A continuous right-skewed statistical distribution also Known as Snedecor’s F distribution or the Fisher - Snedecor distribution ( After R.A. Fisher and George W. Snedecor)(2) which arises in the testing of whether two observed samples have the same variance. (1) Note that three of the most important distributions (namely the normal distribution, the t distribution, and the chi-square distribution) may be seen as special cases of the F distribution: (3)

Example: We want to measure the monthly sales volume from Microsoft and Apple. We collect data for a year ( 12 months). We calculate the variance for both and define the “degrees of freedom’ (n-1= 11) and then we can build the F-distribution.

F statistic ():
Defined as the ratio of the dispersions of the two distributions, in other words it is the value calculated by the ratio of two sample variances . F always >=1. The F statistic can test the null hypothesis: (1) that the two sample variances are from normal populations with a common variance; (2) that two population means are equal; (3) that no connection exists between the dependent variable and all or some of the independent variables. |

Where and be independent variates distributed as chi-squared with and degrees of freedom. Example: We want to measure the monthly sales volume from Microsoft and Apple. We collect data for a year ( 12 months). We calculate the variance for both and define the “degrees of freedom’ (n-1= 11) . Then we calculate F= (V² (M) /m)/ V²(A)/a, where V(M) variance for Microsoft, V(A) variance for Apple and m,a degrees of freedom for Microsoft and Apple respectively.

Chi-square Distribution:
The distribution of the sum of the squares of a set of variables, each of which has a normal distribution and is expressed in standardized units. It consist in a family of curves based on he number of degrees of distribution and is denoted by the symbol , which is pronounced "Ky square". More precisely, and...

...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...

...Statistics 1
Business Statistics
LaSaundra H. – Lancaster
BUS 308 Statistics for Managers
Instructor Nicole Rodieck
3/2/2014
Statistics 2
When we hear about business statistics, when think about the decisions that a manager makes to help make his/her business successful. But do we really know what it takes to run a business on a statistical level? While some may think that businessstatistics is too much work because it entails a detailed decision making process that includes calculations, I feel that without educating yourself on the processes first you wouldn’t know how to imply statistics. This is a tool managers will need in order to run a successful business. In this paper I will review types of statistical elements like: Descriptive, Inferential, hypothesis development and testing and the evaluation of the results. Also I will discuss what I have learned from business statistics.
My description of Descriptive statistics is that they are the numerical elements that make up a data that can refer to an amount of a categorized description of an item such as the percentage that asks the question, “How many or how much does it take to “ and the outcome numerical amount. According to “Dr. Ashram’s Statistics site” “The quantities most commonly used to measure the dispersion of the...

...What are the characteristics of a population for which a mean/median/mode would be appropriate? Inappropriate?
The analysis of data begins with descriptive statistics such as the mean, median, mode, range, standard deviation, variance, standard error of the mean, and confidence intervals. These statistics are used to summarize data and provide information about the sample from which the data were drawn and the accuracy with which the sample represents the population of interest. The mean, median, and mode are measurements of the “central tendency” of the data. The range, standard deviation, variance, standard error of the mean, and confidence intervals provide information about the “dispersion” or variability of the data about the measurements of central tendency.
MEASUREMENTS OF CENTRAL TENDENCY The appropriateness of using the mean, median, or mode in data analysis is dependent upon the nature of the data set and its distribution (normal vs non-normal). The mean (denoted by x) is calculated by dividing the sum of the individual data points (where Σ equals “sum of”) by the number of observations (denoted by n). It is the arithmetic average of the observations and is used to describe the center of a data set.
mean=x= One of the most basic purposes of statistics is simply to enable us to make sense of large numbers. For example, if you want to know how the students in your school are doing in the statewide...

...POINT MEASURE (Quartiles, Deciles, Percentiles)
Quartiles
The term quartile is derived from the word quarter which means one fourth of something. Thus a quartile is a certain fourth of a data set. When you arrange a date set increasing order from the lowest to the highest, then you divide this data into groups of four, you end up with quartiles. There are three quartiles that are studied in statistics.
• First Quartile (Q1) →the data at the lower fourth (1⁄4) mark of the data
→ lower quartile
• Second Quartile (Q2) →the data value at the second fourth (2⁄4) mark of the data
→ median
• Third Quartile (Q3) → the data value at the third fourth (3⁄4) mark of the data
→ upper quartile
Calculating the Different Quartiles
The different quartiles can be calculated using the same method as with the median.
• First Quartile
The first quartile can be calculated by first arranging the data in an ordered list, then finding then dividing the data into two groups. If the total number of elements in the data set is odd, you exclude the median (the element in the middle).
After this you only look at the lower half of the data and then find the median for this new subset of data using the method for finding median described in the section on averages.
This median will be your First Quartile.
OR
Using a formula you can locate the position of the First Quartile (Q1) as:
(Q1)position = 1 (n+1)
4
• Second Quartile...

...Kolmogorov-Smirnov test (Chakravart, Laha, and Roy, 1967) is used to decide if a sample comes from a population with a specific distribution.
The Kolmogorov-Smirnov (K-S) test is based on the empirical distribution function (ECDF). Given N ordereddata points Y1, Y2, ..., YN, the ECDF is defined as
\[ E_{N} = n(i)/N \]
where n(i) is the number of points less than Yi and the Yiare ordered from smallest to largest value. This is a step function that increases by 1/N at the value of each ordered data point.
The graph below is a plot of the empirical distribution function with a normal cumulative distribution function for 100 normal random numbers. The K-S test is based on the maximum distance between these two curves.
Characteristics and Limitations of the K-S TestAn attractive feature of this test is that the distribution of the K-S test statistic itself does not depend on the underlying cumulative distribution function being tested. Another advantage is that it is an exact test (the chi-square goodness-of-fit test depends on an adequate sample size for the approximations to be valid). Despite these advantages, the K-S test has several important limitations:
1. It only applies to continuous distributions.
2. It tends to be more sensitive near the center of the distribution than at the tails.
3. Perhaps the most serious limitation is that the...

...Major Statistics Assignment
Mary Grace Rivero
050853639
CNUR860-011
Vaska Micevski
Friday, March 30, 2012
Major Statistics Assignment
This major statistics assignment will finally pull together everything that was learned in this course. The application of all content within this course will be incorporated to three different research scenarios. Within each scenario, hypothesis testing will be done, followed by a discussion of relevant descriptive statistics and finally, a discussion of the findings which includes nursing practice implications and research implications.
Research Scenario #1
In this research scenario, the researchers were interested in the following research question: “Is there a difference in nurses’ abilities to identify nursing skills that reflect knowledge of client centered care values of A) respect and human dignity B) consistency, continuity and timelessness of care or C) patient autonomy, patient voice and patient as decision maker.” To answer this research question, a hypothesis testing will be conducted followed by a discussion of the findings. The discussion of the findings will include a discussion of descriptive statistics, followed by nursing and research implications.
Hypothesis Testing
Step 1. The first step in hypothesis testing is to state the null and research hypothesis. The null hypothesis can be: “There is no difference in the nurse’s abilities...

...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 characteristics of the population.
In Chapter 5 we look at the topic of regression analysis which is used to study relationships
between variables.
In Chapter 6 we...

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