This document discusses statistical concepts like inferential statistics, normal distributions, z-scores, t-scores, standardization, and correlations. Some key points covered include:
1. Inferential statistics helps determine if observations from a sample represent the population. It assumes the sample is similar to the population and follows a normal distribution.
2. Z-scores and t-scores are used to standardize scores from different distributions to allow comparisons. Standardization converts scores to distance from the mean in standard deviation units.
3. Scatter plots show relationships between two variables and can suggest correlations. A line of best fit indicates the direction of the relationship, whether positive or negative. Covariance and correlation coefficients measure the strength
In statistics, the standard score is the (signed) number of standard deviations an observation or datum is above the mean. Thus, a positive standard score represents a datum above the mean, while a negative standard score represents a datum below the mean. It is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing (however, "normalizing" can refer to many types of ratios; see normalization (statistics) for more).Standard scores are also called z-values, z-scores, normal scores, and standardized variables; the use of "Z" is because the normal distribution is also known as the "Z distribution". They are most frequently used to compare a sample to a standard normal deviate (standard normal distribution, with μ = 0 and σ = 1), though they can be defined without assumptions of normality.
In statistics, the standard score is the (signed) number of standard deviations an observation or datum is above the mean. Thus, a positive standard score represents a datum above the mean, while a negative standard score represents a datum below the mean. It is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. This conversion process is called standardizing or normalizing (however, "normalizing" can refer to many types of ratios; see normalization (statistics) for more).Standard scores are also called z-values, z-scores, normal scores, and standardized variables; the use of "Z" is because the normal distribution is also known as the "Z distribution". They are most frequently used to compare a sample to a standard normal deviate (standard normal distribution, with μ = 0 and σ = 1), though they can be defined without assumptions of normality.
TOPIC OUTLINE: 1. The Normal Curve
a. Definition/Description
b. Area Under Normal Curve
2. Standard Scores
a. Z-Scores
b. T-Scores
c. Other Standard Scores
Karl Friedrich Gauss:
one of the scientist that developed the concept of normal curve.
Normal Curve
is a continuous probability distribution in statistics
Karl Pearson:
first to refer to the curve as “Normal Curve”
Asymptotic:
approaching the x-axis but never touches it
Symmetric:
made up of exactly similar parts facing each other
STANDARD SCORES
-is a raw score that has been converted from one scale to another scale.
Z-scores
called a zero plus or minus one scale
Scores can be positive and negative
T-Scores
a none of the scores is negative. It can be called a 50 plus or minus ten scale. ( 50 mean set and 10 SD set )
Stanine: Standard Nine
(STAndard NINE) is a method of scaling test scores on a nine-point standard scale with a mean of five and a standard deviation of two.
Understanding the Z- score (Application on evaluating a Learner`s performance)Lawrence Avillano
Application of Z-score or standard score on evaluating a students performance. It includes the formula for z-value, interpretation of in relation to the mean and stdev, sample step by step calculation and interpretationof z-score, and sample real scenario application.
TOPIC OUTLINE: 1. The Normal Curve
a. Definition/Description
b. Area Under Normal Curve
2. Standard Scores
a. Z-Scores
b. T-Scores
c. Other Standard Scores
Karl Friedrich Gauss:
one of the scientist that developed the concept of normal curve.
Normal Curve
is a continuous probability distribution in statistics
Karl Pearson:
first to refer to the curve as “Normal Curve”
Asymptotic:
approaching the x-axis but never touches it
Symmetric:
made up of exactly similar parts facing each other
STANDARD SCORES
-is a raw score that has been converted from one scale to another scale.
Z-scores
called a zero plus or minus one scale
Scores can be positive and negative
T-Scores
a none of the scores is negative. It can be called a 50 plus or minus ten scale. ( 50 mean set and 10 SD set )
Stanine: Standard Nine
(STAndard NINE) is a method of scaling test scores on a nine-point standard scale with a mean of five and a standard deviation of two.
Understanding the Z- score (Application on evaluating a Learner`s performance)Lawrence Avillano
Application of Z-score or standard score on evaluating a students performance. It includes the formula for z-value, interpretation of in relation to the mean and stdev, sample step by step calculation and interpretationof z-score, and sample real scenario application.
Blog Planning: Using Content Trending And Social Analytics To Overcome Corpo...Beyond
Finding sufficient inspiration to fuel a daily, weekly or even monthly blog post can prove a struggle – and choosing a subject that will also attract traffic is an even tougher call. Here are some simple tips for planning a content schedule that will take the headache out of blogging.
F ProjHOSPITAL INPATIENT P & L20162017Variance Variance Per DC 20.docxmecklenburgstrelitzh
F ProjHOSPITAL INPATIENT P & L20162017Variance Variance %Per DC 2016Per DC 2017Total Number of Beds149149Maximum Occupancy55,74554,561Total Patient Days37,25037,926Actual Occupancy %ALOSDischarges by PayerMedicare/Medicaid4,9224,989Commercial Ins5,2415,099Private Pay/Bad Debt1,2801,162Total DischargesREVENUEGross Patient Revenue$ 161,325,872$ 135,365,715Contract Allowances, Uncollectables$ (84,696,083)$ (65,680,261) Net Patient RevenueMisc Income$ 378,530$ 303,233 NET REVENUEPatient Care Expenses Salaries $ 18,387,223$ 18,244,610Benefits $ 4,140,146$ 4,211,157Contract Labor $ 1,724,507$ 1,820,377Physician Contract Services$ 6,439,165$ 6,335,188Lab Services $ 1,589,648$ 1,575,808Radiology Services$ 2,336,043$ 2,343,920Rehabilitation Services$ 655,766$ 679,444General Supplies $ 653,941$ 689,766Medical Supplies $ 1,006,220$ 1,029,151Cost of Food $ 576,245$ 612,890Patient Transportation $ 35,324$ 36,031Total Patient Care ExpensesGeneral and Administrative ExpensesSalaries$ 8,450,134$ 8,629,126Benefits$ 2,001,199$ 1,993,174Contract Labor$ 157,925$ 161,015Purchased Services $ 1,285,925$ 1,355,602Medical Director $ 162,909$ 167,207Telephone$ 586,985$ 596,466Meals & Entertainment $ 254,517$ 289,185Travel$ 126,951$ 141,561General Supplies $ 332,069$ 337,874Postage$ 53,760$ 57,383Building Expense$ 2,685,376$ 2,950,379Equipment Rents $ 363,302$ 429,694Repairs and Maintenance $ 337,711$ 366,311Insurance$ 644,384$ 715,563Utilities $ 504,959$ 556,226Total General and Administrative ExpensesNet Operating Expenses NET PROFIT (LOSS) before Interest, Taxes and Depreciation (EBITDA)NET PROFIT (LOSS) %2017CASH FLOW 2016RELEVANT FINANCIAL RATIOS 2016What is your average Daily Revenue?Return on Assets (ROA)Return on Assets (ROA)Assume your AR Days are 55, what is your Total AR?Return on Equity (ROE)Return on Equity (ROE)What is your Average Daily Expense?Current RatioCurrent RatioAssume your AP Days are 35, what is your total AP?Debt RatioDebt RatioBALANCE SHEET 2016ASSETS Cash and EquivalentsAssume 45 days of ExpensesAssume 45 days of Expenses Accounts Receivable$ - 0$ - 0 Inventory All SuppliesAssume 55 days of suppliesAssume 55 days of suppliesTotal Current AssetsFixed Assets:xxxxxxxxxxxxxxxxxxxxxxxxxxxx Bldg and Equipment$ 14,700,779$14,700,779Total AssetsLIABILITIES AND EQUITYCurrent Liabilitiesxxxxxxxxxxxxxxxxxxxxxxxxxxxx Accounts Payable$ - 0$0Long Term Debtxxxxxxxxxxxxxxxxxxxxxxxxxxxx Bldg and Equipment$ 8,149,152$8,149,152Total LiabilitiesEquityTotal Liabilities and EquityITEMSPOINT VALUEOccupany Calcs2Hospital Cols B & C3Variance (2014-2013) $ and %2PPD 2013 - 20142Cash flow 20142Balance Sheet Calculations5Relevant Financial Ratios4Sub-Total20
35879 Topic: Discussion6
Number of Pages: 1 (Double Spaced)
Number of sources: 1
Writing Style: APA
Type of document: Essay
Academic Level:Master
.
Work hard to make certain that the results you have are accurate b.docxkeilenettie
Work hard to make certain that the results you have are accurate based on class material.
Use T- table and Z-table when needed.
Feel free to consult and cite the notes and previous assignments in preparing this exam.
Please show all of your working out so I am able to see your path to your answer. Mistakes will be penalized however showing your working out will allow me to deduct fewer points. If no working out is shown, I will be forced to deduct full points for mistakes.
**
.
Z table and T table are attached.
Please read carefully
!
When appropriate and possible, express your answer in the same units as the variable.
For example, if the question asks for the mean years of formal education and you have calculated the mean to be 18.44, your answer should be expressed as “
18.44 years of formal education
.”
Equations to Use
Median Position = N+1/2
The
Median Value
is the midpoint between the scores.
Mean
=
å
x
/ N
Standard Deviation =
Z score =
x – mean / standard deviation
CI =
For samples sizes ≥ 100,
the formula for the
CI
is:
CI
=
(the sample mean) + & - Z(
s / √N – 1)
CI =
For samples sizes < 100,
the formula for the
CI
is:
CI
=
(the sample mean) + & - T(
s / √N – 1)
Please answer the following questions:
You are interested in the effects of release with aftercare for a small number of drug offenders. The number of additional months without drug use for a sample
of 6 offenders
is recorded. The data on the six (6) subjects are as follows:
2
8
5
2
8
2
What are the
median position
and the
median value
?
(3 points)
What is the mean?
(
2 points)
What is the most frequently occurring score in this distribution of scores - mode?
(2 point)
2. Computation of a mode is most appropriate when a variable is measured at which level?
(2 points)
A. interval-ratio
B. ordinal
C. nominal
D. discrete
Answer: ________________________
3.
Assume that the distribution of a college entrance exam is normal with
a mean of 500 and a standard deviation of 100
.
For each score below, find the equivalent Z score, the percentage of the area above the score, and the percentage of the area below the score.
( 5 each = total 10 points)
Score Z score % Area Above % Area Below
a) 437
b) 526
4. The class intervals below represent ages of respondents. Which list is both exhaustive and mutually exclusive?
(2 points)
A. 119–120, 120–121, 121–122
B. 119–120, 121–122, 123–124
C. 119–121, 123–125, 127–129
D. 119–120, 122–123, 125–126
Answer: ______________________
5. The parole board is alarmed by the low number of years actually spent in prison for those inmates sentences to 15-year sentences. To help them make parole recommendations they gather data on the number of years served for a small sample of 7 (
seven) p
otential parolees. The number of years served for these seven parol.
O Z Scores 68 O The Normal Curve 73 O Sample and Popul.docxhopeaustin33688
O Z Scores 68
O The Normal Curve 73
O Sample and Population 83
O Probability 88
O Controversies: Is the Normal Curve
Really So Normal? and Using
Nonrandom Samples 93
• Z Scores, Normal Curves, Samples
and Populations, and Probabilities
in Research Articles 95
O Advanced Topic: Probability Rules
and Conditional Probabilities 96
O Summary 97
• Key Terms 98
O Example Worked-Out Problems 99
O Practice Problems 102
O Using SPSS 105
O Chapter Notes 106
CHAPTER 3
Some Key Ingredients
for Inferential Statistics
Z Scores, the Normal Curve, Sample
versus Population, and Probability
Chapter Outline
IMETII'M'Ir919W1191.7P9MTIPlw
0 rdinarily, psychologists conduct research to test a theoretical principle or the effectiveness of a practical procedure. For example, a psychophysiologist might measure changes in heart rate from before to after solving a difficult problem.
The measurements are then used to test a theory predicting that heart rate should change
following successful problem solving. An applied social psychologist might examine
Before beginning this chapter, be
sure you have mastered the mater-
ial in Chapter 1 on the shapes of
distributions and the material in
Chapter 2 on the mean and stan-
dard deviation.
67
68 Chapter 3
Z score number of standard deviations
that a score is above (or below, if it is
negative) the mean of its distribution; it
is thus an ordinary score transformed so
that it better describes the score's location
in a distribution.
the effectiveness of a program of neighborhood meetings intended to promote water
conservation. Such studies are carried out with a particular group of research partici-
pants. But researchers use inferential statistics to make more general conclusions about
the theoretical principle or procedure being studied. These conclusions go beyond the
particular group of research participants studied.
This chapter and Chapters 4, 5, and 6 introduce inferential statistics. In this
chapter, we consider four topics: Z scores, the normal curve, sample versus popula-
tion, and probability. This chapter prepares the way for the next ones, which are
more demanding conceptually.
Z Scores
In Chapter 2, you learned how to describe a group of scores in terms and the mean
and variation around the mean. In this section you learn how to describe a particular
score in terms of where it fits into the overall group of scores. That is, you learn how
to use the mean and standard deviation to create a Z score; a Z score describes a score
in terms of how much it is above or below the average.
Suppose you are told that a student, Jerome, is asked the question, "To what extent
are you a morning person?" Jerome responds with a 5 on a 7-point scale, where 1 =
not at all and 7 = extremely. Now suppose that we do not know anything about how
other students answer this question. In this situation, it is hard to tell whether Jerome is
more or less of a m.
35880 Topic Discussion7Number of Pages 1 (Double Spaced).docxdomenicacullison
35880 Topic: Discussion7
Number of Pages: 1 (Double Spaced)
Number of sources: 1
Writing Style: APA
Type of document: Essay
Academic Level:Master
Category: Psychology
Language Style: English (U.S.)
Order Instructions: Attached
I will attach the instruction
Please follow them carefully
Discussion3: Please discuss, elaborate and give example on the topic below. Please use only the reference I attach. Please be careful with grammar and spelling. No running head please.
Author: Jackson, S.L. (2017). Statistics Plain and Simple (4th ed.): Cengage Learning
Topic:
You find out that the average 10th grade math score, for Section 6 of the local high school, is 87 for the 25 students in the class. The average test score for all 10th grade math students across the state is 85 for 1,800 students. The standard deviation for the state is 3.8.
Answer the following questions:
· What z score do you calculate?
· What is the area between the mean and the z score found in Appendix A of the textbook?
· What does this mean about the probability of this test score difference occurring by chance? Is it
less than 0.05?
Reference
Module 9: The Single-Sample z Test
The z Test: What It Is and What It Does
The Sampling Distribution
The Standard Error of the Mean
Calculations for the One-Tailed z Test
Interpreting the One-Tailed z Test
Calculations for the Two-Tailed z Test
Interpreting the Two-Tailed z Test
Statistical Power
Assumptions and Appropriate Use of the z Test
Confidence Intervals Based on the z Distribution
Review of Key Terms
Module Exercises
Critical Thinking Check Answers
Module 10: The Single-Sample t Test
The t Test: What It Is and What It Does
Student's t Distribution
Calculations for the One-Tailed t Test
The Estimated Standard Error of the Mean
Interpreting the One-Tailed t Test
Calculations for the Two-Tailed t Test
Interpreting the Two-Tailed t Test
Assumptions and Appropriate Use of the Single-Sample t Test
Confidence Intervals Based on the t Distribution
Review of Key Terms
Module Exercises
Critical Thinking Check Answers
Chapter 5 Summary and Review
Chapter 5 Statistical Software Resources
In this chapter, we continue our discussion of inferential statistics—procedures for drawing conclusions about a population based on data collected from a sample. We will address two different statistical tests: the z test and t test. After reading this chapter, engaging in the Critical Thinking checks, and working through the problems at the end of each module and at the end of the chapter, you should understand the differences between the two tests covered in this chapter, when to use each test, how to use each to test a hypothesis, and the assumptions of each test.
MODULE 9
The Single-Sample z Test
Learning Objectives
•Explain what a z test is and what it does.
•Calculate a z test.
•Explain what statistical power is and how to make statistical tests more powerful.
•List the assumptions of the z test.
•Calculate confidence intervals usi.
35878 Topic Discussion5Number of Pages 1 (Double Spaced).docxrhetttrevannion
35878 Topic: Discussion5
Number of Pages: 1 (Double Spaced)
Number of sources: 1
Writing Style: APA
Type of document: Essay
Academic Level:Master
Category: Psychology
Language Style: English (U.S.)
Order Instructions: Attached
I will attach the instruction
Please follow them carefully
General Business Page 9
Unit 4
Due Wed 12/12
800-1,000 words / these will be turned into slides and added to your key assignment.
Study the following document: Methods for Managing Differences. Assume this communication strategy has been recommended by your employer for mediation when working with potential and existing business clients and partners.
Consider that there are basically two distinct types of cultures. One type is more cooperative, and the other is more competitive. It has been discovered that there are some conflicts occurring between some of the key players who need to come to agreement on specific critical areas of the deal for it to move forward. The top management would really like this deal to happen.
Imagine being in this situation, and create the scenario as you go through the process using the methods approach from above.
· Describe the steps you would take and any considerations along the way.
· How would you use the recommended method when working with individuals who exhibit a generally competitive culture?
· How would you use the recommended method when working with individuals who exhibit a generally cooperative culture?
· Would this cultural factor change the way you apply this method for managing differences? Why or why not? Explain.
Create Section 4 of your Key Assignment presentation: Global Negotiations. Refer to Unit 1 Discussion Board 2 for a description of this section. Submit a draft of your entire presentation for your instructor to review.
Discussion 2: Discuss, elaborate and give example on the topic below. Please use only the reference I attach. Please be careful with grammar and spelling. No running head Please.
Author: Jackson, S.L. (2017). Statistics Plain and Simple (4th ed.): Cengage Learning
Topic
Review this week’s course materials and learning activities, and reflect on your learning so far this week. Respond to one or more of the following prompts in one to two paragraphs:
1. Provide citation and reference to the material(s) you discuss. Describe what you found interesting regarding this topic, and why.
2. Describe how you will apply that learning in your daily life, including your work life.
3. Describe what may be unclear to you, and what you would like to learn.
Reference:
Module 9: The Single-Sample z Test
The z Test: What It Is and What It Does
The Sampling Distribution
The Standard Error of the Mean
Calculations for the One-Tailed z Test
Interpreting the One-Tailed z Test
Calculations for the Two-Tailed z Test
Interpreting the Two-Tailed z Test
Statistical Power
Assumptions and Appropriate Use of the z Test
Confidence Intervals Based on the z Distribution
Review of Key Term.
35881 DiscussionNumber of Pages 1 (Double Spaced)Number o.docxrhetttrevannion
35881 Discussion
Number of Pages: 1 (Double Spaced)
Number of sources: 1
Writing Style: APA
Type of document: Essay
Academic Level:Master
Category: Psychology
Language Style: English (U.S.)
Order Instructions: Attached
I will attach the instruction
Please follow them carefully
35876 Topic: Discussion3
Number of Pages: 1 (Double Spaced)
Number of sources: 1
Writing Style: APA
Type of document: Essay
Academic Level:Master
Category: Psychology
Language Style: English (U.S.)
Order Instructions: Attached
I will attach the instruction
Please follow them carefully
Discussion: Please discuss, elaborate and give example on the topic. Be careful with grammar and spelling. No running head please. Please Use only the reference I will attach as the professor will not be able to give grade.
Author: (Jackson, S. L. (2017). Statistics plain and simple. (4th ed.). Boston, MA: Cengage Learning.)
Topic
What level of measurement can be used for this test for the independent and dependent variables?
Reference:
Module 9: The Single-Sample z Test
The z Test: What It Is and What It Does
The Sampling Distribution
The Standard Error of the Mean
Calculations for the One-Tailed z Test
Interpreting the One-Tailed z Test
Calculations for the Two-Tailed z Test
Interpreting the Two-Tailed z Test
Statistical Power
Assumptions and Appropriate Use of the z Test
Confidence Intervals Based on the z Distribution
Review of Key Terms
Module Exercises
Critical Thinking Check Answers
Module 10: The Single-Sample t Test
The t Test: What It Is and What It Does
Student's t Distribution
Calculations for the One-Tailed t Test
The Estimated Standard Error of the Mean
Interpreting the One-Tailed t Test
Calculations for the Two-Tailed t Test
Interpreting the Two-Tailed t Test
Assumptions and Appropriate Use of the Single-Sample t Test
Confidence Intervals Based on the t Distribution
Review of Key Terms
Module Exercises
Critical Thinking Check Answers
Chapter 5 Summary and Review
Chapter 5 Statistical Software Resources
In this chapter, we continue our discussion of inferential statistics—procedures for drawing conclusions about a population based on data collected from a sample. We will address two different statistical tests: the z test and t test. After reading this chapter, engaging in the Critical Thinking checks, and working through the problems at the end of each module and at the end of the chapter, you should understand the differences between the two tests covered in this chapter, when to use each test, how to use each to test a hypothesis, and the assumptions of each test.
MODULE 9
The Single-Sample z Test
Learning Objectives
•Explain what a z test is and what it does.
•Calculate a z test.
•Explain what statistical power is and how to make statistical tests more powerful.
•List the assumptions of the z test.
•Calculate confidence intervals using the z distribution.
The z Test: What It Is and What It Does
The z test is a parametric statistical te.
This is my report in my Assessment II subject. I am assigned to discuss on how to interpret test scores by standard deviation unit, Z-score, T-score, Stanine, Deviation IQ and NCE.
Introduction to writing research questions and determining what variables to use. Introductory concepts for school personnel interested in action research.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
2. What we have Learned!What we have Learned!
1. Inferential statistics helps us to
determine if what we have observed in a
sample, represents a similar phenomenon
in the population.
2. The assumption is that our sample is
quite similar to the population being
studied and we operate under the premise
that we have a obtained a normal
distribution in our sample when looking
at scores of any type.
3. More…More…
3. Normal distributions have standard
deviations and are symmetrical.
4. There is a probability that we may not
have a normal distribution from our
sample (error), therefore we cannot make
inferences if that’s the case.
4. What do we do?What do we do?
A. We try to make our distributions as normal
as possible so that it represents the one in the
population.
B. When this does not happen, we rectify the
problem by utilizing other statistics that are
associated with central tendency measures.
Solutions:
z- z scores
t- family of t scores
5. What are z and t scores?What are z and t scores?
A z score is used to determine where one
particular score stands with the rest of the
scores in a distribution. Central Tendency
measures gives us parameters but not the
distance of each score from the mean.
However using the mean and the standard
deviation allows to calculate the z score.
z cores also help us to compare two individual
scores when we compare two variables.
(e.g. a Math test score and a Spelling score)
6. The Answer is : StandardizationThe Answer is : Standardization
z scores help us to standardize scores in order
to compare individual scores with different
variables.
Scores in different tests use different scales and
does not permit to compare the scores from
different distributions unless we standardize
them.
Standardization is a process of converting each
individual score into a distribution to a z score,
thus telling you how far from the means a
given score is.
7. ExampleExample
Student X has taken two exams, one in Biology
and the other in Statistics. Here are the scores
from the total number of answers in each exam.
• Biology 65 out of 100 items
• Statistics 42 out of 200 items
• Question?- In which test did student X do
better?
• What do you mean by better?
8. Let’s look at each of theseLet’s look at each of these
distributions:distributions:
Score Mean SD
Biology 65 60 10
Statistics 42 37 5
So in what test did student X perform
better?
9. What did you mean by better?What did you mean by better?
1. If I am asking the percentage of correct
answers then my obvious answer is
__________.
2. But wait a minute that is not fair, the
Statistics exam was more difficult!
3. What is the dilemma?
10. Your answer should be:Your answer should be:
A) How did Student X do in comparison to
other students?
B) We could answer this by looking at the
mean and standard deviation in each of
the two exams. They are different
distributions.
11. ConclusionsConclusions
1. Can we compare two scores if the scales are
different?
A) Depending on your answer what is the next
step?
B) Think before you answer!
12. StandardizationStandardization
You cannot compare two different scores
when the scales are different.
We need the same scale(standardization)
When we take raw scores from a test we can
convert them into standard deviation units
through the use of z scores.
Formula: z= raw score-mean
standard deviation
13. Let’s pretend thatLet’s pretend that
Student X took a spelling test and
received a 1.0 in her z score. What can you
tell from this score?
1) __________________________
2) __________________________
3) __________________________
14. Now that you know how to find a z score letsNow that you know how to find a z score lets
consider the following:consider the following:
When a distribution of scores is standardized
the average (mean) for the distribution is 0 and
the standard deviation is 1.0
What does z score tell us if a z score= -1.5
What does a z score tell us if a z score=.29
It can also tell us if:
A) An individual does better or worse than the
average person.
B) How much a score is above or below the average
C) If the score is better or worse to the rest of other
scores
15. The z scores formula depends on whether youThe z scores formula depends on whether you
are observing a population or sampleare observing a population or sample
A normal distribution that is standardized (so that it has
a mean of 0 and a SD of 1) is called the standard normal
distribution, or the normal distribution of z-scores. If we
know the mean m ("mu"), and standard deviation s
("sigma") of a set of scores which are normally
distributed, we can standardize each "raw" score, x, by
converting it into a z score by using the following
formula on each individual score:
Where x-bar and s are used as estimators for the
population's true mean and standard deviation. Both
formulas essentially calculate the same thing:
16. What is it from this scoreWhat is it from this score
that I do not know?that I do not know?
1. I don’t know of the student did better
or worse than the average score.
2. I don’t know how much the score is
below or above the mean.
3) I don’t know how relatively better or
worse this score in comparison to the rest
of those scores that are associated with the
distribution of scores from that given
Spelling Test..
17. Suppose I told you the following:Suppose I told you the following:
The average score in that Spelling test was 12
and the total items in this Spelling test was 50.
The test taker is 7 year old!
Don’t despair, statisticians have already
figured out and can predict the percentage of
scores that will fall between the mean and a z
score!
18. z scores can provide you with:z scores can provide you with:
1) determine percentile scores.
2) The mean in a z score is equal to 0.
3) From this point we can determine that
50% of scores fall on either side of the
means.
Can you explain why?
19. Figuring Out Percentiles with z scoresFiguring Out Percentiles with z scores
Step 1Step 1
The average SAT score for a white male is 517.
Suppose I want to know what score marks the
90th
percentile?
Step 1-Use the z score table. And find the z score
that marks closet to 90th
percentile. The closest is
8997. The z score is 1.28 (intersection)
So a z score of 1.28 corresponds to the 90th
percentile.
What would be a z score that represents the 75th
percentile?
20. Step 2 Convert z score to a raw scoreStep 2 Convert z score to a raw score
We know what score represents the 90th
percentile and we know the means is 517. But
we do not know the real score that marks the
90th
percentile.
X values can be changed into z-scores just as
z-scores can be changed into X values
Step 2- Convert the z score into the original unit
of measurement. We use this formula:
21. z-scores (cont.)z-scores (cont.)
The formula for changing X values into z-scores
is
X = μ + (z) (σ)
X=517 + (1.28) (100)
X=517 +128
X=645
X – μ is a standard deviation score of a z score.
22. Answer using this formula isAnswer using this formula is
X=517 + (1.28) (100)
X=517 +128
X=645
The score that marks the 90th
percentile for
white males that took the SAT score in
2008 is 647.
23. We can also use a z score toWe can also use a z score to
convert an know raw score into aconvert an know raw score into a
percentile scorepercentile score
If student X in my SAT distribution has a score
of 425 on the SAT Math test. And if I want to
know how many students scored above or
below this score? Then:
Step 1-Convert the raw score back into a z score
24. Step 1 Covert Raw Score toStep 1 Covert Raw Score to
a z scorea z score
z=425-517
100
Z= -92
100
Z= -.92
25. Step 2 Use Appendix AStep 2 Use Appendix A
Find the z score that is equivalent to .92 on the
left column moving vertically. Z scores are not
reported as negative because the scores in a
normal distribution are symmetrical. So the
proportion falling above or below is the same.
So what does the z score tell me? It tells me by
using the table that 82.12 % of scores scored
below a z score of .92. It also tells me that
17.88% of the distribution will fall beyond a z
value of .92.
26. Step 3Step 3
A z score of -.92 corresponds to a raw
score of 425 on the Sat –Math exam. A
score of 425 of this test marks the 17.88th
percentile among the distribution of white
males taking the exam in 2008.
27. z-scores (cont.)z-scores (cont.)
We are able to transform every raw score in our
distribution into a distribution of z-scores
This new distribution of z-scores will have 3 main
properties
1. It will have the same shape as the distribution of X
values (if the X distribution was normal, the z
distribution will be normal)
2. It will always have a mean of zero
3. It will always have a standard deviation of one
(example on problem
This z-score distribution is called a standardized
distribution (being standardized now enables us to
compare distributions that we weren’t able to compare
before)
28. z scores can also determine thez scores can also determine the
proportion of scores that fallproportion of scores that fall
between two scoresbetween two scores
Suppose that John received a score of 417
on the Sat Exam. His cousin Mark
received a score of 567. The Joes family
are always quarreling as to whose son is
the brightest. Mark gets smart and says to
John, “I blew you away, there must 50 %
of the students that took this test between
you and me.”
John is upset and want to show his cousin
he is wrong! What must he do?
29. Comparing Raw ScoresComparing Raw Scores
using z scoresusing z scores
The formula for changing X values into z-scores
is
z = X – μ
σ
Step 1-Convert both raw scores to z scores
417-517
100 z= -100
100 z=-1.00
31. Step 2 Using Appendix AStep 2 Using Appendix A
Find the z scores that correspond to -1.00
and .50. Appendix A tells us that .8413 of
the distribution falls below a z value of
1.00. (Remember that the means splits
both distributions by 50/50. So 50% of
scores will fall below the mean. .8413-.50,
this tells us that 34.13 % of the normal
distribution will fall below between the
mean and a z score of 1.00
32. Step 2 Continued…Step 2 Continued…
Using the same process we know that a z
score of .50 that 69.15 of the distribution
falls below a z score of .50. Thus 19.15% of
the scores fall between the mean and a z
score of .50.
Recall that one z score is positive and the
other is negative. So if we add the both
area of scores we find the total area of
these we find the total distribution of
scores between these two scores and the
answer is .34.13 + .1915+ 53.28%. John
must accept defeat!
33. You are on your own.You are on your own.
Mark has another cousin, Martin who
scored 617 in the Math Test score.
1. Determine the proportion of the
population that scored between 617 and
517?
36. Scatter PlotsScatter Plots
We can prepare a scatter plotscatter plot by placing one point for
each pair of two variables that represent an
observation in the data set. The scatter plot provides
a picture of the data including the following:
1. Range of each variable;
2. Pattern of values over the range;
3. A suggestion as to a possible relationship between
the two variables;
4. Indication of outliers (extreme points).
37. Here are the types ofHere are the types of
scatter plots you are likelyscatter plots you are likely
to see:to see:
This could show how the distance
travelled in a vehicle increases as time
increases, if the vehicle maintains a
constant speed.
This could show the increase in a
student's height as their grade
38. Scattergrams or ScatterScattergrams or Scatter
PlotsPlots
Scatter plots are used by researchers to
look for correlations. A correlation is a
relationship between the data, which can
suggest that one event may affect another
event. For example, you might want to
discover whether more hours of studying
will affect your Math mark in school. Perhaps
a scientist wants to find out if the distance
people live from a major city affects their
health.
39. X and Y AxisX and Y Axis
In order to use scatter plots in this way, you
must have two sets of numerical data. One set is
plotted on the x-axis of a graph, and the other
set is plotted on the y-axis. The resulting scatter
plot will often show at a glance whether a
relationship exists between the two sets of data.
40. ExampleExample
Relationship between hours
studying and test score
Here's an example.
Suppose you want to find
out whether more hours
spent studying will have an
affect on a person's mark.
You set up an experiment
with some people,
recording how many hours
they spent studying and
then recording what
happened to their mark.
A correlation is a relationship
between the data, which can suggest
that one event may affect another
event.
41. Seeing Patterns toSeeing Patterns to
determine Relationshipdetermine Relationship
You can see the data in the table at the
right.
It's difficult to see any pattern in the table,
although it's clear that different things
happened to different people. One person
studied for 1 hour and had their mark go
up 2%, while another person who also
studied for 1 hour saw a drop of 1%!
42. Line of Best FitLine of Best Fit
Here is the graph again. We've shown a line that
seems to describe the direction the points are
heading in. This is called the line of best fit.
47. CovarianceCovariance
The covariancecovariance is a measure of the linear relationship
between two variables. A positive value indicates a
direct or increasing linear relationship and a negative
value indicates a decreasing linear relationship. The
covariance calculation is defined by the equation
where xi and yi are the observed values, X and Y are the sample
means, and n is the sample size.
1
))((
),( 1
−
−−
==
∑=
n
YyXx
syxCov
n
i
ii
xy
48. CovarianceCovariance
Scatter Plots of IdealizedScatter Plots of Idealized
Positive and Negative CovariancePositive and Negative Covariance
X
Y
x
y
*
* *
*
*
*
*
*
*
*
*
*
*
Positive Covariance
(Figure 3.5a)
X
Y
x
y
*
* *
*
*
*
*
*
*
*
*
*
Negative Covariance
(Figure 3.5b)
50. Correlation CoefficientCorrelation Coefficient
1. The correlation ranges from –1 to +1 with,
• rxy = +1 indicates a perfect positive linear relationship – the X and
Y points would plot an increasing straight line.
• rxy = 0 indicates no linear relationship between X and Y.
• rxy = -1 indicates a perfect negative linear relationship – the X and
Y points would plot a decreasing straight line.
1.1. Positive correlationsPositive correlations indicate positive or increasing linear
relationships with values closer to +1 indicating data points
closer to a straight line and closer to 0 indicating greater
deviations from a straight line.
2.2. Negative correlationsNegative correlations indicate decreasing linear relationships
with values closer to –1 indicating points closer to a straight
line and closer to 0 indicating greater deviations from a
straight line.
51. Scatter Plots andScatter Plots and
CorrelationCorrelation
(Figure 3.6)(Figure 3.6)
X
Y
(a) r = .8(a) r = .8
52. X
Y
(b)r = -.8(b)r = -.8
Scatter Plots andScatter Plots and
CorrelationCorrelation
(Figure 3.6)(Figure 3.6)
53. Scatter Plots andScatter Plots and
CorrelationCorrelation
(Figure 3.6)(Figure 3.6)
X
Y
(c) r = 0(c) r = 0
54. Linear RelationshipsLinear Relationships
Linear relationshipsLinear relationships can be represented by the basic
equation
where Y is the dependent or endogenous variable that is a
function of X the independent or exogenous variable. The
model contains two parameters, β0 and β1 that are defined
as model coefficients. The coefficient β0, is the intercept
on the Y-axis and the coefficient β1 is the change in Y for
every unit change in X.
XY 10 ββ +=
55. Linear RelationshipsLinear Relationships
(continued)(continued)
The nominal assumption made in linear applications is
that different values of X can be set and there will be a
corresponding mean value of Y that results because of the
underlying linear process being studied. The linear
equation model computes the mean of Y for every value
of X. This idea is the basis for Pearson’s Product
Moment Coefficient in obtaining and partitioning the
relationship between variables and how much effect they
have with one another. In educational issues, there is no
56. Least Squares RegressionLeast Squares Regression
Least Squares RegressionLeast Squares Regression is a technique
used to obtain estimates (i.e. numerical
values) for the linear coefficients β0 and
β1. These estimates are usually defined
as b0 and b1 respectively.
57. Cross TablesCross Tables
Cross TablesCross Tables present the number of observations
that are defined by the joint occurrence of specific
intervals for two variables. The combination of
all possible intervals for the two variables defines
the cells in a table.
58. Key WordsKey Words
Least Squares
Estimation Procedure
Least Squares
Regression
Sample Correlation
Coefficient
Sample Covariance
Scatter Plot
59. References for Additional HelpReferences for Additional Help
http://www.worsleyschool.net/science/files/scat
http://www.oswego.edu/~srp/stats/z.htm