Statistical Analysis Methods: Difference and Relationship Tests

Understanding statistical analysis methods is crucial for effectively interpreting data relationships and differences in research.

### Understanding Statistical Analysis: Difference Tests and Relationship Tests
* 📊 In statistical analysis, two primary types of methods are recognized: **difference tests** and **relationship tests**, each serving distinct purposes in research.
* 🔍 Difference tests focus on examining the differences between groups, with specific methods like **t-tests** and **ANOVA** depending on the **number of groups involved**.
* On the other hand, relationship tests analyze how variables relate to one another, employing techniques such as **correlation analysis**, **regression analysis**, and **logistic regression** to explore these connections.
* 📈 "Correlation analysis examines the relationship between two variables without implying a **cause-and-effect dynamic**," while regression analysis delves into **causal relationships** among multiple variables.
* 🎮 The speaker shared past research on online gaming, highlighting the **factors influencing player immersion**, which illustrates the application of **regression analysis** in understanding **complex interactions**.
* 📉 Hierarchical regression was introduced as a method to assess how **third-party influences can moderate relationships** between primary variables, emphasizing the need to **consider multiple factors simultaneously**.
* 📑 The session concluded with an overview of the methodologies, stating there are **seven types of difference tests** and **four types of relationship tests**, which will be explored using SPSS in upcoming lessons.
* 🛠 Understanding which statistical method to use is **crucial for effective analysis**, and the ability to **interpret hypothesis test results** will be developed in future sessions.

During the break, a question came up, so let me explain. Here, we have two groups, right? There are also two here. If there are three or more, that works too. What I mean is that until now, we have only used one grouping variable. However, here we have two grouping variables. One is temperature and machine, and the other is group and time point. Just like this, we are considering two things simultaneously, which is why there is no such method in TTS. Therefore, it doesn't matter whether there are two or three groups for that one variable. As we discussed, it depends on how many variables there are. It’s not about how many groups there are for one variable. We can clearly distinguish between groups and variables. Here, we are looking at how many groups there are for one variable, whether it’s three or four. In this case, we need to see how many grouping variables are relevant to the variable of interest. So, that’s what we are looking at.

There is a term called way, and there are one-way and two-way analyses. The way refers to the number of variables. In a one-way analysis, there is one variable of interest, and that variable should be divided into three or more groups. In a two-way analysis, there are two or more variables of interest. So, if I have three variables of interest, is it possible? It might be complicated, especially when there are three interactions involved. However, it is indeed possible. In that case, what do we call it? One-way, two-way, and what else? There can be three-way analyses as well. So, is there a three-way analysis? Yes, there is. Four-way and five-way analyses exist too. But when you go beyond three dimensions, do you understand it? No, it's difficult, right? The same applies to our research; studies usually go up to three variables, but beyond that, it can be overwhelming. Typically, we use up to two variables, but occasionally, some researchers do study up to three variables. It is possible, indeed.

The term variable refers to continuously including the variables I am interested in. You can think of it that way. I provided a brief explanation. The second point is relationship testing. Now, instead of looking at the differences between group A and group B, we are asking everyone. As I mentioned earlier, a satisfaction survey will be conducted this week. Please make sure to check it, as we will analyze the relationship between what you checked and the variables. Various policies will be developed based on this. The most commonly used methods are correlation analysis, regression analysis, and cross-tabulation analysis. If you are not familiar with these, there is one clear method. As I mentioned earlier, there are several types of data formats, and broadly speaking, there are two main categories.

There are qualitative variables and continuous variables. Now, if you look closely, all relationship tests involve either continuous variables or qualitative variables. The two types of variables are the same. They are not different. Both are represented as squares, and both are not circles. Everything else is a circle, except for this one, right? You can understand that if the variables are the same, it is definitely a relationship test. Anyway, that's a problem for later. Let's take a look at the content. 

There is a method called cross-analysis, but I will skip that for now. The most fundamental aspect of relationship testing is correlation analysis. You need to understand correlation analysis in order to understand what comes next, so I will skip ahead. This is about correlation analysis—how much relationship exists or not between variables, such as between men and women.

Is there a dominant role? Should a woman necessarily like a man, or should a man necessarily like a woman? Right? A man should like her, right? Regardless of that, first of all, there is no cause and effect between men and women. Both men and women can like each other. I want to see the influence in an equal relationship like that. Then it becomes a correlation. As you can see here, do tall people tend to weigh more or less? Generally, taller people tend to weigh more, right? They have heavier bones. Of course, it may not always be proportional, but then, do people who weigh more tend to be taller or shorter? If we only look at weight without considering body type, we can understand that people who weigh more tend to be taller because of their bone weight.

There is a relationship between height and weight, meaning that they influence each other without a clear cause-and-effect relationship. When there is such a relationship, we refer to it as correlation. In English, it's called correlation. In any case, when two variables are of interest, there is no distinction between which is the cause and which is the effect. 

On the other hand, regression analysis, as mentioned below, involves causal relationships, meaning that there is a clear cause and effect. The table that follows will show that when we conduct regression analysis and correlation analysis, we create graphs and draw lines based on the data. By gathering this data, we can determine whether there is a relationship based on the scores. 

There are various methods available, including those similar to correlation analysis. Additionally, here, I will share some research I conducted back in 2002. In 2002,

I researched online games, and at that time, did you all know about Lineage? Those who don't know are probably quite new, while those who do know are likely to be older players. Right? In 2002, when Lineage 1 was released, there was a shift to 3D graphics. You probably don’t remember that, do you? How old were you ten years ago? No, it’s actually been 14 or 15 years. So, you were in kindergarten back then. This is what I researched. What kind of research did I conduct? At that time, online games like Lineage were booming, and I was curious about how people could immerse themselves in games. What needs to be done for people to become absorbed in games? I have studied this, and there’s a paper I presented on it, which you can still find today. So, what I did was categorize the various factors that contribute to game immersion.

Back then, it was called a tool avatar. The term avatar is now a common term, but at that time, it was not widely used. It was around the time when MMORPGs first came out, so people creating and moving avatars was quite a novelty. Nowadays, it might be hard to understand what I'm talking about. There was a time when games like Galaga were popular. You know Galaga, right? It was an era when people played shooting games without avatars. The quality of these tools significantly affects how immersed players become in the game. Then there's the reward system; when you die, you receive feedback. Each time you kill an enemy, you level up. Should leveling up happen quickly to keep players engaged, or is it better to level up more slowly? In any case, leveling up requires defeating a certain number of monsters.

When we do something like this, the speed and amount of feedback and rewards we give can have an impact. Then, how much information we provide about the information game matters. At that time, it was the era of 2D design, so should we go for something simple or more complex? Now, everything is 3D, but there was a time when 3D might have been either good or bad, especially since computers were very slow back then, which significantly affected graphics and network speed. 

Furthermore, in a community, like a guild in an MMORPG, the important thing is having your own guild. There was a time when players would gather and say, Hey, what time are we meeting today? and everyone would rush to play together. Do people still do that nowadays? I haven't been playing games recently, so I'm not sure. This is what we are investigating. So, what does this mean?

There are indeed five causes, and among these causes, we are looking to find which one has the greatest impact on immersion. Out of the five variables, some will be more important while others will be less significant. In other words, there will be factors that influence immersion and some that do not. Our task is to identify these influences, and among those that do impact immersion, we need to determine which have a greater effect and which have a lesser effect. This method is called regression. Do you understand? Regression, also referred to as regression analysis. At the beginning, we have correlation analysis, and at the end, we have regression analysis. However, if we look closely, we can see that correlation analysis examines one variable against another in a one-on-one manner. Right? But when we conduct correlation analysis with multiple variables, it proceeds in a tournament style. What I mean is...

When it comes to the World Cup, during the round of 32, four teams take turns playing; they don't face off one-on-one. In correlation analysis, if I have more than two variables of interest, say three or four, I examine all pairwise correlations. It's a tournament format where I look at the relationship between variable one and variable two, then between variable one and variable three, and so on. This is correlation analysis. 

But what about regression analysis? It's one-to-one. For example, I fought with a ratio of 17 to 1. This represents regression analysis. In other words, rather than examining five variables separately, we look at the differences in influence when they are considered simultaneously. So the difference between regression analysis and correlation analysis lies in that. There are two aspects: one is that when we interpret correlation analysis, the two variables are independent of each other. We assess the influence without determining whether one affects the other; they are considered equal in terms of influence. In correlation analysis, the method is to analyze pairwise. This is correlation analysis.

Regression analysis is a type of analysis that examines the relationship between cause and effect. When analyzing, we consider multiple variables simultaneously. Now, moving on to the next topic, there is hierarchical regression. We won't cover this in class, but let me briefly explain it. Satisfaction affects loyalty, but as addiction to games increases, the impact of satisfaction on loyalty changes. Let me give you an example. I am in a relationship. Earlier, I mentioned that this is how it works. This is an example. We are dating. Yes, we are dating each other. So, how much do you like me? One? Okay, one. This time, you say you can't live without me. Now, I am looking at this from a perspective of an equal relationship, which relates to the correlation we discussed earlier.

It's an analysis. I looked at it from an equal perspective. However, the problem is that I developed feelings for someone else. So, we have two people: the first is my original partner, and the second is my new partner. I met them separately. In this case, how much do they both like me? They both like me equally, at a level of 1. Okay, that seems fair. Anyway, both like me at level 1, and now we have this relationship. So, I analyzed it separately. This analysis was done from an equal standpoint even with three people involved. However, I mistakenly sent a message. I sent a message about a certain date and place to both of them at the same time. Both of them received it simultaneously, and they now know that I’m seeing both of them. In that situation, will the values change? No, they won’t. How will the values change? Yes, they will still change. How will they change to? 0.5 for each.

Has it changed? Is it changing or not? It does change. Now, let's discuss the difference between correlation analysis and regression analysis. Of course, we also look at whether there are causes and effects, but here we are looking at a one-to-one relationship, while here we are trying to examine the influence of all the variables of interest simultaneously. That is the main significance of regression analysis. The difference is whether we analyze in a one-to-one manner or a one-to-many manner. So, if you look at the content we saw earlier, what do you see? It indicates whether it's one-to-one or one-to-many. That is its meaning. So, when analyzing one variable, the method of analyzing it from an equal standpoint is correlation analysis. However, when we include all the variables of interest simultaneously, the outcome variable is always one. I mean, there are many, but there is only one outcome.

This is the meaning of regression analysis. It's not about a general relationship; it's a one-to-one relationship. Please don't get confused. So, what you can see here is regression. Now, what is hierarchical regression? This is what we refer to as a moderating effect. For example, let's say we really like each other. Throughout today, we have been in a relationship where we like each other. Earlier, I mentioned that we like each other equally. But then, a friend comes along. This friend comes and starts talking badly about me. Does that change things? Yes, it does. What has changed? The value has decreased. In our relationship, a third party has influenced it. Did they influence it directly? No, they did not.

Without asking me directly, it changed indirectly, right? The relationship between the two has changed, hasn't it? It has changed. This relationship is like this: we both like each other, but there is an influence from a third party intervening. As a result, the feelings between the two have shifted. This is the hierarchical regression analysis we are discussing. So, they both like each other, but suddenly a third party appears. Many people have been involved simultaneously, and I've been juggling multiple relationships. In regression analysis, if they both like each other and a third party comes in to intervene, we can organize it as a moderating effect. You don't need to know the rest, but there is one thing we must learn. You don’t have to learn this part, but you need to learn this: we have feelings of affection, and those feelings are represented by a circle at the front.

What it is, is that usually when we measure, we give scores between 1 and 5. So, we rate things as very good, good, average, and so on. Since there are several values like this, we treat this as a continuous variable. However, when conducting research, there are cases where there is a cause, but the result ends with a yes or no outcome. For example, did you go bankrupt or not? When I go to the bank to borrow money, there’s a high probability that this person will go bankrupt. So, did they go bankrupt or not? Will they lend me money or not? There’s a clear decision to be made. As you can see here, the causes are the same, but the two outcomes are different. They both represent regression. However, what’s the difference between these two? One is a circle, and the other is a square. This indicates that the result can end with a yes or no. Did they go bankrupt or not? Now, when our company goes to a bank, what happens is...

There is a program that takes various scores and values. When a company comes to apply for a loan, it inputs the company's sales figures, current sales, debt ratio, and so on. Then, once you run the program, it determines whether to grant the loan or not with a clear yes or no result. In solving our problems, we use a method called logistic regression in such cases. As you can see, everything has been transformed: correlation analysis leads to regression analysis, and regression analysis leads to logistic regression. This process gradually evolves. Correlation analysis is one-to-one, regression analysis is one-to-many, and logistic regression results in a yes or no outcome. This gradual transformation forms the problem we are discussing. What we are talking about now is the solution when we face a problem.

So when you are conducting a relationship test, one of three things will be involved. Since one of the three is included, you need to keep in mind these three, but let's exclude this one. You should remember the two and the correlation analysis that comes before it. Up to this point, there shouldn’t have been any issues understanding, right? So, you should have understood the difference between difference tests and relationship tests. However, there is another type of relationship test. What is it? It is called cross-analysis, or cross-tabulation in English. Cross-analysis refers to chi-square analysis. What it means is that when we conduct an experiment, there are cases like this. For instance, there is a claim that vitamins are effective against colds. There have been studies done in the past where people were given vitamins and a placebo. What did I say earlier? What does that mean?

It's about fake medicine, right? So, what happens is that it's distributed to people. Some people receive vitamins, while others receive fake medicine. This way, we have a group that took vitamins and another group that took fake medicine. Then, winter passes. During the winter, those who were told to take vitamins do so, while those who were told to take fake medicine do that. After winter ends, we check whether they caught a cold or not. At that point, we categorize them into two groups: those who caught a cold and those who didn't. Specifically, we look at the group that took vitamins and check how many caught a cold and how many didn't, and then we do the same for the group that took fake medicine. We analyze this separation to determine whether vitamins had an effect on colds or not.

Well, we call that a correlation test. Some people might get confused between this and difference tests. Many people often mix them up. There are those who say that correlation analysis is not a difference test. But you can approach it that way, and you can also consider it a correlation test. In the context of vitamin analysis, there are cases where it is referred to as correlation verification. It can be said that there are more instances of this. As we see here, both are qualitative variables. So when we distinguish between data, the analysis method depends on the type of data I have. If both variables are qualitative or continuous, it is a correlation test. If only one of the two variables is qualitative, then it is definitely a difference test, except for this one case. Just this one case.

There are two variables. If the types are the same, we conduct a relationship test; if they are different, we perform a difference test. You don't need to worry about the details behind this, as it is mainly relevant for analyzing survey data, so I will leave that out. Let's go back to the beginning and take a look at the first diagram. Everyone, please turn to page 30. If we summarize this, we will be close to finishing. 

Let's review again. We have two main types of statistical analysis methods. One is the method for conducting difference tests, and the second is for conducting relationship tests. When we encounter a problem, it is crucial to accurately analyze what the issue is so that we can clearly distinguish the problem. That is the most important point. Therefore, when faced with an issue, we need to determine which of the 11 methods we have discussed should be used to resolve that problem, focusing on difference tests and relationship tests.

Black examines the differences between groups. This is clear. Relationship tests do not divide groups; instead, they need to accurately distinguish using a single variable. For now, I have chosen to perform a difference test. I believe this will be a difference test. So, there are a couple of methods for analysis. To put it simply, there are just two main types; nothing more, so don't overthink it. Now that we've decided on a difference test, what should we consider? We need to determine whether it's a test or not. You can look at this. However, distinguishing between a test and a situation depends on the number of groups. Don't complicate it. Now that we've moved on to the difference test, the issue is related to difference testing. What should we do next? We need to check whether there are two groups or more than three. Just focus on that; don’t overthink it. If there are two groups, then it’s a t-test. But if it's not about groups and we split it based on time, then it’s an ANOVA.

The sample distinction is very clear. So, whether it’s A or A, it doesn’t matter; once it’s decided, we move on to the testing phase. This means we proceed directly to the difference test. After that, you only need to look at the number of groups and make your decision. If the analysis involves two groups, it’s a difference test; if it’s three groups, then we use a t-test. If there are two groups, it’s clear that we use the t-test as well. When there’s one group, we use a one-sample test, and when there are two groups, we use an independent sample test. However, if we split it over time, it becomes less clear. Now, if there are not just two groups but three or more, we cannot use the t-test. If there are three groups, we use a one-way ANOVA test, which is connected to the independent sample test. They are interrelated, so if there are two groups, we use the independent sample test.

If there are more than three test groups, we use one-way ANOVA. If there are two groups, we can split the time into two, using a paired sample t-test. If we divide the time into three or more, we look at repeated measures. It's clearly defined and formally separated. Then, if I need to use two or more variables, it must be 2-way. However, one of those must be viewed from the perspective of time, meaning it includes pre- and post-measurements. In that case, we would use 2-way repeated measures ANOVA. Knowing this method is essential. When conducting experimental research, we typically use the last method. You only need to apply this in a laboratory setting. 

Now, if we are not distinguishing between groups but rather examining the relationship between two variables, most of the surveys we conduct fall into this category. If you have conducted a survey, then almost 99.9% of the time, it is for relationship testing. When do we use the methods mentioned earlier?

When do we use t-tests? It's not about satisfaction surveys; when you enter a company, there are many cases where you analyze sales figures and such. In these work-related situations, you'll often use difference testing. Generally, when we analyze data collected from surveys, we frequently use correlation validation. In that case, we assess it as independent one-to-one comparisons. Then, if we look at correlations from an equal standpoint, we refer to it as regression or correlation analysis. I'm not talking about a one-on-one match; rather, it's going to be one-to-many. In other words, we will analyze multiple independent variables, which leads us to regression analysis. Among regression analyses, we specifically use the term multiple. What does multiple mean? It refers to the concept of many variables being involved. So, we talk about multiple linear regression. However, one unique aspect of this is that there can be two outcome variables.

When the outcome variable is clearly defined, such as yes or no, retired or not retired, failed or not failed, we specifically use a method called logistic regression. Next, cross-analysis might be something that confuses you a bit. Cross-analysis is used to verify the relationship between two variables when both are nominal variables. That’s it. 

Now, let’s outline the methods. For difference verification, we have three t-tests—one, two, three—and four additional methods, making a total of seven methods for difference verification. For relationship verification, we have one, two, three, and this one combines, resulting in four methods: cross-analysis, correlation, and multiple logistic regression. So, we will learn these four methods.

So, we have seven types of difference tests and four types of relationship tests. These are the seven methodologies that you will learn through SPSS analysis in the remaining time. Let me explain again, but analyzing with SPSS is easy. Anyone can follow along by looking at a book; the illustrations are all there. You just need to look at the pictures and click, click. The problem is that when a question is given in advance, the biggest challenge is figuring out which method to use to solve that problem. If you can make that judgment, the game is over. 

Secondly, you need to interpret the results of the hypothesis tests we learned until last time. When values come out, you need to analyze whether there is a difference between the two groups. So, is it true that I like it? If so, who likes me more? This is the kind of analysis you need to be able to do. Now, the methods of analysis and interpretation that we learned last time...

We learned about hypothesis testing, and starting next week, we will go through one analysis method at a time. We will insert examples and data to work through them, interpreting the SPSS results continuously from next week onward.

11 통계분석방법03

##  채널 설명 ##

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https://cafe.naver.com/kcbig

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-. 빅데이터경영(1-2) : 빅데이터의 개론으로 빅데이터 개념, 정보기술, 하둡, 분석기법 등을 학습
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강서대학교 빅데이터경영학과 이상철 교수

Understanding Grouping Variables and Relationship Testing

The discussion focuses on the importance of grouping variables, highlighting the difference between one-way and two-way analyses.

It emphasizes that the number of variables, rather than the number of groups, is crucial for analysis.

The speaker also introduces relationship testing methods, such as correlation analysis, regression analysis, and cross-tabulation analysis, to analyze the relationship between variables.

The Relationship Between Men and Women: Correlation vs.

Men and women can like each other without a clear cause-and-effect relationship, indicating a correlation rather than dominance.

The relationship between height and weight also demonstrates correlation, as they influence each other without a distinct cause.

Regression analysis, on the other hand, involves causal relationships and can help determine the influence of variables, such as in the research on online game immersion and the impact of avatars and reward systems on player engagement.

The Impact of Feedback and Community in Gaming

The speed and amount of feedback and rewards in gaming can significantly influence player engagement.

The evolution from 2D to 3D design in games has had varying effects, especially with the slow computer graphics and network speed in the past.

The importance of community, such as guilds in MMORPGs, remains crucial for player interaction and immersion, with a focus on identifying the key variables that impact immersion through regression analysis.

Analyzing Relationships and Their Dynamics

The speaker is juggling feelings for two partners, both liking them equally at level 1.

A simultaneous message sent to both partners reveals the situation, causing their affection levels to change to 0.

The speaker then discusses the difference between correlation and regression analysis, emphasizing the one-to-one vs.

one-to-many relationship, and introduces hierarchical regression as a method to analyze the moderating effect of a third party on the dynamics of the relationships.

Understanding Regression and Cross-Analysis

Regression analysis uses scores to predict outcomes, while logistic regression focuses on yes or no decisions.

The process evolves from correlation analysis to regression analysis and finally to logistic regression.

Cross-analysis, or chi-square analysis, is used to determine the effectiveness of an intervention, such as vitamins, by comparing outcomes between different groups.

Correlation tests are often confused with difference tests, but they serve different purposes based on the type of data.

When both variables are qualitative or continuous, a correlation test is used; if one variable is qualitative, a difference test is applied.

The analysis method should focus on the number of groups: a t-test is used for two groups, while ANOVA is used for more than two groups.

The analysis process begins with a distinction between groups, leading to a difference test.

For two groups, a t-test is used, while three or more groups require a one-way ANOVA.

When examining the relationship between variables, correlation validation and regression analysis are employed, with multiple linear regression used for multiple independent variables.

Methods for Outcome and Relationship Verification

Logistic regression is used for clearly defined outcome variables.

Cross-analysis verifies the relationship between two nominal variables.

There are seven methods for difference verification and four methods for relationship verification, which will be taught through SPSS analysis.