Strengths and Weaknesses of Statistics for Research
RES6003 Module 1 Assignment
Strengths and Weaknesses of Statistics for Research
Using statistics effectively includes understanding their scope and limitations. Researchers must identify the contexts most suitable for applying statistics and determine the most appropriate level of data.
In this assignment, you will compose a 3- to 4-page essay analyzing the strengths and weaknesses of statistics for research.
Step 1. Compare
First, brainstorm situations where statistics would be most appropriate to test differences or relationships between certain measures (variables). Consider which level of data might be needed to do so.
Then, compare those situations to other contexts with limitations or barriers to such research. In your comparison, discuss why weaknesses of statistics must be considered when applying them to research problems. You might frame your analysis as advantages versus disadvantages of applying statistics to research problems.
Step 2. Compose
Compose your essay. The essay should have the following structure:
Introduction
Strengths/advantages of statistical research with examples
Weaknesses/disadvantages of statistical research with examples
Summary/conclusion
Include three scholarly references to support your arguments.
Please read the Assignment GuidelinesLinks to an external site. before you begin working.
DISCUSSION MOD 1
What Are the Limits of Statistics?
Statistics can help accurately describe social and behavioral phenomena (if the underlying measures are accurate), but they can also misrepresent them. Statistics can be manipulated or, at least, their limitations can be obfuscated when communicating results.
Develop an original response describing a real-world example where statistics might be used to misrepresent data or where they might not fully represent an underlying truth without adequate disclosure of the limitations of what the data can and can’t say about something. You might discuss:
political polls with wide errors of margin,
earnings before interest, taxes, depreciation, and amortization (EBITDA) projections for a tech startup seeking venture capital, or
patient satisfaction scores across a healthcare system.
Or, think of your own example and share it with the class. For whatever example you choose, use the Module 1 readings to support your points, discussing what factors might need to be “hedged” with limitations when applying statistics to the situation.
APA citations are required only for the original response.
Please read the Discussion Guidelines before posting your response.
Expectations
Hello Scholars,
I thought it would be helpful for me to provide the expectations for class. I would like you to know that my feedback tends to be direct, concise, and to the point so that I can be effective with time. I am full time here at ACE and have other jobs with lots of students and candidates, so I try to be detailed and effective. My comments are NEVER meant to be nasty or malicious. If you do not understand, please email me.
I provide some live classes during the term. I do this when, according to my experience, students tend to need the most help. There will be separate announcements inviting you to our live classes. They will typically be Monday evenings or late afternoon.
Please email for extra help and explain what you need help with and ask your question. Please do not just ask for a meeting because most questions do not require a Zoom or phone call. If it is complicated, I will reply asking you for a meeting or phone call. I prefer to work through email, which I check every day.
The supplemental course materials, lectures, videos, etc., that I provide are, in my opinion, what you really need to know to understand statistics for your dissertations. I will not just stick to what’s in the module because I am trying to teach students quantitative research. I provide more than you need “just to pass the class”. If you’d truly like to understand, go through the materials I also post weekly.
I expect most of your discussion questions to have at least one citation. I expect any papers to use proper APA 7 formatting and references.
ACE does not provide teacher or student access to the statistical package without Microsoft suite. I will show you how to use JASP, which is free and easy to use, and SPSS with Laerd Statistics, which is the most commonly accepted in academia. I will accept statistical analysis with those 2 programs for those who do not want to use Excel or do not have access to the package. I urge any student who plans on doing a quantitative dissertation to use SPSS or a free copycat version, such as PSPP, with Laerd Statistics as most dissertation chairs do not use Excel for statistical analysis either. SPSS will be the most popular.
Consistent with ACE policy, this is a university which promotes open and scholarly discussion. I frequently use real world recent events to support what I’m teaching and to support researcher ethics. I use facts which you may find uncomfortable. I am not asserting, in any way, how you should view these facts or your ethics, as that is for you to decide. You are always welcome to argue a point with me, without fear of repercussions, but I expect scholarly types of arguments. I am more interested in facts than feelings. This class is meant to support scientific analyses and I expect scholarly discussion. The college supports this view and is in the handbook as follows:
A College is a marketplace of ideas, and in the course of the search for truth, it is essential that freedom exists for contrary ideas to be expressed. American College of Education students are expected to conduct themselves as responsible members of the College’s academic community. This requires the demonstration of mutual respect and civility in academic and professional discourse. As such, it is mandatory students interact with other students and all College faculty, administrators, and staff with respect and in a professional manner.
Please treat one another and me with respect. I treat my students with respect always.
Please be aware of our academic honesty policy and of your assignment deadlines. If you know you’re going to be late with a good reason, please email me. If it was an act of God, email me after the fact. You will find that while I teach and love teaching, I’m not much of a disciplinarian.
Here is to a wonderful term. I wish all of you the best!
Week 1 Supplemental Lecture
Hello Scholars,
Statistics is rather like a TV repairman who is trying to cut out the noise or the static to create a better Video picture. In research, stats are typically, an extreme focus to answer very specific research questions. In education research, our questions are typically…
Is there a difference between groups or over time (such as pretest to post test) These are the easiest of tests because they use mean average or median average scores to compare.
Is there a relationship between X and Y? These are correlational and find a line or develop a line chart, if there is a relationship to be found, that describe how 2 things are related and how strong a relationship there is.
Does X predict Y or Z? (or even more variables). This is a regression. This determines if one thing can predict 2 or more other things. E.g. Does temperature predict Ice cream sales and hamburger sales? ACE does NOT use these because we do not teach this.
Now, as you can see from my 3 types of questions here, I have a few different research DESIGNS. Our methodology, which refers to quantitative, qualitative, mixed methods, or exploratory, is QUANTITATIVE. Quantitative studies refers to a methodology that uses numeric data or quantifiable data to test hypotheses. Our research design are types of designs that are quantitative in nature. While there are MANY designs, EDD students are typically expected to learn Experimental (most students cannot use this one due to lack of resources), Quasi-experimental, Correlational, Comparative (aka causal comparative), or Ex post Facto (after the event being studied has occurred). ONLY A TRUE EXPERIMENTAL DESIGN CAN ESTABLISH CAUSE, EFFECT OR IMPACT. Never forget that!
Each of these designs will use variables of some type.
Variable – A variable is any characteristic, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables. It is called a variable because the value may vary between data units in a population, and may change in value over time.
For example; ‘income’ is a variable that can vary between data units in a population (i.e. the people or businesses being studied may not have the same incomes) and can also vary over time for each data unit (i.e. income can go up or down). (Australian Bureau of Statistics, n.d.).
There are a few main types of variables, which Laerd does a wonderful job explaining as you use their test selector (scroll down and read when you do not understand).
Variables are the data that we are using to test. We have numeric variables and categorical variable (grouping variables)
Grouping variables aka nominal variables are usually independent variables. Independent variables (IV) are the influencers or the potential change. These are typically categorical variables with 2 or more categories (it cannot be categorical with one category). E.g. Gender is my independent variable with 2 categories of male vs female. If I were to ask if there’s a difference in height BETWEEN genders (male vs female), my IV is gender because this is the influencer. This is also a BETWEEN groups categorical variable. My question is comparing differences BETWEEN 2 separate and distinct groups.
There are also WITHIN groups variables or TIME points. An example of this is pretest to post test. This asks if there’s a difference for a group under more than one testing circumstance. We can have 2 or more categories of time, such as pretest to posttest or monthly test scores. E.g. Is there a difference over time (spring, summer, and fall) in the number of asthma attacks for preschoolers from NE Ohio? My IV here is time with 3 categories of spring, summer, and fall. PLEASE NOTE THAT THE CONCEPT OF TIME IS SEPARATED FROM THE TEST SCORES.
Dependent variables are typically the numeric variable. So for my between groups example, this would be height. For my within groups example, it would be the number of asthma attacks (summed total score for each time point or season I mentioned).
To get more complicated, each statistical design has its own type of variables. Correlational designs just use variables and they should be numeric. Regressional designs use prediction and outcome variables.
Numeric variables can differ in type. Our main variables are continuous, ordinal dichotomous, and multinominal.
Continuous – Continuous variables include interval and ratio measurement types. Interval variable are measured along a line or continuum. These are numbers that can literally have any value between the lowest and highest number. An example would be temperature, 98.6%, 30.4%… However, notice that 0 temperature does not mean that there is NO temperature.
Ratio variables are the same but we add the condition that zero has value meaning there is none of that. A ratio variable might be distance. We can have gone 0 distance, unlike temperature above.
Ordinal – ordinal variables are ranked data. Examples of ranked data include Likert scales… on a scale of 1-5 with 1 being completely disagree to 5 being totally agree… Letter grades are also ordinal variables or ranked data.
Dichotomous variables are nominal variables with 2 categories. These cannot be ranked nor is there any intrinsic value. E.g. – pet with 2 categories of cat or dog.
Multinominal – These are variables like dichotomous variables but there are 3 or more categories. (Laerd Statistics, 2023).
Here’s a flow chart of the variables discussed from the Australian Bureau of Statistics
Finally, allow me to explain why understanding variable structure is so extremely important… All statistics have assumptions about the data that must be true in order to use that test. Let’s use my first two examples.
Is there a statistically significant difference between genders (male vs female) in height?
My test choice requires data with 1 IV with 2 categories (gender, male vs female) and 1 DV that is continuous. Height is ratio, btw.
My excel file would look like this:
Notice my participants are numbers using excel’s numbers but gender has a column with 2 choices and my DV, height, has the numbers.
Now, what If I wanted to test my asthma kids?
Is there a statistically significant difference over time (spring, summer, fall) in the number of asthma attacks for preschoolers in NE Ohio?
My IV is a within groups categorical variable with 3 categories. Time is the IV and the categories are springs, summer, and fall. My DV is the number of asthma attacks. This is a continuum where zero means No asthma attacks. My data file would look like this:
Please notice the difference in files. This file uses the numbers to the side to number my participants too, but I have 3 columns with the totals for each DV by time point in those columns.
For this reason, you must understand completely, your variable structure. It is necessary for appropriate test selection. I have attached another document I created to help my dissertation candidates in their research design. Keep it for your use and use it for your research.
Dr B
References
Australian Bureau of Statistics . (n.d.). Variables. Retrieved from: https://www.abs.gov.au/statistics/understanding-statistics/statistical-terms-and-concepts/variablesLinks to an external site.
Laerd Statistics. (2023). Type of dependent variable. Retrieved from: https://statistics.laerd.com/premium/sts/groups-between-one-threeplus.php
Statistical Symbols to know
Statistical Symbols To Know
?: significance levelLinks to an external site. (type I errorLinks to an external site.).
b or b0: y interceptLinks to an external site..
b1: slope of a line Links to an external site.(used in regressionLinks to an external site.).
?: probability of a Type II errorLinks to an external site..
1-?: statistical powerLinks to an external site..
BD or BPD: binomial distributionLinks to an external site..
CI: confidence intervalLinks to an external site..
CLT: Central Limit TheoremLinks to an external site..
d: difference between paired dataLinks to an external site..
df: degrees of freedomLinks to an external site..
DPD: discrete probability distributionLinks to an external site..
E = margin of errorLinks to an external site..
f = frequency (i.e. how often something happens).
f/n = relative frequencyLinks to an external site..
Ha = alternative hypothesisLinks to an external site..
H0 = null hypothesisLinks to an external site..
H1 or Ha: alternative hypothesisLinks to an external site..
IQR = interquartile rangeLinks to an external site..
m = slope of a lineLinks to an external site..
M: medianLinks to an external site..
n: sample sizeLinks to an external site. or number of trials in a binomial experimentLinks to an external site..
N: population Links to an external site.size.
ND: normal distributionLinks to an external site..
?: standard deviationLinks to an external site..
?x?: standard error of the meanLinks to an external site..
?p?: standard error of the proportion.
p: p-valueLinks to an external site., or probability of success in a binomial experimentLinks to an external site., or population proportionLinks to an external site..
?: correlation coefficientLinks to an external site. for a population.
p?: sample proportionLinks to an external site..
P(A): probability Links to an external site.of event A.
P(AC) or P(not A): the probability that A doesn’t happen.
P(B|A): the probability that event B occurs, given that event A occurs.
Pk: kth percentile. For example, P90 = 90th percentileLinks to an external site..
q: probability of failure in a binomial or geometric distributionLinks to an external site..
Q1: first quartileLinks to an external site..
Q3: third quartileLinks to an external site..
r: correlation coefficientLinks to an external site. of a sample.
R2: coefficient of determinationLinks to an external site..
s: standard deviationLinks to an external site. of a sampleLinks to an external site..
s.d or SD: standard deviationLinks to an external site..
SEM: standard error of the meanLinks to an external site..
SEP: standard error of the proportion.
t: t-scoreLinks to an external site..
? meanLinks to an external site..
X: a variableLinks to an external site..
?2: chi-squareLinks to an external site..
x: one data value.
x?: mean Links to an external site.of a sampleLinks to an external site..
z: z-scoreLinks to an external site..
Miscellaneous Statistics Symbols
~ has the distribution of (sourceLinks to an external site.).
= equal to.
? almost equal to.
> greater than.
< less than.
? not equal to.
? less than or equal to.
? greater than or equal to.
? Summation.
Reference:
Statistics how to (2024). Statistical Symbols in Alphabetical Order. Retrieved from: https://www.statisticshowto.com/statistics-basics/statistics-symbols/Links to an external site.
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