Self Reflective

Post ID: 3488600

Overview

Answer everything asked in this essay. PLEASE--Number each statement (1-5) in the essay please.

Modules 5, 6,7,and 8 were the most challenging ( I hate statistics so you can be creative with the why).

The purpose of the Student Self-Reflective Essay is to reflect upon what one has learned or how one has performed as compared with one's expectations or goals.

At the end of each course we ask students to respond to five (5) statements. In your essay please respond in sequential order to the five (5) statements below. There is no requirement for length when responding to each statement.

1. Descriptions of how you feel you improved your knowledge, skills, abilities, and yourself in this session through this course. 2. Evaluation of the work you did during the session for the class and explanations of ways you could have performed better.

3. Topics you have identified that you did not understand or were not successful in trying to implement and suggestions you may have about how to improve the course material on those topics.

4. Ways you might measure the future effects of what you have learned in this course or your future progress/improvement. 5. State whether you achieved the course outcomes, (Student Learning Outcomes stated in the Syllabus).

See all modules below along with the details that include the readings for that week:

Descriptive Statistics is the area of measurement that covers ways to summarize data. This area is distinct from inferential statistics, which is the branch of statistics that runs tests to determine if observed differences are mathematically meaningful (i.e., significant).

Before we start delving into the territory of descriptive statistics, we should differentiate between a sample and a population. A population is infinitely large. Although we would get the most reliable measurement from a population, an undertaking of that scale is impractical. Therefore, researchers generally deal with a sample, which is a subset of the population. The hope is that the sample will accurately represent the population. In any event, the statistics we gather will almost always be sample statistics. Each of them has a corresponding population parameter. Two examples include the sample and population mean and the sample and population variance.

Fundamental to descriptive statistics are measurement scales (nominal, ordinal, interval, and ratio). The function of the nominal scale is to name or label data points. The ordinal scale is used to rank order data. The interval and ratio scales are utilized for types of data that have equal intervals, such as feet, monetary amounts, or calendar years. The difference is that a ratio scale has a true zero point, and an interval scale does not. If you have $0.00 in your bank account, you have no money (ratio scale). If it’s zero degrees outside, there is, in fact, a temperature, and you’d better bundle up.

Both the nominal and ordinal scales are used for categorical data (e.g., Coke or Pepsi preferences). The interval and ratio scales are used for continuous data (e.g., how much soda one drinks weekly).

Other areas covered by descriptive statistics include measures of central tendency, measures of variability, normal distributions, and skew. Even that list is not inclusive.

Module 1

Contribution of this course to the program: builds on what students learned in the scholar-practitioner model, research methods, and applied social psychology. It is essential to the successful completion of survey design, quantitative research methods II, and the research seminar series.

Other areas covered by descriptive statistics include measures of central tendency, measures of variability, normal distributions, and skew. Even that list is not inclusive.

Required Reading:

Navarro, D. (2022, July 14). On the psychology of statistics. LibreTexts. https://stats.libretexts.org/Bookshelves/Applied_S...

Bradley University. (n.d.). What’s the difference between descriptive and inferential statistics? OnlineDegrees. https://onlinedegrees.bradley.edu/blog/whats-the-d...

Coursea Staff. (2024, November 7). Descriptive vs. inferential statistics: what’s the difference? Coursea. https://www.coursera.org/articles/descriptive-vs-i...

Math Defined. (2024, January 15). What is a statistical question? Math defined [Video]. YouTube. (4:32)

Objectives

Demonstrate the ability to explain how descriptive statistics are used to convey information.

Module 2

There are four measurement scales: nominal, ordinal, interval, and ratio. We will briefly review each:

The nominal scale is the most basic--it names items. Numbers on football jerseys are nominal, as the numbers have no value. Social security numbers and license plates are examples of nominal data. Nominal data cannot be manipulated arithmetically. Theoretically, one could get the mean of all the football players’ numbers on a team, but the mean would not represent anything meaningful. Generally, we do a frequency count for data that are measured on a nominal scale. If you were to poll everyone in your workplace and ask if they prefer Coke or Pepsi, you would tabulate how many people or what percent of your organization prefers each soda.

The ordinal scale names and rank orders data. You could use this scale to award medals to runners in a marathon. The person who comes in first might run the course in 2 hours. The second-place runner might finish in 2 hours and 10 minutes. The third-place runner could finish in 18 hours. The actual times do not matter; the order in which they appear does. A second point is that the intervals between the times do not have to be uniform. A median is sometimes used to summarize ordinal scale data, but there can be other approaches.

The next scale on the list is the interval scale. This scale does what the other two scales do, but it also provides a measurement where the specific value carries meaning. The rules for an interval scale are as follows: The data must be continuous--meaning they can always be broken down further (I.e., seconds, temperature readings). There need to be equal intervals between the units. (E.g., Twenty degrees is twice as hot as ten degrees). However, the zero point is arbitrary. Calendar years are a good example. It is now 2024. If we count back 2025 years, was there any such thing as time? That is almost a silly question, but it gets the point across.

The final and most complex scale is the ratio scale. The ratio scale has most properties of the three simpler scales plus one more: The ratio scale has a true zero point. Money, height, and weight are all good examples of scales with a true zero point. As long as the data are normally distributed, meaning they form a bell shape when graphed, the mean is the ideal choice of a summary statistic for data measured on interval and ratio scales.

Objectives

Identify and differentiate among the four scales of measurement;

Required Reading:

Stevens, E. (2023, November 21). Measurement: Nominal, Ordinal, Interval & Ratio. CareerFoundry. https://careerfoundry.com/en/blog/data-analytics/data-levels-of-measurement

Shukla, D. (2023). A narrative review on types of data and scales of measurement: An initial step in the statistical analysis of medical data. Cancer Research, Statistics, and Treatment, 6(2), 279–283. https://doi.org/10.4103/crst.crst_1_23

Optional Materials

University of New South Wales. (2023, January 30). Types of data: Nominal, ordinal, interval, and ratio. UNSW Online. https://studyonline.unsw.edu.au/blog/types-of-data

Objectives

Identify and differentiate among the four scales of measurement;

Module 3

Graphs and charts can enhance the ability to understand a concept when they are used properly and judiciously. There’s no question that a picture is worth 1,000 words. While those of us who present data will agree with that, we also need to adhere to the rules of graphing. Different kinds of graphs are used for different kinds of data. Many of these are based on the scale on which the data are measured.

The simplest case is with data that are measured on a nominal scale. Let’s go back to the example of Coke or Pepsi preferences. As we said earlier, this data are measured on a nominal scale; the variable is discrete. Either you like Coke or Pepsi--mixing the two together is an unlikely preference. Assuming you have asked around at work, you might have found that 60% of your co-workers prefer Pepsi and 40% prefer Coke. With this information, you would create a bar graph. The brand of soda would go on the X-axis, and the percentages or frequencies would be on the Y-axis. You would place two bars, ensuring enough space between them. The space depicts the discrete nature of the data. No responses are between the two categories.

Now, assume you were measuring vocabulary for different grade levels in an elementary school. Would you want to create bars that touch or bars that have space between them? Your answer might depend on how you conceptualized the research. If you had a year-end measurement, you might consider the data discrete. On the other hand, if you are taking measurements throughout the school year, the bars might touch to show a more continuous view of how vocabulary develops.

When the data are continuous, we use histograms or line graphs. In the end, they look similar. A histogram is based on a bar graph that is made with bars that touch. A dot is placed at the midpoint of each bar, and dots are connected to show continuity. A line graph is constructed by placing the dots directly above the different levels of independent variables on the X-axis (e.g., grade in school) at a point corresponding to the dependent variables (e.g., frequency or percent achieved), shown on the Y-axis.

Objectives

Demonstrate an understanding of how graphs are used

Required Reading:

Statistics How To. (n.d.). Misleading graphs: Real life examples. https://www.statisticshowto.com/probability-and-st...

Stat Trek. (n.d.). Bar charts and histograms. http://stattrek.com/statistics/charts/histogram.as...

Visme. (2022, May 19). Data visualization in 2022 | The ultimate guide [Video]. YouTube. (11:01)

Rose, Q. (2023, September 19). Top 7 types of statistics graphs for data representation. StatAnalytica. https://statanalytica.com/blog/statistics-graphs/

Visme. (2022, May 19). Data visualiztion in 2024 | The ultimate guide [Video]. YouTube. (11:01)

SAS. (n.d.). Types of statistical graphs. http://support.sas.com/documentation/cdl/en/grnvwu...

Module 4

One of the most important topics we will discuss in this course is sampling. Psychology professionals must be particularly sensitive to the importance of appropriately considered samples. The background reading in this module will cover essential concepts related to this topic.

Objectives

Develop an appropriate sampling strategy

Required Reading:

Lane, D. (n.d.). Sampling bias. Retrieved from http://onlinestatbook.com/2/research_design/sampli...

Wyzant. (n.d.). Sampling. https://www.wyzant.com/resources/lessons/math/stat...

SPSS Help for Case Assignment:

Biostatistics Resource Channel. (2012, September 10). How to use SPSS - Frequency distributions & measures of central tendency [Video]. YouTube. (8:42)

Complete Dissertation. (n.d.). Descriptive statistics and interpreting statistics. https://www.statisticssolutions.com/dissertation-r...

Optional Materials:

LibreTexts Statistics. (2013). Observational studies and sampling strategies. Retrieved from https://stats.libretexts.org/Textbook_Maps/General...

Tuovila, A. (2022, December 24). Standard error of the mean vs. standard deviation: What’s the difference? Investopedia. https://www.investopedia.com/ask/answers/042415/wh...

Module 5

Measures of central tendency are of primary importance in statistics. These measures include the mean, median, and mode. Although there can be some overlap, each measure is most often associated with a different type of scale.

The mode measures the most popular category. Pepsi (60% preference) was the mode in the soda preference example. In a survey of ice cream flavor preferences, chances are pretty good that chocolate-based flavors would be the mode. The mode is most frequently used for nominal or categorical data. The categories cannot be mathematically manipulated. It is impossible to get a mean for ice cream flavor preferences. The only data available are frequencies of choice--the only possible measure of central tendency is the most popular category.

The median, which measures the point below which 50% of the distribution falls, is used with ordinal data or interval/ratio data when the sample is skewed. In terms of ordinal data, If ten runners are running a marathon, the running times may cluster at either end of the distribution. There may be a number of very fast runners and a number of very slow runners. If the data are not normally distributed, meaning there’s no pile-up around the mean, the mean is not a great indication of central tendency. (For example, if half of your grades are As and the other half are Ds, a mean of B- doesn’t describe your academic performance as no grades are actually B-). The median is a better measure as it pinpoints the running time above and below half of where the distribution falls.

If the faculty at a university wanted to get a measure of central tendency for their income, which is on a ratio scale, the distribution would be normally distributed--which means it’s bell-shaped, and the mean, median, and mode are at the same point. In that case, a mean would be fine as it would be an accurate representation of the distribution. However, if the University President’s income was thrown into the mix, that outlier would pull the mean upward, which means that the mean would no longer be a good representation of income. In that case, a median may be a better choice.

Objectives

Differentiate among the measures of central tendency and dispersion

Required Reading:

International Research Institute Data Library. (n.d.). Measures of dispersion. Retrieved from http://iridl.ldeo.columbia.edu/dochelp/StatTutorial/Dispersion/index.html

Online Statistics Book. (n.d.). Measures of central tendency. Retrieved from http://onlinestatbook.com/2/summarizing_distributions/measures.html

Sage Publication. (n.d.). Mode, median, and mean. Retrieved from http://www.sagepub.com/upm-data/35399_Module5.pdf

Bhandari, P. (2023, June 21). Central Tendency: Understanding Mean, Median, and Mode. Scribbr. https://www.scribbr.com/statistics/central-tendenc...

Optional

Laerd Statistics. (2013). Measures of central tendency. Retrieved from https://statistics.laerd.com/statistical-guides/measures-central-tendency-mean-mode-median.php

Module 6

Another critical topic in Descriptive Statistics are Measures of Variability. The most widely known are variance and standard deviation. The standard deviation is very simply the square root of the variance, which provides an “average” measure of distance from the mean of the distribution. In a normal distribution, approximately 34% of the scores will lie within one standard deviation above the mean, and another 34% will lie within one deviation below the mean.

Objectives

Demonstrate an understanding of measures of variability

Required Reading:

Lane, D. M. (n.d.). Measures of variability. Retrieved from http://onlinestatbook.com/2/summarizing_distributions/variability.html

Siegrist, K. (2022, April 24). The sample variance. LibreTexts Statistics. https://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/06%3A_Random_Samples/6.05%3A_The_Sample_Variance

Bhandari, P. (2024, March 28). How to calculate standard deviation (guide) | calculator & examples. Scribbr. https://www.scribbr.com/statistics/standard-deviation/

Optional Materials

Eberly College of Science. (n.d.). Stat 500 1.5.3 – measures of variability. The Pennsylvania State University. https://online.stat.psu.edu/stat500/Lesson01#measures-of-variability

Module 7

When we work with a population, distribution is assumed to be normal. This means that the data form a bell-shaped curve. The highest concentration of scores is located in the middle of the curve, which is the also then the mode. The distribution is symmetrical, so the median (which denotes the point below which 50% of the scores fall) is also right in the middle. The mean, which is the average of all the scores, is also at the same point as the median and the mode, meaning that the three central tendency measures are the same.

The shape of the normal curve is such that 34% of the scores fall between the mean and one standard deviation point above or below the mean, and 68% of the scores lie between the two deviations (from one below to one above). Approximately 15% of the scores lie between the 1st and 2nd deviations above or below the mean, and 49% of the scores lie between the mean and the 2nd deviation. Only 2% of the distribution (1% above and 1% below the mean) lies beyond the 2nd deviation in both directions. These percentages do not vary if the distribution is normal.

To measure individual performance on standardized tests, we can utilize z-scores. The tests have been standardized on very large samples or populations. The mean of a z-distribution is 0. The first standard deviation is labeled +1 or -1, for the points above or below the mean, respectively. The second standard deviation is +2 or -2 for the same reason. A z-score of +1.5 tells us that the individual scored one and a half standard deviations above the mean. A score of -2.33 lets us know that the individual scored 2 and one-third standard deviations below the mean.

Z-scores have many applications--one of which is utilized for standardized tests in elementary education. Any normal distribution can be transformed into z-scores. This would include many intelligence tests.

The nice thing about z-scores is that they are straightforward to interpret: The mean is 0. All scores that are positive numbers are above the mean, and all scores that are negative numbers are below the mean. Each deviation is a multiple of one.

Objectives

Identify the components of a normal distribution

Required Reading:

Nevil, S. (2025, July 23). Z-Score: meaning and formula. Investopedia. https://www.investopedia.com/terms/z/zscore.asp

Regents Prep. (n.d.). Z-score table & chart. https://www.regentsprep.org/z-score-chart/

Optional Materials

Laerd Statistics. (2013). Standard score. Retrieved from https://statistics.laerd.com/statistical-guides/standard-score.php

Math and Science. (2023, July 2). Intro to standard z-score & normal distribution in statistics [Video]. YouTube. https://www.youtube.com/watch?v=OavI_GiQUtI (19:06)

McLeod, S. (2023, October 6). Z-score: Definition, calculation & interpretation. SimplyPsychology. https://www.simplypsychology.org/z-score.html

Module 8

The normal distribution has one mode. There is one most frequent score, which is called a unimodal distribution. Because it is symmetrical, the distribution is not skewed. However, many distributions are skewed and/or have multiple modes.

Let’s address skew first. If I give a very easy test, most of the scores will fall on the high end of the distribution--probably in the high 90s. If we were to plot the scores, the highest point would be to the right of the X-axis; the distribution would taper off toward zero. This is called a negative skew. In a negative skew, the mode is greater than the median, which is greater than the mean. The few low scores pull down the mean.

Let’s reverse the scenario. If I were to give a test that’s either very difficult or for which nobody bothered to study, the scores would cluster on the low end of the distribution. The mode would be in the 20s or 30s. The tail would taper off toward the higher scores on the right of the X-axis. This is called a positive skew. It’s counterintuitive, but these distributions are named for the direction the tail goes--not where the mode is. In a positively skewed distribution, the mean is greater than the median, which is greater than the mode. Most of the scores are low, but the few high scores pull on the mean.

Another issue is modality—the normal curve has a single mode. The two distributions I provided as easy or difficult test results also have one mode. Sometimes, we find that students either grasp or fail to grasp the information we are teaching. The result is a distribution with two clusters or modes. Generally, one is in the A-range, and the other is closer to failing. Because there are two modes, this is called a bimodal distribution. The modes don’t have to be exactly equal to qualify as a bimodal distribution. The classification as uni- or b-modal may be a judgment call.

Sometimes, one data point can distort a distribution. If 9 out of 10 students do miserably on a test and beg for a curve and the 10th score, which is high, pulls up the mean, it is also not representative of the class’s performance. This is called an outlier. Sometimes, when outliers are present, the highest and the lowest scores will be excluded from the analysis.

Objectives

Demonstrate the ability to explain how descriptive statistics are used to convey information.
Identify and differentiate among the four scales of measurement;
Demonstrate an understanding of how graphs are used
Develop an appropriate sampling strategy
Differentiate among the measures of central tendency and dispersion
Demonstrate an understanding of measures of variability
Identify the components of a normal distribution
Evaluate the different ways in which skew can affect the interpretation of data

Required Reading:

McLeod, S. (2023, October 6). How to use the z-score table (standard normal table). Simple Psychology. https://www.simplypsychology.org/z-table.html

Geet van dn Berg, S. (2024). SPSS frequencies - quick tutorial. SPSS Tutorials. https://www.spss-tutorials.com/spss-frequencies-command/

SPSS Help for Signature Assignment:

Biostatistics Resource Channel. (2012, September 10). How to use SPSS - Frequency distributions & measures of central tendency [Video]. YouTube. https://www.youtube.com/watch?v=3ejAt1yPhLQ (8:42)

Complete Dissertation. (n.d.). Descriptive statistics and interpreting statistics. https://www.statisticssolutions.com/dissertation-resources/descriptive-statistics/