Using Statistics for Quantitative Reasoning
Presented on Wednesday October 18, 2017
Last updated 11/07/2017
Visual: Presentation opens with title slide "Using Statistics for Quantitative Reasoning"
Audio: Instrumental Music
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Audio: Janine: The first thing that I want to start with is we want to give you a quick overview of what we will be covering in this webinar. First we'll give you a short definition of quantitative reasoning. and then we'll talk about how quantitative reasoning is situated in every degree program at Walden. Tara, our second presenter, will follow that with some details about descriptive statistics, and she will include some examples in specific fields of study. I will then come back to you to talk about the next level of statistics, inferential statistics where we will talk a little bit about the testing of hypotheses. and we will, again, explain that with a couple of examples.
It might be interesting to you, as Shawn said, to know that we are all dissertation students, and we will give you the examples of our actual dissertation work. We will then spend a moment to address the P and alpha values as well, which are such an intricate part of hypothesis testing. And Michael, who is our excellent biostatistics tutor, will present the ins and outs of biostatistics, and he will offer a fairly current example of the ratio. We will conclude the presentation by looking at the application of statistics in the real world when we will also give you a chance to let us know if you're actually using statistics in your workplace. Our total presentation will run about 30 minutes and that will leave us generous time to address any questions you may have.
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Audio: Janine: So without further ado, let's get started. As you can see on the screen, quantitative reasoning is a process. You will be applying basic skills, such as statistics, to address an existing program. I'm sorry. to address an existing problem that you would formulate in a research question and that you would then analyze with statistics. It will exist of real-world quantitative information that we call data. and you will interpret that to draw relevance conclusions. and since we are a social change university, your interpretations are, most of the time, in the context of social change. Now, of course, Walden covers all levels of degrees, and we offer undergraduate and graduate degrees, such as master's and doctorate degrees. and I'm pretty sure we'll probably have people from across the three degree levels. As a matter of fact, Shawn has created a little poll that you can share your degree level with us. Shawn, would you mind pulling up that poll for us?
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Audio: Janine: There, you can see, there are three different answers possible. and please use one box when you fill it out. And if you like, you can also tell us in the chat box what kind of subject you're studying and what specialization you've chosen. We'll give you a moment to fill out the poll. [ pause for poll ] Look at that. Nearly 95% of our audience are doctoral programs, which does not surprise me because we do get a lot of doctoral programs for our tutoring services. But I'm surprised to see that we do not have any bachelor students.
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Audio: Janine: Now, quantitative reasoning skills are paramount and required at every degree level at Walden University. It doesn't matter whether you are an undergraduate, master's or a doctoral student. At one point or another, you will be asked to apply statistics skills towards quantitative reasoning. At that time you will probably be in a statistics course. That's where you will be introduced to quantitative reasoning. And you'll be asked to apply statistics to analyze the data set, formulate a research problem, and interpret statistic results to draw relevant conclusions. So, most of you who are in the doctoral program, that would require SPSS to execute your data analysis, but you might also have some rare courses where Excel is used for the data analysis. for the undergraduate level, you would be introduced to Statdisk, but undergrads are also sometimes asked to use SPSS for data analysis.
Earlier when I mentioned quantitative reasoning, I gave you the process, and as a Walden student, when you are introducing statistics, you will, for the most part, be using secondary data sets. Those are data sets that are produced by somebody else that you are then using to articulate a different research question. At the doctoral level, that is a little bit different. and there it's just a question of what approach you take. If you go and collect your own data, you would then produce a primary data set and if you would use a secondary data set, then that has been produced by another researcher, most likely for another study or in a general context and that you will then apply to your research question. the analysis of data always starts with description of data. That is where you describe your sample size, your variables, you produce frequency tables and graphs, and I will now turn it over to Tara, who will talk a bit more about the use of descriptive statistics. Tara, take it away.
Visual: Slide changes to "Using Statistics for Quantitative Reasoning" and includes information about descriptive statistics such as they are used to understand data and describe variables.
Audio: Tara: Thank you, Janine. Again, I am Tara Garrison, and I am from Virginia. I'm going to talk about basic descriptive statistics, population, sample, unit of analysis, levels of measurement, frequency tables, and other verbiage that you'll see a lot in statistics. The field of statistics involves methods for describing data analysis -- data. Descriptive statistics also enables researchers to summarize and organize data in a meaningful way. This means that they take jumbles and jumbles of numbers and make it something that is meaningful for the population who reads it. For example, descriptive statistics can tell a researcher the average or mean of a data set. Most of us in here, we know what the average numbers are and how to get to that.
But it can also inform us about the frequency of data. Excuse me. One of the things to describe about data is the population. In population is the complete set of relevant data that includes all possible units that have value for that specific insight. and when we talk about a population, we don't always mean a specific population of people. This can also include groups, objects, events, documents, procedures, treatment programs. But, of course, in the real world it's not always possible to get insight on a complete population. That would be too time consuming and probably very expensive. Therefore, we take a piece of the population, and that's also called a sample. And we do that in a representative way to make sure that our results can be generalized across the population.
Let's give an example here. a sample analysis of the age of homeless men and women in one specific region of the U.S. may well be considered representative of a total group or population of homeless men and women across the United States. We could not generally take a group of homeless men and women, let's say, on your street U.S.A. and consider that a generalized assumption for that whole group. We have to have something a little bit larger. Now, in statistics, we also have a term that's ever-present part of the process of quantitative reasoning. It's called a variable. a variable is something that can be identified and measured. Examples of variables are gender, height, weight, ethnicity, attitudes, et cetera. Variables are broke up into two main groups. One is a dependent variable and the other is an independent variable. a dependent variable represents the change a researcher hypothesizes to explain. While an independent variable explains the changes in the dependent variable.
I would like to illustrate that difference with a quick example. and feel free to chime in in the text box, chat box. Can identify the independent and dependent variables in this example? What is the effect that water and sunlight have on plant growth? See some answers here. I'll read it one more time to you so you make sure you get it. So what is the effect that water and sunlight have on plant growth? Oh, look, I'm starting to see correct answers in here. Indeed. You are right when you choose plant growth as your dependent variable. and why is that? Because water and sunlight, also known as your independent variables, change or alter the dependent variable. In this example, you take away water, your plant may not grow the same. Or sun, your plant may not bloom at the end of the day. and another distinction we have between variables belies any level of measurement. That is the classification -- [ dog barking ] -- that describes -- sorry -- that describes the nature of information within the numbers assigned to variables.
There are two overarching groups recognizable in the levels of measurement. One is called categorical variables and continuous variables. Categorical variables are nominal and ordinal. Nominal variables could simply be called labels. Like nominal, we could always say the word name. Some good examples of a nominal variable, as far as gender, male or female, where a person lives, northern or southern United States, or a color of a person's eyes, blue, green, or brown. A good way to remember all of this, again, is that when you say the word nominal, it sounds like the word name.
The next level of measurement is the ordinal variable. These are typically measures of nonnumeric concepts, such as satisfaction, happiness, discomfort and so on. What sets ordinal variables apart from nominal variables is there are groups that can be put in a certain order. for example, if we take clothing sizes, you have sizes such as small, medium, large, and extra large. All of these are four distinctly different levels that can be ordered in some logical way. As I mentioned earlier, the second overarching group of variables are the continuous variables. There we will find the interval and a ratio variable. a classic example of an interval scale is like temperature that can be measured in Celsius or Fahrenheit. Those can be measured and a meaning can be attached to these values on the scale. Each point on a scale has a constant distance to the previous or next measurement. But each are missing a definite zero point. Which makes it called an interval variable.
Now, when a variable is measured at the highest level of measurement, we call that a ratio variable. Which means it has an unambiguous level of zero. An example of this, age, age is a ratio variable. And so is math, length, duration, energy, and so on. All of these examples have a meaningful, yet unique and nonarbitrary zero value. Lastly, much of the data discussed above can be visualized through frequency distribution graphs. These are visual displays that organize and present frequency counts, so that the information can be interpreted more easily. A frequency distribution of data can be shown in a table or graph. Some common methods of showing frequency distributions include frequency tables, histograms or charts. The appropriate display for a variable relates directly to how you measure that variable. Such as pie and bar charts are usually used for categorical variables, nominal and ordinal. While a histogram, scatter plat or a line graph is more appropriate for a continuous variable. Such as interval and ratio.
Visual: Slide changes to "Using Statistics for Quantitative Reasoning" and includes examples of descriptive statistics.
Audio: Tara: Now, we can move here to slide 9. And we got examples of descriptive statistics. In human services, to use descriptive statistics, we would maybe look at participation rate for counseling services. As far as health services goes, we may use prevelance as a measure of the frequency or mode of a disease in a population. And if we look at public policy, understanding election results, mean versus standard deviation.
Visual: Slide changes to "Using Statistics for Quantitative Reasoning" and includes information on descriptive statistics.
Audio: Tara: And on this, I'm going to slide this next section right over to Janine. [ no audio ]
Audio: Janine: As Tara explained, descriptive statistics are used to provide details about groups of data, so that we can understand what the variables are, how they act, what they measure. But now I'd like to talk about the next level of quantitative reasoning and that is inferential statistics.
Inferential statistics elevates the analysis of data to the next level and it uses techniques to draw samples and then explore those samples in a bit more detail. It's important to note that before you can analyze the data, you would have to formulate a research question. That would be your problem statement but in statistics we call it a research question that you're hoping to answer. That research question would then be translated into a testable hypothesis. That hypothesis is called the null hypothesis. We also articulate the alternate hypothesis, but that's not the one we're testing. We're only testing the null hypothesis. And null hypothesis is articulated in a specific way. It's usually articulated negatively, like it might include the word "no" or "not." It would definitely include the variables that you're trying to test, and it will give some kind of reference to a test that you're using. and to illustrate that, we're going to give you a couple of examples,
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Audio: Janine: and like I promised you before, these are straight pulled out of our dissertations, so it gives you a sense of how students might apply these tests in the actual work that they're doing. Tara, I'm going to give it back to you to talk about your dissertation a bit.
Audio: Tara: Okay. Thank you, Janine. Again, my level is in human services. And I am at the chapter 3, going on to my first defense of my dissertation. Now, my research question is, what is the nature of the relationship between media consumption, social response, attitudes, demographic factors and attitudes towards police as a result of police-initiated violence -- actions upon citizens? Now, in my example, my null hypothesis would state that there is no relationship, and I will test this using a multiple regression.
Audio: Janine: Thank you, Tara. I would like to give the microphone to Michael to talk about his dissertation subject for a bit. Take it away, Michael.
Audio: Michael: Thank you, Janine. So, right now I am on my first dissertation, I am working on my prospectus. My research question right now is, is there a relationship between the specialty of physicians and medical malpractice cases in Puerto Rico? So, in this case, my null hypothesis will state that there is no relationship between the specialty of physicians and the malpractice cases in medicine in Puerto Rico. So I will test that by conducting correlation and regression analysis. So that is my part. Take it back, Janine.
Audio: Janine: Thank you, Michael. Thank you for sharing your dissertation subject with us. It's interesting to note that between the three of us, we're all at a different stage of our dissertation. As Tara mentioned, she's currently writing chapter 3. Michael has recently started the process and is working on his prospectus. and I'm actually working on chapter 4, so with the proposal stage behind me, I'm now struggling through the statistical work. and I can share my dissertation subject with you to give you an example of an inferential test. I am studying in the field of public policy and I'm interested in understanding the differences in the refugee policies between Canada and the United States. We know that they're implemented in very different ways. and to get an idea of what might not exactly cause but what might lead to those differences, I'm looking at the effect of the media, specifically how the media in Canada and the United States portrays the subject of refugees. And for that I'm testing a null hypothesis. I have about seven null hypotheses but I'll give you one. And it goes like this. In Canada and the United States, newspapers project a similar tone, in articles that address the subject of refugees. Now, obviously I'm looking for differences. So that would point to a means test. And in my case, I'm looking for a T-test but with a covariate attached which turns it into an ANCOVA.
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Audio: Janine: So I hope you enjoyed these examples of actual dissertations. Now that we know how quantitative reasoning works and that it's the null hypothesis that is being tested, we will introduce the concept of confidence intervals. Just to make clear that in statistics, we are not proving anything, we're merely trying to stay within a certain level of confidence. In the field of social sciences, we work with a 95% confidence interval, which leaves us .05 or 5% chance that we are going to make a mistake and that is called the golden rule, that is the golden standard. That also level of .05 represents the demands we're accidentally rejecting the null hypothesis while it's valid. And since we want to stay within those boundaries of 5%, we will -- we only reject the null hypothesis when that P value, that SPSS gives you, is smaller than alpha.
There are other fields where the alpha level might be set slightly different. for instance, in the medical field, it's a bit tighter. It's set at 1%. But that's because the results of research can induce life-and-death decisions when you're talking about medication or testing treatment. And there's also the possibility that the confidence interval is set at the 90, which allows a 10% of making a mistake. 10% of alpha. That's generally only accepted when it's a truly exploratory study and those are very rare and few between. To my knowledge, students that are working at the dissertation stage at Walden and who have selected a quantitative methodology are expected to evaluate the P value against alpha, .05. I'm not sure, maybe Michael and Tara have a different experience there. But that is my understanding.
Audio: Tara: Yes, Janine, mine is set at an alpha of 5% with a 95% confidence.
Audio: Janine: Thank you, Tara. Michael, can you give us some insight on the alpha level in your field of study?
Audio: Michael: Normally when you're working in clinical research, we use the .01 instead of the .05. Because when you're working with some medications, you are working with people's lives. So, if your drug doesn't work really well, you might kill people. So that's why we keep a tighter alpha value in our field.
Audio: Janine: That's interesting, Michael, thanks for sharing that. That gives us a bit of an idea of what it means, really, to have that alpha level set at a certain value. So now that we have a better idea of what inferential statistics is and see how we can -- and we saw how we can test hypothesis in statistics, I'm turning it over to Michael, who will present insights into biostatistics. Go ahead, Michael.
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Audio: Michael: Thank you, Janine. So, hello, everyone, my name is Dr. Michael Gomez and I am from Puerto Rico as well. I see a couple of you from Puerto Rico, too. So, let's turn now, to understanding of what is biostatistics. So basically it's using statistics to answer questions in medicine, biology and public health. Such questions could be whether a new drug works, what causes cancer and other diseases, and how long a person with a certain illness is likely to survive.
In recent years, the health sciences have become increasingly quantitative. Health scientific thing in the use of statistics include public health by using biostatistics, epidemiology, health education and environmental health. In medicine, we use biostatistics in medicine and clinical trials. In nursing research and in health care administration we use it a lot for operations research and needs assessments. So any field in the life sciences by using certain stat tall tests, such as T tests, ANOVA. The main change here is that we think that statistics, merging of the data and interpretation. On a research level, tend to be more interested in developing new methods and theories to support them. Whereas, tend to be more interested in methods -- sorry -- to new biological problems. Most definitely a fine line in some cases, but, in general.
Visual: Slide changes to "Using Statistics for Quantitative Reasoning" and includes a model of biostatistics of the risk of autism and vaccines odds ratio.
Audio: Michael: Okay, perfect. So I will explain you now in my field, I went to work with the National Science Foundation for a scientific campaign in Russia to study global warming in the polar regions. So when I conducted a global analysis, global warming analysis in Russia, we conducted many many regressions. With multiple variables, such as CO2 concentration and Ph. Also, we used regressions to create models of how permafrost is melting in those areas. So we can predict future concentrations of CO2 in our atmosphere. In this experiment, we concluded that in the next 50 years, we will have three times the CO2 that we have right now in the atmosphere. So, it will increase three times. So, that's how you can apply biostatistics in the real world.
So, as a biostatistics student, you will learn that quantitative reasoning may apply to medicine, public health and we calculate some values, for example, the risk ratios. For instance, you might learn about the risk of a specific disease [missing captions] Ratio, the value that also has a value is often used as a measure of association in both case control and cohort studies. So, how on this screen we have an example that is considered a classic situation. In this details, the purpose of the exercise is to evaluate the relationship between vaccination and the risk of autism. So see if there's merit to that relationship.
To do this research, we multiply the persons with autism who were vaccinated by the numbers of persons without autism, were not vaccinated. Then we divide that product by the number of individuals that were not vaccinated. [missing captions ] That calculation gave us the odds ratio that has a unique way for interpretation. When the odds ratio is 1, exposure to the vaccine will not effect autism. If that ratio is greater than 1, the exposure to the vaccine is associated with the higher risk of autism. and if that ratio is less than 1, exposure to vaccine is associated with larger rates of autism. Since we know that from existing research that there's no relationship between vaccines and autism, we can say that the odds ratio in the real world would be around 1. So, this biostatistic presentation, so I will give it back to Janine now and she will tell us about the statistics in the real world.
Audio: Janine: Thank you, Michael. And thank you for giving us that example of autism and vaccines. It's a very current example and for those of you in the doctoral program who are in some course of public health, you'll be sure to run into this example because as far as I've seen as a tutor, it shows up in nearly every public health course. So thank you for that.
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Audio: Janine: Now, we have a couple of minutes left to talk about statistics in the real world. I know that most of you are in the doctoral program, so, you probably had exposure already to statistics. But I'm curious to see how you experience that in your workplace. So, for that Shawn has been so kind to create another poll for us.
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Audio: Janine: Thank you, Shawn, for bringing that up. Now this is a very easy poll. You are either aware of statistics at your work or you're not. Let's see how many of you are exposed. There you go. 95%. Thereabouts. Give you one more moment. 76%. Okay. Let's call it 78 -- we're going up -- 25% do not use statistics at work or are not exposed to it and about 75% of you guys are.
Now, statistics is just all around us. There is no public policy decision or decision at higher levels that doesn't involve some kind of research that backs that and some kind of result that was statistically deducted.
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Audio: Janine: and that's the kind of experiences you get when you enter your statistics courses, you'll see that it has real-life applications and you will learn as a researcher to apply that as well. To get yourself through the process of quantitative reasoning that you will definitely use at the doctoral level if you choose a quantitative research method.
With that, our presentation has come to an end. But we certainly have some time for your questions. And Tara and Michael, Tara, would you like to answer some questions?
Audio: Tara: Yeah, sure. Okay. If you have any questions for me, just put them in the chat box and I will answer them as best as I possibly can. All right. I got a question here. One second, let me pull my screen up a little bigger. She asks a good question. She asks, how do you determine the instrument of measure? And I will just say, thank you, Valentine, for that question. You know, you got to -- I don't know which measure you're going to use. It really all depends on the variable itself. Like we had said earlier in our presentation that, you know, like nominal variables, for example, something that's related to a name. When you think of gender, male or female, where someone lives, the color of someone's eyes, things of that nature, and that's kind of considered a label. So we call those nominal. and they'll always be nominal variables. Just the same as ordinal variables for sizes of clothes. All of those things fall into those categories. And the more you learn in statistics, the more familiar you'll become with these. Janine, is there anything extra on that?
Audio: Janine: No. I think you've covered it. the only thing that you want to make sure is when you select an instrument for measurement, it has to be validated. You know, it's like standing on the scale in the morning, if your scale is not set to zero before you step on, then you're not going to get accurate results. So the validation process for instruments is usually something that is done by other researchers, if you borrow or, you know, buy an instrument from other researchers. But if you develop or even change an existing instrument, you would have to go through a process of validation. And I can tell you from firsthand experience with my dissertation study, that is not always the easiest route to take. Sometimes it makes sense, if there is an existing instrument to measure something, then I can only recommend you use that. And for more information on that, our Office of Research and Doctoral Services can help you with that and they have resources on that as well. So don't hesitate to reach out to the ORDS or even to our services and we can direct you to the right place for that answer.
Audio: Tara: Do we have any more questions about descriptive statistics or levels of measurement, anything like that we can answer?
Audio: Janine: We have one question about recommendation for a good book of statistics.
Audio: Tara: Yeah. I think I answered -- dub know, I told them I use a multiple array of sources. So it really depends on really the teacher, if it's outside of the classroom, I have a 1988 copy of a Cohen and Cohen book on multiple regression, like my right hand. My other biggest book I think I use is one I took in the very early parts of my PhD which was the basic research methods in social sciences, always go back and forth with that one.
Audio: Janine: You're talking about the -- [ didn't understand ]
Audio: Tara: This one is Frankfurt, Nachimas.
Audio: Janine: I'm not sure if that book still makes an appearance in the statistics courses, once in a while they get replaced with maybe more recent copies, but, yet, as far as the research, -- the resources are concerned, I think the best starting point for you is within the resources of the course and, of course, you can always ask your instructor if you have a need for additional resources.
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Audio: Janine: And as tutors, we get that question, too. If there are areas where you would like some more resources or greater understanding, by all means, you can always come and ask the tutors and we'll direct you in the right direction.
Audio: Tara: Let's see. I think I got a question here. This is a pretty good question. Valentine asked another good question. Can the independent variable and the dependent variable be reversed? Well, that really depends. How do I say this? You know, you got your dependent variable and then you have an independent. Unless the dependent variable causes -- it's not possible that dependent variable would cause a change in the independent variable. If that makes any sense to you. Say if we talk about the flower, plant growth again, you know, plant growth, which was the dependent variable, cannot possibly impact the sun or the rain. So, in that example, you can't reverse 'em, you know, you just cannot do it. I hope that kind of answers your question.
Audio: Janine: It all depends how you've defined that variable in your research question. It's very possible that Tara's example of plant growth as a dependent variable is used by another researcher as an independent variable. for instance, if I want to compare plant growth on two different continents, then, you know, it could be handled differently or if I want to find the relationship between how much you water and how much your plants grow, it all depends on the definition of your research question. The way you formulate your research question will determine what your variables are and it will also determine what kind of test you run. And even before that, it will be a determinant for a choice between quantitative and qualitative -- between the quantitative and the qualitative methodology. So your research question is the key here and it creates your road map for your dissertation.
Audio: Tara: I see one more good one over here. Emmanuel asks, can we have more than one dependent variable? In my experiences, if you have more than one dependent variable, then you've probably not identified or properly dealt with your control variables. Dependent variables are changes that occurred due to the independent variables. Janine or Michael, do you know of any instances where you can have --
Audio: Michael: Yes, I have a couple of examples in my field. For example, if you give a drug to a patient and you're looking at the effect of that drug on the patient, you can see the result in some labs. You can measure out the weight of the patient. You can measure different values. So, yes, you can have more than one dependent variable. For one experiment. Because it will change. But you will need different research questions then.
Audio: Janine: Indeed, Michael. I agree with you, you can have more than one dependent variable. I actually have four different dependent variables that are all part of the frame of the media frame, and, so, there are specific tests for that. When you get to that level in your dissertation, you know, that will become clear to you. It all depends on how you formulate your research question. Michael is right on the point on that.
Audio: Tara: Again, you know --
Audio: Janine: Go ahead.
Audio: Tara: I was just going to say, you know, me, like I said, me, personally, I've never had to deal with it, but, then again, it all is based on your research. All three of us have different experiences. I hope that answered your question.
Audio: Janine: and then I want to close it off with a final question that I see here, do we make ourselves available to discuss our work in open forums to students? Does it relate to our dissertation work or does it relate to our work as a tutor? I can answer that from two different ways. As dissertation student, of course, we would like to talk about -- we love talking about our dissertations, so we take every opportunity we can. And I don't know about Michael and Tara. I've also gone out to a couple of conferences where I've presented a preliminary state of my dissertation. And from a tutor perspective, yes, we have many options for you guys to come and hear us speak. We offer individual tutoring sessions, we also offer group drop-in sessions. And you're more than welcome to use our services. They are free to you. And we can help you get through your stats classes. And with this, I'd like to thank you all for attending. It was a joy for us to present to you. I will now give it back to Shawn who will offer our closing remarks. Shawn?
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Audio: Shawn: Thank you very much, everyone.