Normal Distribution, Standard Scores, and the Bivariate Normal Distribution
3 Hours of Video Lectures
Mini-Course on Statistics: 2
Accredited by: LONDON INSTITUTE OF SKILLS DEVELOPMENT
Highly recommended to Research Students with non - statistics background
Statistics for Non-Math Majors in University, College, and for AP and IBDP Secondary School Programs. Students enrolled in a Ph.D. program with non-Maths/Stats background will find these mini-courses as a key to success in understanding Statistics as a requirement of their degree.
There are five Mini-Courses in this series. You can take all 5 mini-courses or you can pick and choose the ones that best suit your needs.
Each Mini-course includes practice problems, quizzes, and exam questions (with solutions) to help you monitor your understanding at each step along the way. Lessons are short and tight and easy to digest. You can use this curriculum as a stand-alone course or as a supplement to any statistics courses you are currently taking. This course will help you master statistics. It was designed specifically for humanities majors in college or secondary students in AP and IBDP classes.
Created by Dr. Laura Roberts, Ph.D.
Here are the Topics for This Mini-Course 2
- The Normal Distribution and Standard Scores
- The Bivariate Normal Distribution
The chapters are aligned with those in the following text:
Glass, G. V. & Hopkins, K. D. (1996). Statistical Methods in Education and Psychology. Needham Heights, MA: Allyn & Bacon
You may enroll for the entire course or pick and choose among the 5 Mini-Courses, depending on your needs.
The Entire Course Includes
- 17+ hours of on-demand video
- 68+ PowerPoint presentations including notes/transcripts
- Over 100 quiz and exam questions plus answer keys and explanations!
- 100+ downloadable resources
- Access on mobile and TV
Who Should Attend?
- The course is designed for non-math majors and non-STEM majors, arts, humanities, liberal arts, EDUCATIONAL LEADERSHIP STUDENTS, education majors, and nursing students seeking an effective and accessible online Statistics Courses. The course is also appropriate for secondary students in AP and IBDP programs.
- For courses that are offered fully online, these materials can be used as a stand-alone statistics curriculum.
- Alternatively, the materials can be used to supplement any text or coursework students are currently taking.
Often, educators want to describe a set of characteristics of a group of people. For example, teachers may want to describe how much time their students spend on homework, or how resilient and empathic their students are, or any number of other characteristics.
In this course, educators will learn how to describe the characteristics of people in the following ways:
- Suppose an educator could boil down a set of numbers to a single number (e.g. how many minutes a typical student spends on homework each night); what would be the best number to represent the typical values? These statistics could be used: mean, median, or mode.
- Of course, not all students study the same amount each night. So, one may want to know how much students’ scores tend to vary around the typical value. These statistics could be used: range, variance, and standard deviation.
- Suppose an educator wants to show time spent on homework to a parent group. Instead of presenting a long list of numbers and watching the parents’ eyes glaze over, the educator may want to create visual or graphic “pictures” of the numbers (data). These statistical methods could be used: bar graphs, histograms, and scatterplots.
- With these foundational ideas (typical value, variation around the typical value, visual “pictures” of the data, educators can then understand and effectively use the following higher-level statistics.
- Using a sample mean and standard deviation to estimate a population mean and standard deviation. In other words, using a typical value (such as a mean) and typical variation (such as a standard deviation) of a small group of students to estimate a typical value and typical variation of a large group of students. Think of how much time (and money) an educator can save by gathering data on a small group and using that information to make estimates for a larger group (with a precise degree of confidence). For example, an educator could assess the time spent on homework from a small number of students and derive an estimate of the time spent on homework for the whole school.
- Suppose an educator wanted to know if time spent on homework was correlated with the extent to which parents value learning. An educator can use statistics to find out how much these two characteristics (or variables) are correlated. In other words, is time spent on homework greater when parents place a higher value on learning?
- Make predictions about the future using past information. For example, suppose a growing number of teachers were calling in sick due to a virus spreading through the school. For example, suppose the number of absentees double each day. The principal needs to know how many substitute teachers they will need next week and the week after. A principal could estimate the number of absentees next week and the week after (assuming no steps were taken to stop the virus.)
Students will also understand the following statistical methods (the usefulness of these statistics will become clearer as the course progresses):
- Working with special characteristics of normal distributions and z-scores.
- Understanding probability with fun games of chance such as cards and dice.
- Understanding important probability-related concepts such as union, intersection, independent events, dependent events, and Bayes’ theorem.
- Make inferences about nonparametric variables (i.e. grouping variables, e.g. “special needs students” versus “not special needs students.”)
- The most important requirements are a willingness to keep an open mind, a ready spirit, and dedication to the topic.
- The second most important requirement is a willingness to let go of math anxiety.
- The following math skills are a plus, but, be assured, explanations will begin at a basic level and build gradually to higher and higher levels of complexity:
- Knowledge of arithmetic (addition, subtraction, multiplication, division) of whole numbers.
- Knowledge of basic algebraic operations and simple equation solving.
Each Mini Course Includes
- Video Tutorials: I present each lesson in short, easily-digestible chunks. I begin with an overview of the lesson; then I explain each concept in careful detail including concrete examples, and I conclude with a summary and segue to the next lesson. Students will also find each lesson has a fun, entertaining aspect because I have illustrated each one with abstract art from around the world. The great thing about learning with narrated video tutorials is students can stop the action at any point and go over the concept again if it doesn’t “land” the first time through. My modus operandi when I created these videos was to distill the topic down to the essential concepts and to present a streamlined, elegant version of each statistical concept. Many stats textbooks present unnecessary overkill and students become overwhelmed and discouraged. I think students will find my method a refreshing alternative to the traditional method.
- Notes: Students will also get an inside peek into all the PowerPoint slides with notes and transcripts for each lesson. These lessons are to statistics what Sparknotes are for books. Students will find the essential concepts without the showy overkill that appears in lots of textbooks.
- Quizzes: At each step along the way, students can test their knowledge with quizzes and practice problems. I have also provided them with the answer keys, worked problems, and careful explanations of each answer. I have confidence that students will have a great experience with my teaching method.
- Standard Scores (approx. 24 mins.)
- Scales Scores (approx. 12 mins.)
- The Normal Distribution (approx. 14 mins.)
- Some Examples (approx. 16 mins)
- Shape and Skew (approx. 10 mins.)
- Shape and Kurtosis (approx. 10 mins.)
- Qualitative Aspects (approx. 16 mins.)
- The Correlation Coefficient (approx. 18 mins.)
- Interpretation (approx. 26 mins.)
- Properties (approx. 17 mins.)
- Bivariate Normal Distribution (approx. 13 mins.)
- Cumulative Time = approx. 3 Hours
Is This Course a Good Match or You? (Note by the Course Author)
Are you a non-math major who is required to take statistics? Do you break into a cold sweat at the thought of facing another required stat assignment? Have you searched the web looking for help and found nothing that really works for you?
Relax. You’re in the right place.
My name is Dr. Laura Roberts and I was a student just like you. I was a nervous wreck class after the stat class. Dropping wasn’t an option – I needed those classes to graduate. And what I discovered after I earned my doctorate and began teaching my own classes … was this.
Learning statistics doesn’t have to be scary.
Over time, I developed teaching methods that my students found effective. They learned without the frustration and the stress – and they passed their classes with flying colors!
I’m the stat guru behind Right Angle Educators. I’ve put together a series of video tutorials that will help you grasp statistical concepts quickly and easily.
What do My Video Tutorials Have That Other Online Statistics Videos do not Have?
- Unit objectives
- Lesson objectives
- Type-written slides (believe it or not, many online videos offered by other companies are in hand-written script that is very hard to read.)
- Clearly sequenced and integrated lesson presentations
- User-friendly lessons that are based on my 30+ years of experience as a statistics professor. I found many students have high math anxiety. High anxiety interferes with learning. My approach is intentionally designed to lower students’ anxiety and increase their learning.
And if you’re wondering how well my methods actually work, here’s a statistic for you.
Half of the people who start a doctorate never finish.
There are many reasons for this, but one of the biggest? Students don’t “get” the statistical skills necessary for original research. Now here’s another stat – I have a 95% success rate for getting grad students from ABD to Ph.D.
Okay, so let’s get started. My materials will calm your fears and get you feeling like a top-notch number cruncher in no time at all.
HERE'S WHAT SOME STUDENTS HAVE TOLD ABOUT
“COLLEGE STATISTICS FOR NON-MATH MAJORS” AND MY TEACHING APPROACH: