I’m happy to say I’m officially moving on from statistics. I did well enough on the course challenge this week, scoring a 26/30 (but it really should have been 28/30), to feel good about going forward to calculus. The final two units of the course, Prepare for the 2020 AP Statistics Exam and AP Statistics Standards Mappings, only took about 5 minutes to get through meaning I spent most of this week doing the course challenge and the 3 unit tests I needed to redo after getting a few questions wrong on the course challenge in order to bring my scores in those units back up to 100%. I got through the final unit test this morning so I’ll be starting calculus right at the beginning of next week, Week 69 (😏). LET’S. GO.
I started this week by working through the only exercise in the unit Prepare for the 2020 AP Statistics Exam. This exercise was made up of 7 questions, each of which asked me to determine whether a Chi-Square test, Z-test, or T-test was the appropriate test to use based off the scenario described in each question. In terms of having to think about how and when to use each type of test, this was the most helpful exercise I’ve gone through to help me understand the difference between all 3 types of tests. By the end of the exercise I had a much better idea of how and when to use each type of test.
The final unit of the course, AP Statistics Standards Mappings, turned out not to contain any new material. It was a list of all the exercises and videos in the course and associated each with their corresponding course-codes within the U.S. educational system, I believe. I realized there was nothing I had to do in that unit and moved on to the course challenge.
I did the course challenge over two days, Wednesday and Thursday. I ended up getting 4 questions wrong but really should have only gotten 2 questions wrong. I also had to double check my notes for 3 of the questions to make sure I had the right answer before submitting my response. The 7 questions I either got wrong or had to review my notes before answering them were:
- Q. 4) Random Sampling – Clustered VS Stratified
- This question described a situation where someone sampled a population using some type of sampling method and asked me to choose the name of the method they used out of 4 possible options. I had to look up the definitions for clustered sampling and stratified sampling before answering but actually had the correct answer chosen beforehand anyways.
- Stratified Random Sample
- The population is first split up into groups. The overall sample consists of some percent or members from each group. The members from each group are chosen randomly.
- Cluster Random Sample
- The population is first split up into groups. The overall sample consists of every member from a handful of the groups (i.e. clusters). The groups/clusters are selected at random.
- The population is first split up into groups. The overall sample consists of every member from a handful of the groups (i.e. clusters). The groups/clusters are selected at random.
- Stratified Random Sample
- This question described a situation where someone sampled a population using some type of sampling method and asked me to choose the name of the method they used out of 4 possible options. I had to look up the definitions for clustered sampling and stratified sampling before answering but actually had the correct answer chosen beforehand anyways.
- Q. 16) Types of Bias – Response Bias VS Voluntary Response Bias
- This was a question I got wrong but should have gotten correct. The question was, “A principle surveyed a sample of his students about whether they had their phones out during class. Only 10% of students said they did. He looked into the classrooms the next day and saw it was closer to 25%. What type of bias occurred when he interviewed the students?”. There were 5 answers and the first one I saw was “voluntary response bias” which seemed to make sense in my head so I chose it. The correct answer was actually “response bias” which was further down the list. Voluntary response bias is where people can choose whether or not to respond to the question, whereas response bias is when someone has to respond but will likely lie. I would have been able to figure out the right answer if I had looked through the entire list and thought about it a bit longer.
- This was a question I got wrong but should have gotten correct. The question was, “A principle surveyed a sample of his students about whether they had their phones out during class. Only 10% of students said they did. He looked into the classrooms the next day and saw it was closer to 25%. What type of bias occurred when he interviewed the students?”. There were 5 answers and the first one I saw was “voluntary response bias” which seemed to make sense in my head so I chose it. The correct answer was actually “response bias” which was further down the list. Voluntary response bias is where people can choose whether or not to respond to the question, whereas response bias is when someone has to respond but will likely lie. I would have been able to figure out the right answer if I had looked through the entire list and thought about it a bit longer.
- Q. 17) Geometric Series
- This was a question I got correct but had to check my notes before answering and would have gotten wrong if I didn’t. I don’t remember the question exactly but I know it asked me to find the mean and standard deviation of a geometric series. I was able to fully comprehend what the question was asking but couldn’t remember the formulas for either calculation. I looked them up in my notes and found that the formulas are:
- Geometric Series Mean
- μ_X = 1/P
- Geometric Series Standard Deviation
- σ_X = (√(1 – P))/P
- σ_X = (√(1 – P))/P
- Geometric Series Mean
- I still don’t fully understand how or why these formulas work. It’s something I’m going to leave for now and hopefully I’ll find them easier to understand if/when I come back to stats once everything that I’ve learned has had time to settle in my mind.
- This was a question I got correct but had to check my notes before answering and would have gotten wrong if I didn’t. I don’t remember the question exactly but I know it asked me to find the mean and standard deviation of a geometric series. I was able to fully comprehend what the question was asking but couldn’t remember the formulas for either calculation. I looked them up in my notes and found that the formulas are:
- Q. 22) Chi-Square Test for Independence
- Considering how recently I worked through Chi-Square tests, I’m embarrassed that I had to double check my notes for this question. The question asked me to find the expected value of a cell based off the given observed values on a two-way table and given that H_o: all cells independent. For the most part, I remembered how chi-square tests for independence work but forgot how to calculate the expected value for the cell. After looking it up, I remembered the expected value for each cell is calculated with (margin % of cell’s column) * (margin % of cell’s row) * (n).
- Considering how recently I worked through Chi-Square tests, I’m embarrassed that I had to double check my notes for this question. The question asked me to find the expected value of a cell based off the given observed values on a two-way table and given that H_o: all cells independent. For the most part, I remembered how chi-square tests for independence work but forgot how to calculate the expected value for the cell. After looking it up, I remembered the expected value for each cell is calculated with (margin % of cell’s column) * (margin % of cell’s row) * (n).
- Q. 23) P(set A) + P(set B)
- I didn’t fully comprehend this question but, even if I had, I may have still gotten it wrong. Here’s a visual representation of how I misinterpreted the question:
- —
- The question told me that set A was 90% of the population and set B was 82% and that 75% of both sets overlapped. The question asked me what the probability of a data point falling inside set A OR set B was and I thought I was supposed to add (90% – 75%) + (82% – 75%) but really I should have added (15% + 75% + 7%).
- The question told me that set A was 90% of the population and set B was 82% and that 75% of both sets overlapped. The question asked me what the probability of a data point falling inside set A OR set B was and I thought I was supposed to add (90% – 75%) + (82% – 75%) but really I should have added (15% + 75% + 7%).
- Q. 26) P-value
- This question described a critical value on a normal distribution of data and asked me to choose the correct formula to find the p-value. Somehow, I missed the part of the question that stated “p-value” which was the reason I got the question wrong. I had correctly narrowed down my answer to 1 of 2 possibilities. The difference between the two choices was choosing a greater-than or less-than sign, z > σ_P and z < σ_P. If I had read the question properly and taken a bit of extra time to consider that the p-value refers to the tails of the distribution, I would have chosen the correct answer which was z > σ_P. Unfortunately, I didn’t think it through well enough or fully comprehend what I was even being asked and guessed the wrong answer.
- This question described a critical value on a normal distribution of data and asked me to choose the correct formula to find the p-value. Somehow, I missed the part of the question that stated “p-value” which was the reason I got the question wrong. I had correctly narrowed down my answer to 1 of 2 possibilities. The difference between the two choices was choosing a greater-than or less-than sign, z > σ_P and z < σ_P. If I had read the question properly and taken a bit of extra time to consider that the p-value refers to the tails of the distribution, I would have chosen the correct answer which was z > σ_P. Unfortunately, I didn’t think it through well enough or fully comprehend what I was even being asked and guessed the wrong answer.
- Q. 27) Study Design – Block Chain
- This question gave me a description of a sample and asked me to choose the corresponding name for the method that was used out of 5 possible choices. I don’t remember the question exactly but I noted that the correct answer (which I didn’t pick) was a randomized block design sampling method. I still don’t fully understand how this type of study design works but here’s a description I found online:
- Block Design – Springer.com
- “A randomized block design is an experimental design where the experimental units are in groups called blocks. The treatments are randomly allocated to the experimental units inside each block. When all treatments appear at least once in each block, we have a completely randomized block design. Otherwise, we have an incomplete randomized block design.”
- Block Design – Springer.com
- This question gave me a description of a sample and asked me to choose the corresponding name for the method that was used out of 5 possible choices. I don’t remember the question exactly but I noted that the correct answer (which I didn’t pick) was a randomized block design sampling method. I still don’t fully understand how this type of study design works but here’s a description I found online:
Even though I only got an 87% on the course challenge, I feel ok to move on especially considering I could have gotten a 93% if I had taken a bit more time when answering two of the questions I got wrong. As mentioned above however, I did make a point of going back and redoing the 3 unit tests I needed to do to bring my scores in each unit back up to 100%.
The first unit test was from the unit Study Design. I actually had to redo the test 3 times before passing with 100% but, even still, it wasn’t too bad. Redoing it a few times was a good opportunity to review the definitions of each type of study design. As usual, the toughest part was comprehending what each question was actually asking. The second unit test was from the unit Probability which I passed on my first attempt. I had to go back and review how to add sets of information, i.e. “Find the total probability for Set (A) OR Set (B)“. It was also good review on combinations and permutations, as well as weighted probability. Lastly, the third unit test was for the unit Significance Tests (Hypothesis Testing) which I also passed on the first try. I had to review a few things during the test, including the table for Type 1 and Type 2 errors, but fully understood all the concepts the questions asked me and had the right answers chosen before looking up anything in my notes.
On a random side note, I forgot to mention last week that recently, in addition to KA, I’ve been using another YouTube channel called Crashed Course to watch videos on math. The channel has a ton of elearning content and a fairly big playlist on statistics. I find the speakers in their videos go a little too fast but the videos overall are well produced and do a good job of simplifying tricky concepts. When I get stuck on something on KA, if I can find a Crashed Course video about the subject their video will often explain the concept slightly different than KA which can illuminate the part I’m confused about. It’s a great second resource to have and one that I’ll likely use regularly as I move through calculus.
It’s hard to believe that it’s been ~16 months since I first began KA. Learning calculus has been the goal since day one so it feels great to finally be here, not to mention that it was also my goal to start calculus before 2021 so that also feels great. I found stats interesting and useful but I’m happy to put it behind me for the time being. I enjoy doing equations more than learning about theory-based problems and/or definitions which statistics seemed to mostly be about. I’m hoping calculus will be more similar to arithmetic and algebra in terms of the amount of equations I’m asked to do. My new goal is to get through calculus before the 2-year mark which gives me ~8 months. The main reason I’m aiming to finish it by September is I think it would be cool to be able to say I started at arithmetic and learned calculus within two years. Cool in a nerdy type of way, of course.