This website uses cookies to ensure you have the best experience.

Descriptive Statistics Essay

1071 words - 5 pages

Chapter 2: Descriptive Statistics

Prerequisite: Chapter 1

2.1 Review of Univariate Statistics

The central tendency of a more or less symmetric distribution of a set of interval, or higher, scaled scores, is often summarized by the arithmetic mean, which is defined as

[pic]. (2.1)

We can use the mean to create a deviation score,

[pic] (2.2)

so named because it quantifies the deviation of the score from the mean.

Deviation is often measured by squaring, since it equates negative and positive deviations. The sum of squared deviations, usually just called the sum of squares, is given by

[pic] (2.3)

Another method of calculating the sum of squares was ...view middle of the document...

7)

You might note that here we are beginning to see some of the advantages of matrix notation. For example, look at the second line of the above equation. The piece 1'X expresses the operation of adding each of the columns of the X matrix and putting them in a row vector. How many more symbols would it take to express this using scalar notation using the summation operator (?

The mean vector can then be used to create the deviation score matrix, as below.

[pic] (2.8)

We would say of the D matrix that it is column-centered, as we have used the column means to center each column around zero.

Now lets reconsider the matrix X'X. This matrix is known as the raw, or uncorrected, sum of squares and cross products matrix. Often the latter part of this name is abbreviated SSCP. We will use the symbol B for the raw SSCP matrix:

[pic]. (2.9)

In addition, we have seen this matrix expressed row by row and column by column in Equations (1.26) and (1.27). The uncorrected SSCP matrix can be corrected for the mean of each variable in X. Of course, it is then called the corrected SSCP matrix at that point:

A = D(D (2.10)

A[pic] (2.11)

Note that Equation (2.10) is analogous to the classic statement of the sum of squares in Equation (2.3) while the second version in Equation (2.11) resembles the hand calculator formula found in Equation (2.4). The correction for the mean in the formula for the corrected SSCP matrix A can be expressed in a variety of other ways:

[pic]

Now, we come to one of the most important matrices in all of statistics, namely the variance-covariance matrix, often just called the variance matrix. It is created by multiplying the scalar 1/(n-1) times A, i. e.

[pic] (2.12)

This is the unbiased formula for S. From time to time we might have occasion to see the maximum likelihood formula which uses n instead of n - 1. The covariance matrix is a symmetric matrix, square, with as many rows (and columns) as there are variables. We can think of it as summarizing the...

Other Papers Like Descriptive Statistics

643 words - 3 pages Descriptive Statistics Introduction This week’s team assignment is to collect the team member’s descriptive statistics for week four incorporating the best elements into one team data analysis paper, including data and charts. Descriptive Statistics The research topic for this paper is “McDonald’s is Closing Hundreds of Stores.” As part of the research a sample size of 400 was selected to ensure accuracy of results based on the

521 words - 3 pages , military, and many other fields. There are different types of statistics that are used for different purposes, and this paper will discuss them. Different Types and Levels of Statistics Though statistics is usually used as a general term, there are two forms of statistics, which are descriptive and inferential statistics. Descriptive statistics is the analysis of data shows, describes, or summarizes data in a way that show a pattern. The second type of

Res/351

670 words - 3 pages death. But with Cardiovascular research the differences of BMI, overweight and underweight all determining factors on the causes of the primers. As well as diet to play a major role in helping with the research. With the differences in descriptive statistics and inferential, the descriptive in the Cardiovascular research compares in a more mathematical way of determining if the diet, BMI, overweight and underweight determine their health

Research Methods Including Strengths and Weaknesses

1793 words - 8 pages complex computations such as determining factors or interaction effects within a complex data set. There are two major branches of statistics, each with specific goals and specific formulas. The first, descriptive statistics refers to the analysis of data of an entire population. In other words, descriptive statistics is merely using numbers to describe a known data set. The term population means we are using the entire set of possible

Understanding Business Research Terms and Concepts Part 2

1675 words - 7 pages Understanding Business Research Terms and Concepts: Part 2 Justin Wilson RES 351 Business Research 31 Mar 2015 Biman Ghosh Descriptive statistics is the term given to the analysis of data that helps describe, show or summarize data in a meaningful way such that, for example, patterns might emerge from the data. Descriptive statistics do not, however, allow us to make conclusions beyond the data we have analysed or reach conclusions

Quantitative Methods And Analysis Ip U1

891 words - 4 pages , cat two weighs fifteen pounds. In this situation, the descriptive statistics are relatively useless when calculating gender (the qualitative data). The mean, mode, standard deviation and count are important in the quantitative data analysis because these types of statistical information hold value in the decision-making process. These statistics give the company a clear understanding of where their employees’ intrinsic job satisfaction lies

Unit 4 Assingment Ps220

269 words - 2 pages ! ------------------------------------------------------------------------------------------------------- Unit 4 Discussion board: Descriptive statistics Identify your data The data set that I am using is data set one male health exam. The quantitative variable you will be analyzing is cholesterol. Explain the variable The selected variable measures the Cholesterol (in MG) of each male in the exam. Present descriptive statistics

Statistics

578 words - 3 pages , descriptive and inferential statistics. Discriptive statistics are the methods of organizing, summarizing and presenting data in an informative way. Inferential statistics (also known as statistical inference) are the methods used to estimate a property of a population on the basis of a sample. There are two variables/attributes involved in statistics, qualitative and quantitative. Qualitative variables are when the characteristics being

Qualitative Methods and Analysis

1221 words - 5 pages Unit 1 - Fundamentals of Statistics Abstract This document will study AIU (American Intellectual Union) statistical data practicing one part of qualitative data and one part of quantitative data. It will explain the steps of gaining the outcome and provide the end user in company of visuals that will assist the understanding of the statistical data. . Introduction Descriptive statistics is able to possess countless

Spss

340 words - 2 pages labels Analyze Classify Hierarquical Cluster Variables (s) Label Cases by Cluster * Cases Display * Statistics * Plots Statistics * Agglomeration schedule * Proximity matrix * None Plots * Dendogram * None Method * Nearest neighbor * Interval – Squared Euclidean distance * None Save * Single solution – Number of cluesters Analyze – Descriptive – Explore * Dependent List * Factor

Why Statistics Needed in Education Especially in Research

1000 words - 4 pages subsequently recorded, and, for statisticians, ‘data’ usually refers to quantitative data that are numbers In very broad terms, statistics can be divided into two branches – descriptive and inferential statistics. 1. Descriptive statistics is concerned with quantitative data and the methods for describing them. (‘Data’ (facts) is the plural of ‘datum’ (a fact), and therefore always needs a plural verb.)This branch of statistics is the one

Related Essays

Descriptive Statistics Essay

4210 words - 17 pages Report Business Research Methods The third homework (about the descriptive statistics) Question 1: Explain the difference of Mobile Contents Use by gender Crosstabs Case Processing Summary | | Cases | | Valid | Missing | Total | | N | Percent | N | Percent | N | Percent | Sex * Music | 300 | 100.0% | 0 | .0% | 300 | 100.0% | Sex * Movie | 300 | 100.0% | 0 | .0% | 300 | 100.0% | Sex * DMB | 300 | 100.0% | 0 | .0% | 300

Descriptive And Inferential Statistics Essay

1251 words - 6 pages Descriptive and Inferential Statistics Statistics are all-around and used in everyday life. Statistics are used to describe how effective a medication is for a certain disorder to what the most popular color is in the United States. According to Aron, Aron, and Coups, 2009, “statistics is a method of pursuing truth. As a minimum, statistics can tell you the likelihood that your hunch is true in this time and place and with these sorts of people

Descriptive And Inferential Statistics Paper

1210 words - 5 pages Descriptive and Inferential Statistics Paper Terrance Douglas, Katie Faiman, Marika Schlindwein, Christyl Schoultz, & Samantha Sisk PSY/315 February 3, 2013 Dr. Deborah Suzzane Descriptive and Inferential Statistics Paper Have you ever noticed that we just keep moving forward? There are countless, unseen individuals who make this happen each day, but how do they operate? How do they accomplish all of this? We live in