StatisticsHelp https://statisticshelp.org Statistics Help For Students Sat, 24 Apr 2021 04:41:25 +0000 en-US hourly 1 https://wordpress.org/?v=5.7.1 https://statisticshelp.org/wp-content/uploads/2017/09/cropped-SH-favicon2-32x32.png StatisticsHelp https://statisticshelp.org 32 32 Crash Course: Statistics https://statisticshelp.org/crash-course-statistics.php Sat, 24 Apr 2021 04:41:25 +0000 https://statisticshelp.org/?p=1381 Let us pretend for a second you have only a few minutes and you need to learn Statistics. So I have to think, how would I teach it to you. Or at least, how would I teach you the fundamentals of statistics if I had only a few minutes of your attention. Not an easy […]

The post Crash Course: Statistics appeared first on StatisticsHelp.

]]>
Let us pretend for a second you have only a few minutes and you need to learn Statistics. So I have to think, how would I teach it to you. Or at least, how would I teach you the fundamentals of statistics if I had only a few minutes of your attention.

Not an easy task, for sure, but we can give it a try, at least as a mind experiment, to at least get an idea of how hard (or easy) it could be. The only condition is that you put all your attention, and you try to soften your brain to accept information you are about to received.

In the beginning, there was math, and it was good….

First, Stats is pretty much a type of math that analyzes data. The data that we analyze is called “sample data” or “samples” for short. This term is used to refer to a PART of a population that you use to get a taste of how the whole population is. A little bit like when you go to Costco and get some samples, which help you test a brand to decide if you like it or not.

So samples are a small part of a whole, which is called a “population”. So hear this well: statistics is about using information provided by a “sample” to try to make a conclusion about the whole “population”. Or even simpler, it is about using sample data to make claims about a whole population. This crash course on Stats could very well end here….

crash course statistics

Now, why there are thousands and thousands of very long stats books then?

I knew you would ask that. Yeah, I painted a rosy picture of what Stats could look like. Just take some innocent samples (a small part of the population) to make and test claims about the whole population. That looks like a great deal to me. But there is certainly a lot more to say.

Those “claims” we make about the population, are not just any claims. There are properly structured claims that have to do with some specific properties of the population. This is not about perceptions you may have about the population, just because you felt like. You can Stats, in the sense of making claims about populations, provided that you follow certain specific rules for the claims.

“Ok” you say. “But that still does not sound like it could fill up thousands of pages, what else there is???” Good intuition, there is more. When I said you make claims about a population, you cannot use just any population, you need to know some specific populations. Indeed, there is a very strict list of requirements for populations to be able to use in this simple process we described.

“Alright, fair enough”. “No, still there must be more, right?” You are correct. Remember those samples you use to make claims about the population? They cannot be just any sample, they need to be collected in certain ways to be samples that are appropriate to conduct the simple process we described at the beginning.

statistics crash course

So, Stats is full of tricks before you can conduct the simple process we defined at the beginning?

Sort of yes. But you can see it this way: Now, you can see that Statistics is simply a discipline that uses sample data (a small portion of the population) more claims and test those claims about the whole population. Super simple.

BUT, the requirements and procedures for making a claim, using a population, collecting a sample and testing a claim mathematically are very precise, in order to secure that our decisions and claims are sound.

The post Crash Course: Statistics appeared first on StatisticsHelp.

]]>
Statistical Study Guide https://statisticshelp.org/statistical-study-guide.php Fri, 23 Apr 2021 05:35:36 +0000 https://statisticshelp.org/?p=1376 When the time of the Stats exams come, there is only one thing more precious than gold, and that is a statistical study guide. Especially those that come with juicy step-by-step solutions, that come to clarity all your doubts. Universal constants like gravity or Plank’s constant are pretty constant, but another constant thing that exist […]

The post Statistical Study Guide appeared first on StatisticsHelp.

]]>
When the time of the Stats exams come, there is only one thing more precious than gold, and that is a statistical study guide. Especially those that come with juicy step-by-step solutions, that come to clarity all your doubts.

Universal constants like gravity or Plank’s constant are pretty constant, but another constant thing that exist is that you WILL learn if you get a hold a sample problems that contain detailed solutions. The devil is in the details they say.

How many times you have been studying the book, the notes and you go over and over some concepts and you are just simply not clear on how to apply them, but then you see a solved problem and the light bulb gets shinny? “Of course”, you say. “That’s how it is done”.

statistical study guide

Get your stats guide now

So, after my dramatic and emphatic argument about why you need a stats study guide with solved sample problems, I am sure that I convinced you. So now you will go out to get it. Where, though? There are some options and we will discuss them.

To start with, there is always someone around who has solved problems and is willing to share. Ask who is that person. Someone may know. Still, you could be THAT case where no one around have them, so what to do?

Ask your T.A. or instructor where to get some. They may point out to the textbook, but unless you have the solutions manual, the textbook won’t be what you need now. The stats class textbook has its use, but for now, we are looking for detailed solutions to sample problems.

If you are lucky, your instructor will provide you with some, as large majority of them are willing to write preparation material (TIP: Instructors do care about keeping their job, and their job to a certain point depend on students’ evaluations of instructors)

statistics study guides

No luck yet…How do I get my study guide?

So far nothing has worked? Well, there is one way: hire a stats tutor and get a list of problems solved, with all details shown. You don’t have money? Get with other students looking for the same and split the cost.

Make sure you hire a stats tutor who is able to show all the details of the solutions. For the purpose of using this as study material, it is no good to get answers only. Getting detailed solutions may be more expensive, but if you split the cost among several students, there won’t be a problem.

There still one potential problem: What if you get those detailed solutions, and you still do not understand a word of them? Then in that case, probably you should hire a stats tutor to actually explain you the material from the beginning.

The main idea of using a detailed study guide is to fill up the gaps, not to build everything from the bottom. If you really need to start from zero, this plan probably won’t work for you

Summarizing

  1. Using a stats study guide detailed solutions can be a GREAT way of preparing for a stat test
  2. It is way of FILL UP the gaps, not to start from scratch . If you are that lost, get a tutor and start catching up first
  3. Try with your T.A. or lecturer first. They will help if you ask, but there are cases and cases.
  4. Ultimately, you can hire a tutor to prepare a list of step-by-step solutions for you

The post Statistical Study Guide appeared first on StatisticsHelp.

]]>
What are the Statistical Basics You need to Know? https://statisticshelp.org/statistical-basics-need-know.php Tue, 20 Apr 2021 06:45:33 +0000 https://statisticshelp.org/?p=1366 Ok, so you are in college and you are doing pretty well. You were an A student in high school, and though in college you are not the best, you are not the worst either. A little bit of effort and you can pull out a decent GPA that will take you places. But quickly, […]

The post What are the Statistical Basics You need to Know? appeared first on StatisticsHelp.

]]>
Ok, so you are in college and you are doing pretty well. You were an A student in high school, and though in college you are not the best, you are not the worst either. A little bit of effort and you can pull out a decent GPA that will take you places.

But quickly, you learn that career planning is something to think about. Indeed, there are many options and what you choose can have repercussions in your career path. It is a serious deal, and some students are actually lost. That is why schools do have full time career advisors for this reason.

What I have been able to witness throughout the years is that students are often clueless about the statistical basics they need to rock their Stats class. They just don’t know them. Some of them assume that since they took AP Stats in high school, the story will be the same. Many get surprised that things can be quite different in college with Stats.

Statistical Basics

Statistics basic concepts and skills

Stats builds upon many different math concepts. To a great extends, Stats is a very eclectic discipline that takes some elements from Calculus and Probability theory to build its framework. Big words, I know, but all I want you to retain is that Stats is build upon math.

That is why I always advise students to understand that Stats is fairly close to what they understand as math. The distinction seems silly, but I have heard students talking about being “happy to take a Stats class because I don’t like math classes”.

As such, you need to have certain math skills in order to understand how the topics are woven. At the very list, you will need to dominate the following statistics basics down:

  1. Basic descriptive statistics: You need to understand what is a probability distribution and how to estimate its center and dispersion
  2. You need to have graphical abilities: In stats is important to being able to depict graphically certain probability events. This facilitates the calculation and interpretation of probabilities
  3. >Understanding of reading values from tables: One crucial skill in statistics is being able to fetch information from normal probability tables.
  4. Understanding the use of a scientific calculator: You don’t need to know all of them, or you don’t need a sophisticated one. But you need to master one (Excel will suffice).

Statistical Basics

Basic statistics formulas

In Stats you will be continuously asked to use the right formula for the right situation, so that is an important statistics basics. Some of the very simple formulas you will need to know include formulas for z-scores, z-statistics and t-statistics.

Other objects in Statistics (like some probability distributions) have some very complex formulas, and you will not be required to learn them. For those most likely you will be using a scientific calculator most of the cases.

The emphasis in basic statistics is to know what and when to apply a specific formula. Knowing a formula by memory is not always relevant, and often times your instructor will give you a statistics formulas cheat sheet for quizzes and exams.

What is the bottom line?

The bottom line is do not expect Stats to be a non-math class like some students believe. Stats will have math in it, sometimes lots of it, so be prepared. The basic skills required are just few, but are important, so make sure you have those down before undertaking a Stats class.

Overall, you should have a purpose. Don’t just take a Stats class for the sake of taking it. Make sure that it contributes to your career path. And please, treat Stats as any other math class, with its challenges and idiosyncrasies. And make sure that you have down all the statistical basics mentioned in this tutorial.

The post What are the Statistical Basics You need to Know? appeared first on StatisticsHelp.

]]>
Find Someone to teach Statistics https://statisticshelp.org/find-someone-teach-statistics.php Fri, 16 Apr 2021 06:00:12 +0000 https://statisticshelp.org/?p=1360 There are many reasons why you need to find someone to teach you Stats. One of the most common reasons I have seen among my students is that they want to prepare for their Stats class with lots of anticipation, and they start working on preparations with plenty of time, even before the class starts. […]

The post Find Someone to teach Statistics appeared first on StatisticsHelp.

]]>
There are many reasons why you need to find someone to teach you Stats. One of the most common reasons I have seen among my students is that they want to prepare for their Stats class with lots of anticipation, and they start working on preparations with plenty of time, even before the class starts.

Students in college are usually under lots of stress, as they have to carry lots of expectations. Some of their own expectations and what is usually harder to deal with, expectations from others, like for examples, from parents.

There a concrete objectives. Some students are need to a have a flawless, ideally-above-4.0-GPA to apply to pre-med programs or other very competitive spots, where a sharp 4.0 does not necessarily cut it anymore.

teach statistics

Will you choose a statistics teacher online?

In more normal times, it was perhaps one of the biggest questions to whether choose an online stats teacher, or try some find someone from campus, or from somewhere close by. Now with the whole world affect by the covid-19 pandemic, the online option is taking clear advantage.

Many have already learned how to find tutors who teach statistics online. This may not be as easy as it seems, because you want to find a reputable, trustable, and most importantly, dependable. But now that the pandemic has forced some students to take the online route (route that they haven’t taken before), things get a bit more complicated.

statistics teacher online

Will a Stats teacher help you learn statistics easily?

It depends really, but I can tell you one thing: if you start early enough and you devote consistent effort working with a stats tutor, your chances are excellent to ace your class. Things could get more difficult when you get started too late, because then other factors kick in.

Indeed, when leaving this for the last minute, there is a crucial factor that kicks in: ANXIETY. Anxiety can really kill your performance. When you are under pressure to get outstanding grades, the LAST thing you will want to is to anxious, because I can guarantee it will affect your performance.

But if you start early, there will time to identify the weaknesses in your understanding and you will be able to PRACTICE long enough so you gain a large degree of CONFIDENCE, which is what you need when you take a test. Students do not really believe this, but confidence is a strong factor in your performance.

Statistics teaching resources

Honestly, finding material yourself to practice and learn may be a good idea, but you may end up realizing that you need help from a tutor. And if that is the case, I strongly suggest that you do it as soon as possible.

In this case, this is like those motivational lines “try things and fail quick” so that you understand what you did wrong and correct your mistakes. That is great advice. Try finding statistics resources and doing the learning on your own.

Make sure that you quickly assess whether or not you will need a little extra hand. The quicker you start, the better your chances to ace your class, and to get that 4.5 that you need to get accepted at your dream program.

The post Find Someone to teach Statistics appeared first on StatisticsHelp.

]]>
Is AP Stats Hard? https://statisticshelp.org/ap-stats-hard.php Wed, 14 Apr 2021 19:02:19 +0000 https://statisticshelp.org/?p=1345 This kind of questions frequently pop up, especially when students are considering to whether or not take some advanced placement courses. Academic applications are becoming increasingly competitive, and students are looking for options to go beyond and above the 4.0 GPA taking AP classes. But then AP courses and AP Stats specifically can vary substantially. […]

The post Is AP Stats Hard? appeared first on StatisticsHelp.

]]>
This kind of questions frequently pop up, especially when students are considering to whether or not take some advanced placement courses. Academic applications are becoming increasingly competitive, and students are looking for options to go beyond and above the 4.0 GPA taking AP classes.

But then AP courses and AP Stats specifically can vary substantially. It can happen that some AP Stats class is particularly difficult, because one instructor may decide to make it more challenging so to “prepare students for what is coming in college”.

But those instructors wanting to “show the way to college” with their particularly challenging AP Stats class are an exception, statistically speaking (pun intended), and majority of times you will face a fairly standard difficulty level. when taking you AP stats course.

is AP Stats hard

What is covered in AP Stats?

AP Stats will cover some basic Stats topics that can be useful for a future Stats course in college, for a large percentage of the cases. This is what you will learn in AP Statistics

• Data exploration and descriptive statistics: Use measures like the mean and standard deviation to describe the center and dispersion of the distribution, and use graphics to assess the general behavior of the distribution

• Sampling: Different sampling methods are covered. The whole philosophy of sampling as per why de it is covered in relative depth

• Basic Probability Theory: Basic probability properties of continuous and discrete distributions are discussion, including Binomial and Normal distributions

• Inferential Statistics: The basics of hypothesis testing are covered, including sampling distribution, Central Limit Theorem and basic z and t tests

Advanced Placement

Is AP Stats harder than AP Calc?

Here I should say no, and I should make the emphasis on that all AP classes are meant to be at the same level of difficulty. But I am here to tell you as I have seen it, and not to sugar coat it. From what I have seen, AP Stats and AP Calc go about more or less the same difficulty, at least from the point of view of students.

BUT, I have seen some AP Calc classes that are quite difficult for the context of high school students. I have seen AP Calc classes in which not every student should enroll without a second thought (not even good ones), and but most AP Statistics class are usually found easy by good students. Perhaps, AP stats may be among the easiest AP classes.

Is AP Statistics useful?

ABSOLUTELY. The topics cover in AP stats are essentially the same that are covered in STATS 101 in college. So if you did well in AP stats, it is likely you will do well in college. One caveat: Stats 101 in college may a bit deeper, so there are no guarantees here.

Ultimately, taking AP stats is a good opportunity to get a 5.0 to increase your GPA to strengthen your college application, even if you don’t plan to take Stats in college. If you ask me what AP class should I take to improve my GPA, I would say Stats.

So, if you are wondering whether AP Statistics is good for college or not, I will say YES. Either you use to improve your GPA or to get a taste of what Stats 101 will be like, or both, you should take it. And if you have passed AP stats, I would advice to take Stats 101 in college, even if you don’t need to take it. Why? Because you would have done most of the leg work with the AP stats class.

Summarizing

  1. I could not say that AP stats is the easiest AP class, but it is not the hardest for sure
  2. AP Calc could be potentially harder from my point of view
  3. AP Stats can be a great way to increase your GPA, even if you don’t plan to take Stats in college
  4. AP can be a great way of preparing for Stats 101 in college, because you will have done most of the leg work.
  5. The post Is AP Stats Hard? appeared first on StatisticsHelp.

    ]]> Probability vs Statistics https://statisticshelp.org/probability-vs-statistics.php Tue, 13 Apr 2021 16:19:19 +0000 https://statisticshelp.org/?p=1333 Probability vs Statistics: Who is Who? This got to be one of the most question people ask me. I say people in general, not students. Students typically do not know the difference, but they don’t ask, because as soon as they finish their stats class, they are out and forget about everything that they ever […]

    The post Probability vs Statistics appeared first on StatisticsHelp.

    ]]>
    Probability vs Statistics: Who is Who?

    This got to be one of the most question people ask me. I say people in general, not students. Students typically do not know the difference, but they don’t ask, because as soon as they finish their stats class, they are out and forget about everything that they ever learned.

    But there are people out there that have some inclination for math and science, and they are interested overall in data and what we commonly know as statistical data, either from macroeconomics, demographic or scientific data.

    Statistics vs Probability

    Data enthusiasts love working with data, interpreting its consequences, compare things, and that is all great. Hobbyists usually do not see much of a difference, and they see a blurry line between statistics and probability, and they may not know the difference between them.

    Likelihood vs probability statistics

    First of all let us clarify the relationship between likelihood vs probability. Strictly speaking, probability is formally a number between 0 and 1 which quantifies the chances for a certain event to occur (a probability close to 0 means an event with LITTLE chances to occur, and a probability close to 1 indicates that the event has a VERY GOOD chance to occur).

    Now, likelihood refers to exactly the same thing, it is a way of quantifying the chances for an event to occur. Saying a that something has a high likelihood is indicating that something has a good chance to occur.

    So one could say that likelihood and probability are the same, only that a probability is a formal way to express a likelihood or a chance for an event to occur. So then, probability is the formal term that expects to be quantified with a number between 0 and 1. Likelihood is a more loose way of referring to a probability.

    Example of statistical data

    Example of the Difference between probability and statistics

    When seeing some examples you can clearly see the difference between probability vs statistics. Assume that you have a coin that is fair, which has a probability p = 1/2 of getting a head (and then it has a probability 1/2 of getting tail).

    If I toss the coin 10 times, I want to compute what is the probability of getting exactly 6 heads. That probability happens to be approximately 0.2051, and it is computed as \(C_{10, 6} 0.5^6 \times 0.5^4 \approx 0.2051\) (Do you know how to compute that??? You need to use the BINOMIAL distribution). That is an example of what probability does.

    Now, say you hear claims from people playing the tossing game who feel that the coin cannot be fair, because it lands too many heads. You, as a stats detective, go and examine the coin and notice nothing weird, and then toss the coin 100 times and you get 65 heads. You say “if the coin was fair, the likelihood of this 65 heads out of 100 tosses would be quite unlikely, so I conclude that there must be foul play and the coin is not fair”. That is an example of statistics.

    So then, probability as a discipline concerns itself with calculating probabilities using probability distributions that have given population parameters. Statistics, on the other hand, concern itself with collecting sample information (finding “evidence” as a detective) to make plausibility claims about population parameters.

    Difference between mathematical and statistical probability

    Once we have a better understanding of how probability theory operates, we start to realize that the use different strategies to construct probability distributions. On the one hand, sometimes certain random phenomena are really easy to model making assumption of equal probability of simple events.

    For example, when we toss a dice, and the dice is perfectly symmetric and homogeneous in its construction, one could argue that no side has a higher probability than any other to show. So then you would say that each side has equal probability.

    Since there are 6 sides, each with the sample probability, and the total probability is 1, each side must have a probability of 1/6 of showing up. That is an example of mathematical or theoretical probabilities.

    Now, assume that you are an engineer and you are building a road in the jungle with your team, in place where it rains a lot. And you know that when it rains the work could be severely affected, especially when there is a storm.

    You know don’t know if it will rain today, but you know from historical records that out of 10000 days, there has been 300 storms during this season. Then, empirically, you judge that the probability of a storm that day would be 300/10000 = 0.03. That is an example of statistical (or empirical) probability.

    In Summary, what is the difference between Probability vs Statistics

    Summarizing, probability and statistics stack up as follows:

    1. Probability and statistics are like the two sides of a coin: They are tightly related and they in a sense opposite to each other
    2. Probability tries using different strategies to organize and systematize the probability (likelihood) calculation of events related to a specific phenomenon in a content where events with unknown outcomes occur (like tossing a coin)
    3. Statistics, like a detective, attempts to say something about the probability properties of a certain phenomenon, based on some small information about the phenomenon, based on sample. This is, a few pieces of information are collected and we attempt to make claims about the big picture from them.

    The post Probability vs Statistics appeared first on StatisticsHelp.

    ]]>
    Basic Practice Of Stat https://statisticshelp.org/basic-practice-stat.php Sun, 11 Apr 2021 18:24:51 +0000 https://statisticshelp.org/?p=1316 I often times get questions from students about different Stats textbooks. One of the books that is brought up frequently is The Basic Practice of Statistics, which is your classic Statistics 101 textbook. Most of those books are more than adequate for learning statistics. If that is the book you got assigned for your class, […]

    The post Basic Practice Of Stat appeared first on StatisticsHelp.

    ]]>
    I often times get questions from students about different Stats textbooks. One of the books that is brought up frequently is The Basic Practice of Statistics, which is your classic Statistics 101 textbook. Most of those books are more than adequate for learning statistics.

    If that is the book you got assigned for your class, it would be a good idea to stick to it for many reasons: for one, the way of presenting and covering statistics (which can vary substantially from book to book) is that you find in that specific book, and likely, the test questions will look a lot like those from the textbook.

    Basic Practice Of Statistics

    But that is not always the case. Sometimes the textbook is simply a reference, which is the case when the instructor goes for a more standard approach, which is more or less the same in majority of books. The truth is that many textbook try some innovative approach, which could be “hands on” or could be with “real life examples”. Some authors look for a twist to differentiate from the rest, and that is alright.

    So you are looking for pdf answers for the Basic Practice Of Statistics?

    I understand. You are lost and you are looking for the test bank with solutions for your textbook. It makes sense, but I would advise against it, for several reasons. Often times, those pdf copies are sold illegally, without consent of the publisher, and should be avoided at all costs.

    Then, even in case you decided to buy it, fine you have it, but you will be spending money for something that perhaps would not be even useful. Why? Because questions assigned are not always directly from the book, especially with online courses where a platform like MyStatsLab or Blackboard generates questions on the fly, that are not coming directly from the book, or at least they come with different numbers.

    A test bank with solutions could be useful to see how questions are worked out. But the thing is, if your instructor deems that it is useful for you to have the solutions for the textbook, he or she will make it an official requirement as a material for you to get. Otherwise, I would not really bother.

    Math solutions

    Why people are looking for the Basic Practice Of Stats?

    Well, that is easy, it is because instructors are using that book frequently in their Stats 101 classes. Some books go in and out of fashion, and this one is now fashionable. Other Stat textbooks continue being popular nowadays, such as the Triola books, but I have lately seen a less prevalent use of those.

    It is indeed a new phenomenon to see these Stats 101 books with their twists, with a very specific approach. Like the “hands on” or the “layman version”, etc. And also, you see those textbooks specially targeted at students from “Nursing Degrees”, or “Stats for Biostatistics”. So, we have the same old Stats, written specifically to appeal students with different backgrounds, which I think is a good thing.

    I do recommend to stick with the textbook required by your instructor. That is for sure a mandatory buy, but consider that there are always good options to complement that main textbook required in your class.

    The post Basic Practice Of Stat appeared first on StatisticsHelp.

    ]]>
    What is a Statistical Question in math? https://statisticshelp.org/statistical-question-math.php Wed, 07 Apr 2021 23:22:43 +0000 https://statisticshelp.org/?p=1308 Statistics is a field that has a lot draw and attention. People seem to be attracted by Statistics and its ethos, but usually people do not understand the real ethos of Statistics, and they tend to pay attention to certain elements that are perhaps less relevant than others. What is best known about statistics by […]

    The post What is a Statistical Question in math? appeared first on StatisticsHelp.

    ]]>
    Statistics is a field that has a lot draw and attention. People seem to be attracted by Statistics and its ethos, but usually people do not understand the real ethos of Statistics, and they tend to pay attention to certain elements that are perhaps less relevant than others.

    What is best known about statistics by a broad audience? Its graphs, without a doubt. When people think about statistics, the first thing that comes to their mind is bar charts, histograms, scatterplots and all that. And it makes a lot of sense, but graphical depiction of data is the best known side of statistics.

    Histogram

    For example, the above char is a histogram, for a variable called “Elevation above sea level”. The histogram above tells us A LOT about the variable. For example, we can see that the distribution is somewhat symmetric, but yet it has tiny degree of right skewness, which does not appear to be significant.

    What can be answered with descriptive statistics only?

    Descriptive statistics include graphs and statistics like the mean, mode, median and standard deviation among others. Descriptive statistics, like its name indicate so, have as its main purpose to DESCRIBE data. The mean gives a “representative” measure of center, the standard deviation gives a “representative” measure of dispersion, provided that the distribution is not too skewed.

    But often times, this idea of being “representative” is rather loose, and it does not give a clear, concrete representation of things, as it is fairly relative. Besides, let us not forget what is the ultimate objective of Statistics as a discipline: Use sample data to make CLAIMS about population parameters.

    In other words, in Statistics we really want to go far and beyond mere descriptive statistics. Indeed, we want to say something about a population parameter that we don’t know. The most common population parameter used is the population mean, but any population parameter will do.

    Enter Inferential Statistics: Answering Real Statistical Questions in Math

    Statistical questions are beyond wondering how does the distribution looks like when looking at a histogram. Statistics questions are about asking something about a population parameter. For example, consider the “Elevation above sea level” variable. After we have come around seeing that its sample distribution appears to be relatively symmetric, I would perhaps like to ask the following question:

    Question: Is the population mean elevation different from 400 feet?

    This question could be relevant because say we are analyzing a zone for which we don’t have maps for, but we know that the overall elevation in the area is 400 feet, and we sample of N = 64 data, which we would like to use in order to answer the above mentioned question.

    It turns out that one very commonly used procedure to answer a statistical question about a population mean is the t-test for one sample. In this case, the results of a t-test are shown below:

    T-test for one sample

    The beauty of this is that all the hard work is done with software. The output above shows a t-test output from SPSS, which is obtained by pressing a few keystrokes. Now our job is to interpret these results.

    The t-statistic is t = 15.87, and the p-value is p = .0000, which is very small. A small p-value indicates that we reject the null hypothesis (The p-value is the likelihood of obtaining these kind of sample results if we assumed that the null hypothesis is true. A very small p-value discredits the assumption that the null hypothesis is true, and then we reject it).

    Why do we want to answer statistical questions like these and we don’t limit ourselves to graphs?

    Well, it would be much easier for many people to just stick to looking at graphs and interpret them by “saying what we feel” about them. Usually, real life, real math requires more precision. Usually, in many contexts we may be looking for making policy decisions or budget allocations, in which we need concrete evidence to support a decision over another possibility.

    Inferential statistics allow us to answer those more difficult statistical questions and to provide more evidence (if the sample data supports it) that will allow decision makers to make non trivial decisions.

    The post What is a Statistical Question in math? appeared first on StatisticsHelp.

    ]]>
    How To Study For Statistics? https://statisticshelp.org/how-to-study-for-statistics.php Tue, 06 Apr 2021 20:42:50 +0000 https://statisticshelp.org/?p=1294 Test preparation is always a hot topic, especially because students are usually clueless about it. And this is because there is this dubious premise that if you attend to your Stats lecture and pay attention to class, you won’t need anything. But that is far from truth, as it is perfectly possible to find yourself […]

    The post How To Study For Statistics? appeared first on StatisticsHelp.

    ]]>
    Test preparation is always a hot topic, especially because students are usually clueless about it. And this is because there is this dubious premise that if you attend to your Stats lecture and pay attention to class, you won’t need anything.

    But that is far from truth, as it is perfectly possible to find yourself in a situation in which you have done everything “right”: you have attended to class, done your homework and even gone to the library to study, but then you are still feeling lost think “Damn, my Stats midterm is coming soon, and I do not feel confident about it at all”. As a matter of fact, that is a very common situation, even more common that Stats instructors want to believe…. Study for your stats test

    So, how do you prepare for your statistics test?

    Well, that question does not have just one answer, since it depends on the ground you are standing. So then, it all starts with an assessment you need to conduct yourself, by asking the following questions.

    Do I have all the material I need?

    That is something I always advise my students about. Before anything else, collect all the required materials. Go to the syllabus of your stats class and see what is required. Do you have the textbook? Yes? Fine. No? Go get it. Also, don’t forget about aids that could have been released right before the test. Instructors like to post sample midterms, especially for math and stats courses. Take advantage of that.

    Are you part of a study group?

    Study groups can be productive at times, for some students. If you are the kind of students who do better at understanding concepts when working with other people, by all means go ahead and gather your groups. Do it early though, because it is well known that cramming sessions the night before of the test are not all that productive. You can prepare the night before of the test, but probably you should be working on practice stats problems that look like the ones that will be in the test instead of trying to understand concepts at the last minute.

    Can I study for my stats in one day?

    No, you cannot. Unless you have super powers. Look, learning stats require time, so you should not attempt a difficult stunt. And please forget about a night-before-the-test-cramming-session, as those don’t work well. Take time, and start early. “Piano piano si va lontano” or something like that, which I think means slow and steady wins the race.

    Realistically, if you are kind of lost, that did not happen in a day. So, be clear that if you have a problem that was incubating for much more than a day, like you will not be able to solve it in a day, right. There is some law of consistency in the world, so follow it.

    Stats success

    Should I Take notes for my stats class?

    Yes, but don’t overdo it. I see students that go berserk trying to catch every single thing the instructor says, and that is NOT the point of taking notes. Those people get so occupied with writing every single word, that they forget to pay attention.

    The idea is that you write down only things that are worth writing down: some key remarks about how to deal with some special cases, like for example when the instructor says “for this type of normal you do this”, or ‘for the midterm I will probably ask this question”, etc. You catch the drift, I am sure. The main purpose to attend a lecture is to FOLLOW the lecture and ask questions if you have any. Your textbook does not speak, in case you haven’t noticed.

    In summary, here you have your Statistics Tips

    1. Gather all your material: Stats textbook, notes and especially some material the instructor provided to practice for the test
    2. Don’t wait until it is too late
    3. If you find productive working with a study groups, but make sure they don’t delay your logistics
    4. Don’t expect to learn things in a day: learning stats require time
    5. Attend to your lectures, but not just for taking notes for the sake of taking notes.
    6. Practice, practice and practice: solve as many stats problems as you can.

    The post How To Study For Statistics? appeared first on StatisticsHelp.

    ]]>
    State Budget and Days Late https://statisticshelp.org/regression_analysis_problems_9.php Sat, 03 Apr 2021 02:17:17 +0000 https://statisticshelp.org/regression_analysis_problems_9.php State Budget and Days Late. New York State has become notorious for approving the state budget after the annual

    The post State Budget and Days Late appeared first on StatisticsHelp.

    ]]>
    State Budget and Days Late. New York State has become notorious for approving the state budget after the annual deadline April 1. The amounts of the budget (in billions of dollars adjusted for inflation) and the number of days late are listed below with corresponding entries representing the same year. (The data are in order by row.)

    Does it appear that the size of the budget affects the number of days that the budget is late? Use a 0.05 significance level.

    Solution: We have the following scatterplot:

    The correlation coefficient is computed as r = 0.59363. The critical value forand n = 20 is rc = 0.444. Since r > rc, we conclude that there is significant linear relationship between the variables.

    GO TO NEXT PROBLEM >>

    The post State Budget and Days Late appeared first on StatisticsHelp.

    ]]>