of malice. First, Section 299 and 300 in themselves in their wordings do not refer to the death of a specific person or the intended person. Section 299 of IPC, “Where death is caused by bodily injury, the person who causes such bodily injury shall be deemed to have caused the death, although by resorting to proper remedies and skilful treatment...

...Causation
By Manoor Yunus & Bilal Gurjee
Factual Causation
• In ‘result crimes’ a causal link must be proved between the defendants actions
•
•
•
•
and the consequence.
There are 2 types of causation 1) Factual causation 2) Legal causation
Factual causation is where something is a cause of some kind so that ‘but for’
the thing happening the consequence would not occurred.
It must be more than a tiny or trivial cause. In White (1910), where the
defendant tried to poison his mother, he was not even a factual cause because
his mother died of a heart attack before the poison could take effect
To be successful in a claim for a remedy, P needs to prove that the loss for
which he/she seeks compensation was caused in fact by the D’s wrongful act
CAUSATION-IN-FACT
• Causation in fact relates to the factor(s) or conditions
which were causally relevant in producing the
consequences
• Whether a particular condition is sufficient to be causally
relevant depends on whether it was a necessary condition
for the occurrence of the damage
• The necessary condition: causa sine qua non
Blaue, R v (1975) CA
• [Causation - novus actus inteveniens - death occurring from V’s own
actions does not break causation – think skull rule]
• D stabbed an 18-year-old woman V and punctured her lung. At the
hospital, V was told she would need a blood transfusion to...

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