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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 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

Transcription: Overview of Statistics

Hi, welcome to 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-test0461

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 chi0504

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 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, thank you so much for watching.1083