Statistics for Social Science (IS2204)

Office: KIC Bldg #212, Office Hour: Wednesday 15:00-16:30, email: wontak at khu dot ac dot kr

Do not send or request anything related to graded material electronically.
Blindly copying and submitting AI's answer is plagiarism and will result F.
FINAL
9 Jun 2026

Finally we are discussing the Pepsi vs Coca cola exclusive deal(p442) that was introduced at the very beginning of this course. The key question is to get an estimate of number of cans that will be sold. This is unknown for both Pepsi and Coca cola as they would not share this vital information to each other. However, to close the deal this number is needed. Hopefully now you see why and how statistics is different to mathematics. Feel free to use the case study workbook. To find out the number a random sample of 500 students asked each to keep track of the number of soft drinks they purchase on campus. Here is the random sample of 500 students. You have two options from here :1) Create CI and use LCL(not UCL) in the workbook. You can conclude right away or 2) Find the break even point in the workbook first(quick trial and error gives 1.165714) and then use the value to set the null hypothesis. Use H_0:mu=1.165 and H_1:mu>1.165 for example. Hope you see this problem becomes identical to Example 12.1 except the parameter (Newspaper Recyclying Plant). The t-test statistic is 3.318. You can use the rejection region method or p-value to draw conclusion. Note that your test should be one-sided.

If you would like to study beyond Chapter 13 in the coming fall semester, let me know before the final day that you are interested to do independent study. I believe you've learned the basic and reached our goal this semester. I won't repeat what is written in our book. Please read the top of p328.

Below is the glimps of what is ahead (Ch14). (Not included in final)

The analysis of variance(ANOVA) is the technique that allows us to compare two or more populations of interval data. ANOVA determines whether differences exist between population means. Ironically, the procedure works by analyzing the sample variance, hence the name.

The first formal ANOVA analysis was introduced by Ronald A. Fisher in 1921, where he applied variance partitioning to agricultural data.

What Fisher Did
  1. Problem: Crop yields varied a lot, but it wasn't clear whether differences were due to fertilizer treatments or just random fluctuations (soil, weather, chance).
  2. Idea: Partition the total variability in yields into:
  3. Method: He calculated sums of squares for each source of variation, then divided by degrees of freedom to get mean squares.
  4. Test: By taking the ratio of treatment mean square to error mean square, Fisher introduced the F-statistic - the core of ANOVA.
Simplified Example

Imagine three fertilizer treatments applied to wheat plots:

Fertilizer Plot 1 Plot 2 Plot 3 Mean Yield
Nitrogen 20 22 21 21.0
Phosphorus 18 19 17 18.0
Potassium 23 24 22 23.0

Fisher showed that if the between-groups variance is much larger than the within-groups variance, then fertilizer treatment truly affects yield , not just chance. Click here for more detail.

4 Jun 2026

If H_0 is true, the chance you get a false positive equals the TYPE I Error rate, alpha. A false positive is the event; TYPE I Error is the probability of that event. i.e., P(reject H_0|H_0 true) = alpha. If it is truly important, alpha needs to be small. Thus, the name significance level!

For example, when making a decision such as installing nuclear power plant, you want to avoid mistakes such as meltdown. The alpha is chosen less than 1 of million years in practice. When it comes to Superintelligence, the risk is much severe, human extinction. So we want to set the alpha much smaller than 1 over million. However, the tech giants do not know how to make it safe. They are currently gambling with alpha=0.25! If the risk is human extinction, the alpha should be much lower than the nuclear power plant.

The example 13.1 contains two stages: You first need to know whether the two populations have the same variance or not(the assumption is that the variance is unknown). Thus, in our text book the first inference is done with H_0:sigma_1^2/sigma_2^2=1 (skipping H_1). You need to determine whether the two population share the same variance or not to proceed further (use pooled estimate or individual sample variance). However, this inference is not the main inference. The main inference is H_0:mu_1-mu_2=0(skipping H_1 again).
2 Jun 2026

Inference for population mean with unknown population standard deviation requires t test statistics and inference for population variance needs chi-squared test statistics. Confidence intervals and hypothesis tests are two sides of the same coin.

Two-sided tests One-sided tests

The interval often feels more intuitive because it shows how far your estimate is from the threshold and gives a sense of uncertainty, while the hypothesis test gives a crisp reject/retain decision.

28 May 2026

To perform hypothesis testing, you can use either rejection region or p-value. The latter is used more often, however, the rejection region is much simpler and thus easy to understand.

Aspect Hypothesis Testing Statistical Inference
Definition A formal procedure to test whether data supports or rejects a specific claim (null vs. alternative hypothesis). The general process of using sample data to make conclusions about a population.
Scope Narrow, focused on a single claim or comparison. Broad, includes estimation, confidence intervals, prediction, and hypothesis testing.
Process - Define null (H_0) and alternative (H_a) hypotheses.
- Choose significance level α.
- Collect data and compute test statistic.
- Decide to reject or fail to reject H_0. 		- Use sample data to estimate population parameters.
- Construct confidence intervals.
- Make predictions.
- Test hypotheses.
Outcome Binary decision: reject or fail to reject the null hypothesis. Quantitative or qualitative conclusions about population characteristics, often with uncertainty measures.
Example Testing if a new drug lowers blood pressure compared to placebo. Estimating the average blood pressure reduction in the population and predicting outcomes for new patients.

Homework (6th4th June)
26 May 2026

There are two types of errors(mistakes by doing hypothesis testing); Type I error and Type II error. The probability of a Type I error is α and the probabiltiy of a Type II error is beta. Note that we call 1-α as confidence level and 1-beta "the power of the test". The ratio between α and β is called the Blackstone ratio. We would like to keep this ratio as low as possible. The idea behind this ratio is that "it is better many guilty persons escape the court than making one innocent person to suffer". If you mistakenly switch the null and alternative hypothesis, this ratio will blow up.
Please read p358-359 if you don't understand why the null hypothesis always state that the parameter equals(not inequality) the value specified in the research hypothesis.
To perform inference, you can use either rejection region or p-value. The latter is used more often, however, the rejection region is much simpler and intuitive to understand. When the sample mean falls to the rejection region defined by α, you will be rejecting the null hypothesis with significance α(or equally with confidence 1-α but people rarely express in this way). We are skipping section 11-3.
21 May 2026

There are two types of estimators; point and interval. Also, these estimators produce two types of esimates; one is point and the other is interval. For example, Sample mean Xbar(uppercase) is a point estimator and sample mean xbar(lowercase) is a point estimate. There are three desirable quality related to an estimator. 1) Unbiased 2) Consistency 3) Relative efficiency. If you take sample mean as an example, Xbar is unbiased and consistent estimator. Also, Xbar with large sample size will be more efficient compared to small sample size.

We started to talk about Hypothesis testing. Perhaps the most important step in the procedure is to set up the null hypothesis. Often it is confusing and students ask "Can we interchange the null and alternative(research) hypothesis? It seems there is little difference". In fact, if we make no mistake, it won't matter. However, we all know making no mistake is impossible. So you have to compare the cost of mistake or misjudgment. For example, think about which one is more damaging in the following cases: We (should) choose the null as less damaging case by comparing social cost in the long run.

Ch09 lecture slide Ch10 lecture slide (Skip 10-2a,2d,2e, and 10-3)

Ch11 lecture slide

Ch12 lecture slide

Homework (Due 2 June)
14 May 2026

Central limit theorem(CLT) is one of the most important result so far. It is the cornerstone of inferential statistics. It states, that under conditions, the mean of a large number of random variables (Xbar;captial X overline bar) has normal density. The center E(Xbar)=mu does not change with size of sample n. The V(Xbar)=sigma^2/n drops by n and as you've seen in the simulation, the larger n is, the narrower the density becomes. The reason why your science teacher told you to average multiple observations! He/She probably didn't explain why but the boring part(repeating) is what makes the average accurate.

We are done with descriptive statistics. We will do inferential statistics starting from next week. The CLT will become the main tool.

Homework (Due 28th May - a single page would be enough combine with Ch8 HW)
12 May 2026

Both normal density and student-t density are bell shaped(symmetric and unimodal). Key point to remember: 1) Student-t has thicker tail (because of this feature it is often called Fat-tail distribution) 2) normal has two parameters and student-t has only one. 3) Student-t gets close to standard normal if nu gets bigger.
I've noticed many students are turning to outside help (generative AI, web searches, tutors, etc.). While these help can be useful, please remember the goal of homework is to practice problem-solving and develop clear, logical explanations that will prepare you for the final. You may type or handwrite your work - either is fine - but screenshots of Excel with just a single number or an isolated answer aren't helpful. Show your steps and reasoning so I can follow how you reached the result. For example, if you want P(X < 4) for the Pat Statdude problem, write how you calculated it, e.g., =BINOM.DIST(3,10,0.2,TRUE), rather than only submitting 0.879126. Again, you can do entire homework by handwriting. Write how you used Excel. Both normal density and student-t density are bell shaped(symmetric and unimodal). Key point to remember: 1) Student-t has thicker tail (because of this feature it is often called Fat-tail distribution) 2) normal has two parameters and student-t has only one. 3) Student-t gets close to standard normal if nu gets bigger.

Homework (Due 28 May)
7 May 2026

In chapter 8, we focus on continuous random variables. Unlike discrete random varialbe, pointwise probability is always zero, P(X=c)=0 for any number c. It is because how the probability is defined. We use probablity density f(x) to define probability of continuous random variable; the area enclosed between the graph of f(x) and x-axis within given interval is the probability.
30 April 2026

midterm result Example 7.1(p218) is using survey(census) to derive the probability distribution P(x) and this P(x) is used to calculate E(X) and V(X). There is another way to get P(x). By doing experiment! In Chapter 7, you see two experiments: 1) Binomial experiment and 2) Poisson experiment. It is difficult to spot and relate these experiment in our real life, but if you do, it will save tremendous amount of time and effort because you can use pre-computed table or simply run Excel to get the P(x). Homework Homework due: 712 May
23 April 2026

There are six (three for expectation and three for variance) rules. These set of rules will help you to recycle already computed expectation and variance for a random variable X if the new random variable Y is expressed Y=aX+b, where a and b are numbers.
In short, there is no need to recompute the probability density of Y to get E(Y) and V(Y). Using six rules, E(Y)=aE(X)+b and V(Y)=a^2V(X).
In class, we discussed P=0.3S-6000, where random varaible S represent the sale and random varialbe P represent the profit. When E(S) and V(S) are given, E(P) and V(P) can be obtained quickly. Often, people only focuses on increasing E(P) and forget about V(P) but ignoring V(P) is where most business end up filing bankrupcy. If the standard deviation is too big, it becomes a gamble (An extreme event will wipe out all the profit accumulated).
23 April 2026

Chapters 7 and 8 are about random variables and their probability distributions. A random variable is denoted by X, and its observed values are written as x, which we call data. So far our focus was on x(lower case) but we are shifting our focus to X(upper case). We are tracking down the source!

Chapter 7 focuses on discrete random variables, while Chapter 8 deals with continuous random variables. For a discrete random variable, we describe its behavior using a probability distribution P(x). For a continuous random variable, we use something called 'probability density function', instead of 'probability distribution'. If the probability distribution is known, we can calculate the population mean and variance of X (not x): μ = E(X) = ∑ xP(x) σ² = V(X) = ∑ (x - μ)²P(x) These are population parameters!!! It may seem confusing that we suddenly talk like knowing μ and σ². The truth is we don't and never will. Here, the book author is assuming we know the true probability distribution, just to explain the concepts of mean and variance. In real applications, the distribution is almost always an approximation, so instead of the true parameters, we compute estimates from data. These estimates are written with a hat, such as μ^ and σ^, to remind us that they are estimates rather than the true population values. The expression μ = E(X) and σ² = V(X) is telling us that knowing probability distribution and knowing population parameters is essentially the same thing(equally daunting task). There is a good (and super important) reason why we are rewriting the parameters in this way. The answer will show up soon, in Ch9.

Last time we talked about how to make a better decision using Bayes' Law. The probability is really affecting our lives and the way we do stuff, especially where fairness is important. No additional homework other than reporting the win rates of monty hall problem below.
21 April 2026

The driving factor of Bayes' formula, surprisingly, is not P(B|A) but P(A). P(A|B)=P(A and B)/P(B) = P(B|A)P(A)/{P(B|A)P(A) + P(B|A^c)P(A^c)}.

Suppose event A is "having a disease" and event B is "testing positive." The probability P(B|A) can be extremely accurate-for example, 99.9%-yet P(A|B) can still be very small. This means that testing positive may not be as serious as it first appears. The problem is that many people confuse these two probabilities. They interpret P(B|A)=99.9% (the probability of testing positive given you have the disease) as if it were P(A|B) (the probability of having the disease given you tested positive). But they are not the same. The rarer the disease, the smaller P(A|B) becomes. You can see this by adjusting last week's calculator: keep everything fixed and only change P(A), the prevalence of the disease, from small to large. Notice that the true positive rate (TPR) has less impact. It's quite counterintuitive! If the disease is widespread (high P(A)), then even a less accurate test-for example, P(B|A)=0.7-can still be very effective. In this case, a positive test result most likely indicates that the person truly has the disease. This was the case with COVID-19 testing. When people said the test kits were "effective," it wasn't about the accuracy P(B|A) of the test itself, but about how widely the virus had spread, P(A). Don't get fooled by 99.9% of TPR! There are other dimensions to consider.
Reducing FP and FN simutaneously is impossible. Reducing one will increase the other. Good news is that almost always one of them is more importantthan the other. For example,

Remark on one of Homework: How do you show advertisement is effective or not? Hopefully you can connect this with Example 6.9. P(Scoring high|prep course) > P(Scoring high). In Example 6.9, what you wanted to show is whether buying prep course is effective or not. Going back to advertisement problem, it has nothing to do with low or high value of P(Buy|Ad). If P(Buy|Ad)=P(Buy) then these two events become independent and advertisement adds no value. Thus, if you want to argue that the advertisement is effective, you need to show that P(Buy|Ad) > P(Buy). The real interesting question is how to really estimate these two probabilities. One of the methods is to do simulation! You can set up an experiment like the 'find me' homework. In fact, you can compare P(win|changed) and P(win). Then you can talk about whether changing the door is effective strategy or not.
16 April 2026

If P(A|B)=P(A), then we say event A and B are independent. Do not define 'dependent' event. Instead, call it 'not independent'. The Bayes' Law(or Rule) is using P(B|A) to get P(A|B), where P(A|B) is the posterior probability of interest. The key idea is to decompose the event B into two mutually exclusive events: B = (B and A) or (B and A^c). Then P(B) = P(B and A) + P(B and A^c) = P(B|A)P(A) + P(B|A^c)P(A^c). Therefore, we have the Bayes' formula, P(A|B)=P(A and B)/P(B) = P(B|A)P(A)/{P(B|A)P(A) + P(B|A^c)P(A^c)}.

The Ex6.9 uses subjective probability for P(A)=0.1 and will invest $500 only if P(A|B) exceeds 0.2. Plug in the given probabilities P(B|A)=0.52, P(A)=0.1, P(B|A^c)=0.23, P(A^c)=0.9 into the Bayes' formula we get P(A|B)=0.201. Homework
14 April 2026

Sample space S is a set of all possible outcomes from a random experiment. We define a probability, using the outcomes in S. Two conditions should be met to be able to call numbers (attached to outcomes) probability. Each outcome is also called a simple event and an event is a set of one or more simple event. 'Probability of an event' will be calculated using 'probability of simple events'. One special event is an event 'A and B', where A and B are events. 'A and B' is the event's name(or label). The probability of the event 'A and B' is called joint probability of event 'A and B'. Given two events 'A' and 'B'(think about cross classification table), there are four joint probabilities and four marginal probabilities. A conditional probability is the ratio between joint probability and marginal probability, P(A|B)=P(A and B)/P(B). Homework Due: 21 April
9 April 2026

Chapter 6 is not difficult, if you pay attention to the words(terminologies). Be sure you know the difference between "outcomes" and "events", also their probability.

Using the "probability of outcomes", we created probability of event and then introduced the concept of joint probability. After having "joint probability", we defined marginal probability from the joint probability table. Finally, the ratio between "joint probability" and "marginal probability" resulted conditional probability. The "conditional probability" will be used to determine independent events. Do not define an useless word "dependent" event. Say "not independent" whenever you need.

As you can see, a new concept builds upon the ones before. So it is super important to keep up with the material, especially Ch6!

added below - 14th April There are three different ways to collect data; Direct Observation, Experiment, and Surveys. Out of these three, surveys are the most difficult one to do it right. The most important survey parameter is the response rate. All trustworthy survey result report this and all garbage survey does not have it. There are two reasons why you don't see the response rate in the result. The first reason is not educated and don't know this needs to be reported (Red flag). Second reason could be criminal act depending on the case but from time to time people cheat about the rate and choose not to disclose (+Red flag). Stay away from garbage surveys. Between 'sampling error' and 'non-sampling error', non-sampling error is more serious as once it sneaks into the data it is impossible to remove it. Three examples are i) errors in data acquisition, ii) nonresponse error, and iii) selection bias. In this introductory class, we will not worry about these issues and use the data as given, but do know that real data could have all three in it. Can you imagine training AI with biased data sets?
7 April 2026

Ch6 is about probability. Pay special attention to the terminologies in this chapter. We define probability of outcomes from a random experiemnt.
Ch5 is the only chapter that talks about data collection. Do not pay attention to a survey that has no or low response rate. The non-response is a typical non-sampling error. Because statistic is a numerical summary of a Sample, the quality of statistic heavily depends on the Sample. Homework (Please check the Chapter 4 homework due below.) When doing homework, try to show and explain what you are doing or trying. I am not interested your final answer. That is not the point of giving you an assignment. I will grade based on answers in midterm and final, but not for the homework. Homework due: 14th April
2 April 2026

Three important materials covered this week; Covariance, Coefficient of correlation, and the Least Squares Methods. Pay attention to the sign only when using covariance. The magnitude of covariance could be misleading (the housing size vs price example). If you want to measure how strong the linear relationship is you have to divide the covariance with each of the standard deviation and use 'Coefficient of correlation'. The 'rho' or 'r' is in between -1 and 1 so you can now say how strong the positive and negative linear relationship is. Take a close look at the three sets in our textbook to compare covariance and correlation. Don't forget that strong correlation does not imply causation.

You can construct the least squares line or regression line with few clicks in Excel- review Example 4.15.

There are many names for median. 50th percentile, second quartile, and Q2. The interquartile range is important because it tells you where the 50% of middle chunk of data is located. Lastly, we studied how to find the three quartiles.
26 March 2026

Starting from Ch4, we will focus exclusively on mean. Mean is applicable only for the interval data type. This does not imply interval data type is more important than others. It is because mean is easy to calculate the center (remember? this class is introductory). Depending on your future major study other central measures could be more important.

Chapter 4 is about central and variability measure of data type. There is a good reason why we are learning this after studying overall data visualization and distribution. It is because the single number(mean, median, mode, range, variance, etc.), which we call summary, sometimes is not a good representation of sample (or population) and thus misleading. Also, Ch5 is relatively short and this does not mean it is less important. As matter of fact, Ch5 alone can be expanded and stuided for semesters.

Homework data set for *homework. Homework due: 9th April
24 March 2026
The core idea in chapter 4 is to find where the center (of the data) is. Considering data type, we should ask what center means in each cases. The center for nominal is mode, for ordinal is median (or mode), and for interval all three -- mode median, mean. I wish you can confidently answer the question, "Do GPA accurately reflect student's overall academic performance?" From now on we will use the word arithmetc mean instead of average. Mean, Median, and Mode, which one is better? depends on the data and rarely there is the best one. I recommend to check all three for interval data.
19 March 2026


Ordinals can be treated like nominals (Nominals can not be treated like ordinals. Never do that), so one can use pie or bar to represent them. Histogram is a way to represent interval data. Histogram and Bar chart is completely different tool. We also discussed about the shape of Histogram. Homework data set for homework. Remember Correlation is not causation. Here is the website on spurius correlations.

We are still in the descriptive statistics zone (first half) and will stay for about a month. Depending on your background, upcoming chapters may or maynot be easy to follow. Please do your own reading.
17 March 2026

I will give extra credit for homework assignment if you apply for Study Group.

Here is Excel tutorials for Histogram, Line chart, and scatter plot. These will be tested(pass or fail). Make sure you can do this within five minutes.
12 March 2026

Some important keywords from this week: (Random)Varialbe, univariate, bivariate, multivariate, and most importantly the Data. There are three data types. Data types are needed to find 1) the correct center and 2) the right graphical representation. Studied how to represent nominal data using table(frequency table) and graph(pie and bar). Homework
5 March 2026

What is statistics and why you want to learn it. There are two branches of statistics(descriptive and inferential). In Descriptive statisics the main focus is on center and variability. Inference, is more than just deducing number, it is more on using the number to make a decision. Among all things you learned today, significance level(α) is the most important one to remember. Homework
3 Mar 2026

Your eventual goal should be; 1) understand the basic terminologies in written form, 2) able to apply/use statistics in the correct way, and 3) able communicate using statistics.

Also, here is the reason why you must learn terminologies: The neccessary condition of good prompt to use AI-assistant effectively is use the correct word. If your prompt is vague the answer will be vague. However, if your prompt is sharp, you will get professional quality results. The first step to create a good prompt is to start to use correct words.

Homework