For more information, please see full course syllabus of Statistics

For more information, please see full course syllabus of Statistics

### Overview of Statistics

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- Roadmap
- The Statistical Tests (HT) We've Covered
- Organizing the Tests We've Covered…
- One Sample: Continuous DV and Categorical DV
- Two Samples: Continuous DV and Categorical DV
- More Than Two Samples: Continuous DV and Categorical DV
- The Following Data: OK Cupid
- Example 1: Weird-MySpace-Angle Profile Photo
- Example 2: Geniuses
- Example 3: Promiscuous iPhone Users
- Example 4: Women, Aging, and Messaging

- Intro 0:00
- Roadmap 0:07
- Roadmap
- The Statistical Tests (HT) We've Covered 0:28
- The Statistical Tests (HT) We've Covered
- Organizing the Tests We've Covered… 1:08
- One Sample: Continuous DV and Categorical DV
- Two Samples: Continuous DV and Categorical DV
- More Than Two Samples: Continuous DV and Categorical DV
- The Following Data: OK Cupid 10:10
- The Following Data: OK Cupid
- Example 1: Weird-MySpace-Angle Profile Photo 10:38
- Example 2: Geniuses 12:30
- Example 3: Promiscuous iPhone Users 13:37
- Example 4: Women, Aging, and Messaging 16:07

### General Statistics Online Course

### Transcription: Overview of Statistics

*Hi, welcome to educator.com. *0000

*Today we are going to overview all the statistical tests we covered so far. *0002

*So this is the last lesson in this series.*0008

*We are first going to list all the statistical tests that we covered. *0011

*In particular we are going to cover the hypothesis test. *0016

*We are going to organized them into a chart so that you can tell which test was performed by looking at a set of results.*0020

*So here is a giant list of hypothesis test that we covered so far.*0031

*Other one sample z-test, the one sample t-test, independent samples T paired samples T one-way ANOVA *0036

*also called the independent samples ANOVA, repeated measures ANOVA chi-square goodness of fit chi-squared test of homogeneity.*0044

*In more advance statistics courses, you may undercover also cover hypothesis testing with regression. *0055

*It does exist however we have not covered it in the set of lesson. *0062

*So the question is how do we know which of these tests that we should perform when we see a set of data *0069

*or how you look at a set of results and figure out which is the test that they did in order to come up to this result. *0076

*It actually helped to organize all of this different type in this table right here so there is a couple of dimension. *0084

*One dimension is how many samples you have, so one sample test, 2 sample tests and more than two sample test. *0093

*Now these hypothesis tests are all similar and that they all require at least one sample and because of that *0102

*they might also be called having a categorical independent variable so that is what they all have in common.*0113

*But they have different levels of the independent variable. *0121

*So this only has one level that has two levels and this has more than two levels. *0125

*But also we need to know what is the measurement what is the dependent variable that they are interested in. *0132

*There might be categorical dependent variables such as are they satisfied or unsatisfied. *0139

*Did they pick red blue or green or there might be continuous dependent variables. *0145

*How much did they improve on a test how fast were they going how many inches did they grow? *0153

*Different DVs like that had a numerical value were we can find the mean as well as the variance and standard deviation. *0163

*When we have categorical DVs such as yes and no where red blue and green we cannot find the meaning of those kind of value. *0172

*So let us start organizing our test. *0183

*When we think about one sample test there a couple of one sample tests we have talked about already. *0186

*Some of them literary have the word one sample in their title such as the one sample Z test and the one simple t-test. *0191

*The one sample Z -test and one simple t-test obviously use the mean as well as standard error which is *0199

*calculated by tabulating standard deviation of the sample so that would fall into the continuous dependent variable box right here.*0207

*So there is the one sample Z as well as the one sample T. *0218

*How you know when to perform the one sample z-test versus the one simple t-test well you know how to do that if you know Sigma. *0227

*So if sigma is known the actual population standard deviation then you go ahead and use the one sample Z- test. *0238

*If sigma is unknown a.k.a. you have to use S instead then use the one sample t-test and that is because the *0247

*T is more variable and it is much more like the normal distribution as N your sample size becomes greater and greater. *0267

*How about the categorical DV which is the one sample tests that we could put in here, well the categorical *0278

*DV that we have looked at are all called chi-squared test. *0288

*So there is a chi-squared test which might be written as chi-square or chi-squared there is a chi-squared test *0292

*that only uses one sample and compares it to a population but here they take that one sample and look at *0305

*the samples proportion and see if that matches the population’s proportion. *0313

*That test is called the goodness of fit test because that goodness of fit is looking at how the sample fit with the population, goodness of fit. *0319

*So, we have already tick-tuck three tests. *0330

*Now let us talk about two sample test, when there is two examples and we often want to look at whether *0338

*those samples are similar in that, the new of one minus the new other equals zero or we want to look at *0349

*whether they are different in that the means of these populations do not equal each other . *0358

*Those tests are called t-test. *0365

*Right so the two sample t-test and obviously t-tests require calculating a T which requires mean standard error standard deviation so does t-test belong in here. *0370

*So the first t-test we learned about where the independent samples t-test, as well as the paired samples t-test. *0384

*This is both t-tests that take into account 2 sample and they have a continuous dependent variable. *0402

*How do we know which one to use well you has to check for whether the samples are actually independent? *0414

*If the samples are independent use the independent samples t-test sort of a no-brainer. *0421

*If the samples are linked in some way then use the paired samples so with independent samples use the *0426

*independent samples t-test with link samples use the paired samples t-test. *0435

*Linked or dependent samples. *0442

*Now what about when you have a categorical DV and you have more than one sample you can no longer *0446

*use the chi-square goodness of fit test instead you have to use the chi-square test of homogeneity . *0453

*This test whether 2 population are similar to each other in terms of their proportion or not just like the t-test*0461

*look at whether 2 sample are similar to each other in terms of their means or not and so in that way these tests all have that in common. *0480

*What they have different from each other that's different from each other is that this chi-square use categorical DV and the t-test use continuous DV. *0491

*So what about if we have more than one sample. *0501

*Well actually if we had more than one sample and we have a categorical DV we can continue to use the chi*0504

*square test of homogeneity because here we can use it for two sample 3 sample whatever however many *0510

*samples you like as long as it is not one so we could just say chi-square tests of homogeneity, and life is simple. *0517

*However if you have a continuous DV now you can use t-test anymore because T-test only compare *0530

*two distribution now we need to compare multiple distribution how do we do that. *0538

*We use the F test also called ANOVA analysis of variance. *0544

*So there are two kinds of analysis of variance test that you learned. *0549

*One was the independent samples ANOVA and the other was the repeated measures ANOVA. *0553

*How do you know which one to use, well it is just like this separation right here with independent samples *0568

*use the independent samples ANOVA with link samples or dependent samples you use the repeated measures ANOVA. *0581

*So that is how we know which test to do so we could look at a set of data look at whether it had *0589

*continuous DV or not look at whether has to samples one sample more than one sample and we could *0597

*follow this chart to figure out which tests should be performed and which does we can perform. *0603

*So now let us practice. *0609

*The following data are from OkCupid, an Internet dating website that does a lot of cool things with the data. *0613

*So you could check out the blog at blog.okcupid.com and many of these figures are adapted from that website. *0621

*The following data may be offensive to some of you because some of the data to mention sex and some of the data mention cleavage. *0630

*Example 1 so here is a statistical conclusion and we need to figure out what statistical tests we should do. *0637

*The statistical conclusion is this. *0647

*The weird MySpace angle profile photo the one it looks like this, that results in more messages than other *0651

*photo contacts, so here are the different photo contacts, things like my space shot in bed, outdoors travel *0659

*with friends and the dependent variable is the new contacts monthly. *0666

*How many new contacts they have per month so these are my two variables, photo contacts as well as number of contacts monthly. *0672

*My number of contacts is my dependent variable and my photo contacts this happens to be my multiple groups, my different samples right. *0688

*So I have a sample of people who has this as their profile shot this is their profile shot is that their profile shot. *0704

*So these are my sample here and I have eight samples with continuous DV so which statistical tests should be performed? *0711

*Well it should be an independent samples ANOVA because we have more than two group, 2 groups and are devious continuous. *0722

*So we can analyze the variance between the groups over as a ratio of the variance within the groups. *0734

*So example 2, use the statistical conclusion straight and bisexual men are more likely to believe they are geniuses than gay man. *0747

*What are the variables and which statistical tests should be performed? *0760

*So they are comparing three different groups of men bisexual men gay men and straight man so that things *0764

*like samples already and what they are asking them is just yes or no. *0773

*Do you think you are a genius are you a genius , yes or no, that is a categorical variable and the we have a *0778

*categorical dependent variable so what statistical tests should be performed? *0785

*Well, three groups in a categorical dependent variable this seems like this seems to call for the chi-square test of homogeneity. *0792

*We want to know whether these three different samples have similar proportion or different proportion. *0802

*Example 3 the statistical conclusion says this. *0813

*Both male and female iPhone users are more promiscuous than blackberry and android users. *0823

*So what are the variables and which statistical tests should be performed? *0829

*This is actually a little bit of a trick question. *0834

*You can answer the best of your ability but I'll show you how to go one step beyond what we actually know, okay. *0837

*So one thing we could do is just compare these three groups of three groups of cell phone users so that *0844

*seems like three samples to me that are independent. *0852

*Usually people do not have more than one cell phone and this looks like the average number of sexual *0855

*partners at age 30 so this is the bar graph right here not a histogram which should be a frequency *0862

*distribution and this seems like a continuous dependent variable. *0868

*After all in order to compete an average you have to have a continuous variable so we have a continuous *0875

*DV with three groups of cell phone users. *0882

*The one answer that we could come up with is to say perhaps the one one-way ANOVA also called *0885

*independent samples ANOVA but and that would be a good answer given what we have learned so far. *0895

*Hopefully you will have learned enough about statistics that you can take multivariate statistics which is sort of the next level . *0909

*In the next level which you will learn about in when you have more than more than two independent variables. *0915

*Here we have independent variable of cell phone as well as the independent variable of gender and when you cross them together we get six groups. *0923

*Android users were male android users who are female and blackberry users or male and blackberry users who are female, iPhone male, iPhone female. *0934

*With six different groups now later on when you look at this factorial ANOVA, they can actually almost like doing 2 ANOVA at the same time.*0946

*And so this would actually technically be a factorial ANOVA but if you can answer the nova you are pretty close. *0958

*So example 4, older women cleavage pictures are associated with greater improvement in monthly contact them for younger women. *0966

*Okay so one of the ways we can look at this is looking at age and we can look at the difference between this *0978

*as the dependent variable and that is definitely continuous and we can look at the difference here as well and compared those 2 differences. *0987

*Just at age 18 and age 32 so we looked at these two groups of women that so the 18-year-old women and the 32-year-old women. *0997

*We look at those two groups of women and look at the DV of improvement how much improvements what kind of test would we do? *1008

*Well it seems as though we should do a t-test of some sort because this is a continuous variable and we *1021

*have 2 groups and the groups seem independent. *1030

*We cannot be 18 and 32 at the same time and I do not think they are following the 18-year-old until they *1033

*become 32 so I do not think they are linked so it seemed like an independent samples t-test. *1041

*But there are other ways you can look at this, you can look at this as a regression correlation you can look *1046

*at the regression line for women with women showing cleavage in light blue and women not showing *1061

*cleavage in the dark, dark blue so you can look at those two regression line so that is another way that you could go on this. *1072

*So that is the end for statistics on educator.com, thank you so much for watching.*1083

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