Choosing a Statistical Procedure

welcome this is Amanda rockin sands AB Q and in this tutorial we're going to talk about choosing a specific statistical procedure in the introduction tutorial you'll remember we talked about factors for choosing a statistical method and we really looked at the difference between choosing a parametric versus nonparametric procedure here we're going to get a little bit more specific go a little bit deeper and we're going to look at the decision making process for choosing a specific statistical procedure so let's get started now if you remember back to the introduction tutorial you'll remember that we talked about three factors for choosing a statistical method we first talked about variables and we talked about how you need to identify the type of variable in the level of measurement because this helps you determine whether or not you're going to do a parametric or nonparametric analysis remember if you have a dependent variable or variable of interest that's at the interval or ratio level you choose a parametric analysis if you have a variable that's a dependent variable or variable of interest at the nominal level or ordinal level you choose a nonparametric analysis we also talked about assumption violation remember with all data sets you do assumption testing and that there are certain assumptions that we make about the population especially when we do parametric analyses so if assumptions aren't via violated you choose a parametric procedure most of the time as long as you've met the first criteria of levels of measurements if the assumptions are violated and grossly violated and you have a small sample size then you may want to choose a nonparametric analysis we also talked briefly about research design and how the purpose of the research design guides the researcher toward the hypothesis or proposing a hypothesis of either Association or a hypothesis of difference we're now going to talk about each of these factors as well as other factors more in depth and talk about how we choose a specific statistical procedure now here you see a list of questions for making a decision about which statistical procedure to use let's go over these briefly and then we'll take a more in-depth look by walking through an example the first question you need to ask about the hypothesis that you're proposing or research question that you're proposing is what are the variables under study you then need to identify those variables label those variables such as label them independent dependent or variables of interest and identify their scales of measurement ratio interval ordinal or nominal remember you use a nonparametric test when you're working with variables of interest or dependent variables measured at the ordinal or nominal level and you use a parametric analysis when you're working with variables of interest or dependent variables at the interval or ratio level the next question that you need to ask is does the research question or hypothesis imply a hypothesis of difference or hypothesis of Association are you working with relationship or prediction or are you working with difference and this will determine whether or not you're going to do a test that looks at difference or a test that looks at relationship the next question that you need to ask is related to a hypothesis of Association if the hypothesis is a hypothesis of Association then you need to ask the question about what type of relationship are you looking for are you looking for a relationship between variables are you looking for a predictive relationship between variables now if you have a hypothesis of difference you're going to ask a few other questions the first question you're going to ask is the data you're looking at is it dependent or is it dependent are you looking at the difference between two separate groups or you looking at the difference between the times in which the dependent with dependent measure was taken for example are you looking at pretest versus post-test you also want to look at how many groups or levels you have in your independent variable do you have two levels such as let's say a control and treatment group or do you have more than two levels and the final thing that you want to ask if you have a hypothesis the difference is how many dependent variables do you have do you have one dependent variable do you have multiple dependent variables and if you have multiple dependent variables are they related and then finally you're going to ask what are the assumptions that are violated so after you've collected the data you're going to do assumption testing and you're going to look at assumption violation now we're going to take a look at an example and walk through the decision-making process now before we take these questions and walk through a specific example let's take a moment and review different procedures that we can perform now it's important to note here that this is a short list of procedures there's probably thousands of different statistical procedures you can choose from but these are some of the most common used with hypotheses of difference and hypotheses of Association let's look at a few procedures that test hypotheses of difference first first of all we'll start with the most simple we'll start with a dependent t-test remember that the dependent t-test is used when we want to know the difference between either a matched pair or if we want to know the difference between two scores in one group for example I may ask the question do University students differ in their statistical knowledge before and after taking a statistics course so here you'll see I have one independent variable with two levels and one dependent variable and again this is a width this is a within group analysis so I have one group or one set of match or one set of matched pairs the second procedure is the independent t-test remember the independent t-test helps us understand if a difference exists between two groups for example I may pose the question do University students perform differently on their statistics final exam based on whether they take a statistics course online or residentially I have two groups the online group and the residential group and I'm looking at one dependent variable which is the score on their final exam so for an independent t-test you need one independent variable with two levels and one dependent variable we then have the one-way ANOVA which is very similar to the independent t-test here we look at the differences between three or more groups on one dependent variable for example I may expand the question to do students differ in their statistics final exam score based on the type of course they participate in whether it's online residential or blended here I have three different groups online residential and blended so for a one-way ANOVA you need one independent variable with three or more levels or groups and one dependent variable we then move on to the two way ANOVA now the two way ANOVA difference from the one-way ANOVA because we're actually looking at two groupings or two independent variables and so we want to know is there a difference between these two dependent variables and the groups within these two dependent variables and also if there's an it or independent variables independent variables we want to know if there's a difference between groups within these independent variables on the dependent variable and then we also want to know if there's an interaction between these independent variables so for example we may say do University students differ in their statistics final exam scores based on both the type of course they take online or residential as well as their gender whether they're male or female so for the two ANOVA we have we need two independent variables that have at least two groups or two levels and one dependent variable we then have the repeated measures ANOVA now this is similar to the dependent t-test here we're working again with one group of individuals and we're measuring them multiple times at least three or more times or we're working with matched pairs or a group that we want to measure on three different let's say three different scores but the repeated measures ANOVA an example of this let's go back to the one we were using for the dependent t-test or one that's similar what we might say is is do University students increase in their statistical knowledge B before during and after taking a educational statistics course so here we've measured three times statistical knowledge we measure before during and after a course and the final the final procedure I want to talk about that test hypotheses of difference is the manova now it's a manova you have one independent variable you're looking at the difference between groups either two groups or three groups or four groups however many groups you have so the difference between groups on a linear combination of related variable so you're looking at the difference between groups on several dependent variables that are related so for example let's say that we don't want to just know about students statistical knowledge based on the final exam but we also want to know their perception of knowledge or their perception of learning and we know in the literature these two variables are related so we we might ask the question do University students differ in their statistical knowledge based on their final exam score and their perceived learning based on what type of course they're enrolled in so here we see that we have two and we're going to deal with two groups again we have two groups the online versus the residential and we want to know if they differ both in their statistical knowledge based on their final exam and their perceived knowledge and again these are two related dependent variables so here with the manova you need one independent variable with two or more levels and two or more related dependent variables now let's take a look at a list of procedures used to test the hypotheses of association again this is not an exhaustive list but these are probably the most common bivariate and multivariate analyses used to test hypotheses of association the simplest is probably the bivariate correlation Pearson's R Spearman row here the researcher wants to know the relationship between two variables so he or she may ask is there a relationship between university students sense of community and their course points here for a bivariate correlation you see we need two variables of interest and here we have course points and sense of community then there's the partial correlation in the partial correlation the researchers interested in knowing the relationship between two variables while controlling for or adjusting for a third fourth or fifth variable for example the researcher may ask is there a relationship between students course points and their sense of community while controlling for their level of confidence with the course material here you see we have two variables of interest see a partial correlation needs two variables of interest and one control variable and here we saw we have the two variables of interest our course points and since a community and the control variable is level of confidence the next analysis is the bivariate linear regression the aim here is to determine if one predictor variable can predict a criterion variable so the researcher may ask the question can university students sense of community predict their course point we then move on to multi variants first of all we have a multi variate linear regression now there are different types of multi variate linear regressions in that and how you ask the question and the overall aim determines the type however we're just going to talk in general about multivariate linear regressions here the multivariate linear regression is used when the researcher wants to know if multiple predictor variables can predict one criterion variable so here let's say our sense of community has two separate scales learning and connectedness and here the researcher may want to know can learning and sense of connectedness predict the course points in for university students so we have two here you can see what's needed for a multiple regression is two or more predictor variables in one criterion variable and we have two predictor variables learning community and connectedness and one criterion variable which is course points that firmly brings me to the canonical correlation the canonical correlation is used when a researcher wants to know the relationship between two sets of variables let's say here the researcher wants to know is there a relationship between the two subscales a sense of community learning community and connectedness and not only course points but also perceived learning so is there a relationship between connectedness and connectedness and learning community and course points and perceived learning so here you can see for our canonical correlation you need two sets of variables so now we have gone over the potential statistical procedures that we can choose from let's go ahead and take a look at an example let's walk through the list of questions for the decision-making process for this question and corresponding hypothesis the question that we're going to look at is is there a difference in college students course points based on whether or not they participate in an online statistics course as opposed to the residential statistics course and the corresponding hypothesis is something we're going to formulate in a minute once we determine our variables so the first question we asked in the decision-making process is this what are the variables under study we need to label them and then we need to identify them as independent dependent variables variables of interest and we need to identify their scales of measurement or their levels of measurement ratio interval ordinal nominal so let's take a look at the question remember the question is is there a difference in college student scores points based on whether they participate in an online statistics course as opposed to a residential statistics course now I encourage you to go ahead and pause this tutorial and identify the variables label them and identify their skills of measurement here we see that the researcher wants to know the influence of one variable on another variable so we have independent and dependent variables here first of all the independent variable the variable that the researcher is either manipulating or looking to have an effect on the dependent variable is type of statistics course and here we see we there's two levels and that's residential and online and since this has two categories that can't be ranked ordered or measured then we can identify it at the nominal level of measurement next we have the dependent variable what is the researcher here looking to effect well course points and course points are measured from zero to a thousand so they can there there's categories the different points one two three four five there are they can be ranked ordered and they can be measured and there's an absolute zero somebody can have a zero number of course points so this is measured at the ratio level now if we remember back to the hypothesis tutorial we remember if we have one independent variable and one dependent variable we only need one null hypothesis to test so the null hypothesis here is is that there is no statistically significant difference in college student scores points based on whether they participate in either an online statistics course or a residential statistics course so we've answered the first question we're going to move on to the second question in a moment but let's talk a little bit about what the answers to the B this question or these questions tell us so at this point we know that our dependent variable is measured at the ratio level therefore it's appropriate to do a parametric analysis or procedure so we can rule out non parametric procedures at this point and look at the parametric procedures now we just went over a number of parametric procedures that are commonly used for analysis purposes but here is the list of parametric procedures that we can potentially choose from you'll also see a list of non parametric listed here and again at this point we can rule those out so let's move on to the second question in our decision-making process the second question or questions are these does the research question imply a correlation a prediction or a test of difference and therefore are we using a hypothesis of Association or a hypothesis of difference I encourage you again pause the tutorial and make a decision answer these questions well here we see the question asked is there a difference between two groups the word difference implies that we're looking at a difference test and therefore a hypothesis of difference since we've determined that we are testing a hypothesis of difference we can rule out procedures associated with testing hypotheses of relationship or Association so we can roll those out and so now we know we're looking at higher or we're looking at procedures which tests the difference so here's a list of procedures that test hypotheses of difference you can see we could potentially be doing a dependent t-test and independent t-test some type of ANOVA or may ANOVA so now in our decision-making process we can move on and focus on the questions that look at hypothesis of difference so the first question we're going to ask is our data is it independent or we're looking at two separate groups or we looking at a dependent group or matched pairs are we looking at one group with two scores or matched pairs each with a score another way to ask this is is the design concerned with within group or is it concerned with between group comparison and also related to that if we determine that we have two separate groups we have dependence or dependent groups what we need to decide then is is how many levels does this independent basically independent variable have or how many categories or groups are we dealing with here so that's related to the independent variable we then also need to ask the question how many dependent variables do we have and here we've already identified the independent variable independent variable so we can ask these questions specifically related to this independent variable and dependent variable so in types of statistics course are we looking at two independent groups are we looking at a dependent group and how many groups or levels does this independent variable have and then finally with our dependent variable this is a pretty easy question how many dependent variables do we have listed here again I encourage you pause the tutorial and through these questions and then move on well let's start with the independent variable first of all for the independent variable are we dealing with two groups that are independent of one another that means that each groups are separate or are we dealing with dependent groups or a dependent group one group within group well here we see that we have two separate groups residential and online so we're dealing with independent data the second question that we remember we asked about the independent variable here was how many groups do we have well we have two groups residential and online the next question we asked was about the dependent variable how many dependent variables do we have well we have one listed here course points so the answer to this question is one now the final question we're going to ask in our decision-making process is what assumptions are violated now ideally what you need to do is identify your data identify your analysis and run your assumptions related to that analysis are related to that procedure and then answer this question however we know that most analyses require that the assumption of normality we met we also know that many of our independence are actually all of our independence procedures that test difference need to meet the assumption of homogeneity of variance now let's assume in this case that our assumptions have been met they're not violated our data is normal we can assume equal variance and therefore what that tells us is that we can move on with a parametric analyses because again remember we have a dependent variable that's measured at the ratio level if our assumptions are not violated we can then perform a parametric analysis if our assumptions are grossly violated we may want to consider a nonparametric alternative and remember we looked at those a little bit earlier so now that we've answered all the questions we've collected everything we need to make a decision about the procedure that we need to perform to analyze the data we remember we've determined that we're going we're testing a hypothesis of difference therefore we're going to do a test of difference so we're just going to look at a table or a chart that shows us the test of difference because we ruled out tests of Association now I will say this chart here comes from the statistics guide which is available with the tutorial so this is from the statistics guide now let's use the questions the answers to our questions to make a decision about which tests the difference we're going to use first of all we need to take the information about our independent variable and its level of measurement remember we had one independent variable so that means we rule out this bottom choice here so we have one independent variable and remember that our independent variable had two groups online versus residential so we can go ahead and say choose the first category here or the first row here next we need to take our information about the dependent variable and determine what we have here remember we had one dependent variable and it was measured at the ratio level so all of these choices listed here are appropriate but we're going to continue down the row that corresponds with our information about the independent variable so we have one nominal independent variable with two levels one dependent variable that was measured at ratio level the next question relates back to the independent variable remember we looked at was our data independent or dependent and we determined that it was in pendants and we also determined that we just had two groups so here again since we have two independent groups we're going to continue down the row that we have been which is the very top one and we see the significance test that we need to perform then is an independent samples t-test now this makes sense think about the different procedures that we reviewed at toward the beginning of this tutorial remember we looked at what you need for different procedures and what their purpose is remember the purpose of an independent samples t-test is to test the difference between two groups on one measure and remember in our question we asked the question is there a difference in college students course points based on whether they participate in an online statistics class as opposed to a residential class so we are asking about the difference between two groups one independent variable on one dependent variable and for an independent samples t-test we need one independent variable at with two groups no more than two groups and one dependent variable now let's say for a moment so we've determined that but let's say for a moment we change that question and we say that we have three groups so we're looking at the difference between residential online and blended um and we're looking at their dose three categories or those three treatments affect our dependent variable of course points what we see then is is that this changes our significance test and the only thing really that it changes is our information about the independent variable we're now looking at one independent variable with three or more groups so what you'll see is we'll need to that our independent samples t-test isn't going to work in this chart if we move down one two three four rows here and move across the column what we'll see is is that we have one nominal variable with three or more groups we have one dependent variable our our groups are still independent of one another so our appropriate analysis would be a one-way repeated measures ANOVA now just to make sure we completely understand or have a good grasp of this decision-making process we're going to briefly look at a few more examples so let's go ahead and look at another example now this time instead of walking through this process in depth we're going to take a look at the scenario and then we're going to walk through the questions on this slide so my recommendation to you free this scenario as well as the ones coming up is that you go ahead read the scenario pause the tutorial and to the questions and then come back and discuss them with me so let's take a look at this scenario every semester a professor gives his students a pretest and a post-test to determine if they improve in their understanding of course concepts thus the researcher asked this question is there a difference in the number of course points earned on their educational statistics pretest and the post-test so first of all we need to identify the variables label them and identify their levels or scales of measurements so here we see that we have two different variables and we're going to identify them as independent and dependent because we're looking at the difference and we're looking at how something affects something else or one thing affects something else so let's start with our independent variable our independent variable is actually time the time of the pretest and the time of the post-test and this is a nominal level measurement because we're looking at two different categories next we have and we can't really rank order them you know we just have before and after and we can't say one is better than the other in any way so their nominal next we have the dependent variable and here we see the dependent variable is the number of course points earned since this number of course points they can be measured and we can say that there's zero course points so we're looking at this dependent variable being measured at the ratio level of measurements so since we have a dependent variable at the ratio level of measurement remember we can then assume that we're going to continue with a parametric analysis and we're going to come back to that this information we just identified in a moment to further answer other questions but the next question we have is is does the research question imply relationship prediction or difference well again here we can see that the the question is is there a difference this implies we're looking at difference and therefore we have a hypothesis of difference and our hypothesis of difference here would be again because we have one independent and one dependent variable we need one hypothesis so it would be there will be a statistically significant difference in the number of course points that students earn on their educational statistics pretest and post-test so we don't have to answer questions about hypothesis of association so we move on to hypotheses of difference and we know that we're going to do a test of difference now so for if we have a hypothesis of difference with the next question we ask is is our data independent we have two separate groups or do we have dependent data well let's think about this we have one group of students and we're going to take a measurement at their pretest and a measurement at their post-test these groups aren't separate so they're dependent upon one another so we have we're going to be doing a within group analysis the next question is is how many how many groups do we have or in this case the better question would probably be how many levels does our independent variable have well we just said we have time one and time two a pretest a post-test so it has two levels the next question we need to ask is how many dependent variables do we have we've already determined we have one dependent variable the number of course points the final question we'd ask would are there any assumption violations and let's assume in this case no so in this scenario the researcher wants to know if there is a difference in one dependent variable based on two different times he's using dependent dependent data or the group is dependent on each other so since the researcher wants to know this is there a difference between course points earned by students from pretest to post-test wants you to think about what would be the best analysis now since we're looking at dependent groups that really narrows our choices to two different analyses that we've gone over in the tutorials and and in this tutorial specifically and that is the dependent t-test and the repeated measures ANOVA and since we don't have three levels of our independent variable we only have two levels probably the best choice in this scenario would be a dependent t-test so we went through our decision-making charts in the statistics guide we and we took all this information we'd probably come up with or hopefully come up with the dependent t-test let's take a look at another case so here we see the professor is thinking about requiring a remedial statistics course for his students who don't do well on the pretest however he's not sure if it would be helpful does he's interested if prior statistical knowledge assist students in their performance on their final exam so he poses this question what is the relationship between pretest scores and final exam scores after controlling for cumulative GPA in previous statistics courses now he wants to know the relationship between the pretest and the final exam also without the influence of the GPA so let's walk through this scenario now again I encourage you go ahead and pause the tutorial walk through these questions and then come back and discuss them with me our first question here is what are the variables under study and we're going to label them and we're going to identify their scales of measurements here we see that the the researchers simply interested in the relationship between two variables he's not looking to see if one variable necessarily impacts the other variable or causes effect on the other variable so he has variables of interest here and he actually has three variables of interest the statistics pretest scores the final exam scores and the GPA so we just identified there are three different variables and we're going to say that and we know that all these variables scores GPA they can be measured they can be ranked ordered they can be put into categories and let's say that they all have a zero people could have a zero for a GPA a zebra on a final exam a zebra on a pretest so we can say they're measured at the ratio level our next question then becomes this does the researcher imply a correlation prediction or difference test so are we dealing with a hypothesis of association or hypothesis of difference when we just said that the researcher doesn't necessarily want to know if how one variable affects another you just wants to know about the relationship between variables therefore we're dealing with an a hypothesis of Association so based on these two questions what we can say is is because we're looking at variables measured at the ratio level we can say we're going to probably continue with a parametric analysis and since we have a hypothesis of Association we can then continue were just looking at tests of Association or test of relationship now we didn't let me take a moment here and talk about hypothesis because we did we forgot to write our hypothesis our hypotheses or actually we would have hypotheses because we're dealing really with three variables so the first hypothesis would just deal with the relationship between the two variables there will be no statistically significant difference between the pretest scores and the post-test scores so that's the first thing we're interested in that zero order correlation and then we are also interested in testing the hypothesis that there will be no statistically significant difference between the pretest scores and the final exam scores after controlling for our adjusting for the cumulative GPA in statistics courses so those are two hypotheses and again we're looking at relationship so we then move on and ask the next question related to hypothesis Association and there's just one and it's this question um is the focus actually there's two I apologize there's two first of all is the focus of the hypothesis of Association is it on relationship or predictive relationship well we're not asking does one variable predict another so it's on it's just simply on relationship the next question we're going to look at is how many variables are we looking at here and what types of relationships are we looking at between them are we looking at a relationship between one to one variable and in the first hypothesis we are but we're going to even take it a step further we're looking at the relationship between one to one variable while controlling for another we're not looking at the relationship between many to one variables we're not looking at how many variables predict another variable we're not looking at sets you know how do two different sets of variables relate we're looking at the relationship between one variable to one variable and we're controlling for our adjusting for another variable so then that we get that brings us to the final question and the final question is do we have any violations in our assumption and we're going to assume no here so we can take a moment and look at our chart and look at specifically the tests for Association and which test tests the relationship between variables while controlling for another variable if you said a partial correlation you're correct so they're probably the best statistical procedure to choose here would be a partial correlation okay let's look at one more example here's this example the same professor wants to examine if there's a difference in course points based not only on the delivery system used or the environment the online versus residential but also race if he finds a difference he really could realize or determine if he needs to evaluate his own course ethnic sensitivity he may realize based on these results that he is more effective as a teacher in one environment and better at adapting his teaching methods to be ethnically sensitive in one environment over another so he then proposes this question do students differ in terms of their course points based on their race and the delivery environment again I encourage you at this point pause this tutorial walk through the questions and then come back and discuss them with me so the first question we're going to look at here is what are the variables under study we're going to label them and then we're going to identify their skills or levels of measurement so here we see that the researcher wants to know if two different factors influence another factor so the two factors that the researcher wants to look at that affect another factor are race and delivery system so we can say that race and delivery system are independent variables now race is category Caucasian african-american Hispanic they can't they can't be ranked they can only be put into categories therefore race is nominal we can say the same about delivery system online versus residential there are two categories that can't be ranked ordered so these are this variable is also measured at the nominal level we're looking then to influence one variable here and have you determined what that was course points cents course points can be put into categories numbers can be put into categories they can be rank ordered to may is higher than one and they can be measured and there's an absolute zero you can zero course points we can say course points is measured at the ratio level okay so we've determined we have two independent variables and one dependent variable the next question then we're going to and we determine that dependent variable before we move on to the expression we determined that the dependent variable is measured at the ratio level therefore we can make the determination that we'll probably continue with the parametric analysis as long as all our assumptions are not violated so then when that moves us there that brings us to the next question the question we're asking here are we looking for a difference are we looking for a relationship are we going to test a hypothesis a difference or a hypothesis with Association well based on the fact that we have two independent variables in one dependent variable thinking back to our hypothesis tutorial that means we have three null hypotheses and this is what they are students will not statistically significantly differ in their course point based on their race students will not statistically significantly differ based on their based on the delivery environment and then finally students will not statistically significantly differ in course points I miss that word and course points based on both the race and the delivery system so in each one of those hypotheses what word did you hear two here differ therefore we're dealing with hypotheses of difference so we move on then to the next question and focus that focuses on the hypotheses of difference and since we're again using hypothesis the difference we are going to do a test of difference our next questions then are is our data independent or is it dependent so look back to that independent variable there are independent variables actually independent variables race and delivery system are we looking at separate groups are the delivery system groups are they separate first of all yes because students are enrolled in either an online or residential they're not enrolled in both we're not measuring them in both we're measuring them in one of the other so that's a separate group we then need to look at our other independent variable and that's race here again we're going to have categories of race and students are going to fit into one so maybe we have Caucasian african-american Hispanic biracial so those are separate groups so our data is separate we're then going to ask the question we're going to look at each independent variable and say okay how many groups or how many levels do we have well with race we have multiple levels I just mentioned I think four or five so we have four or five different levels with delivery system we have two online versus residential we now then move on to looking at our dependent variable or variables and we ask how many dependent variables do we have well we have we've already established that we have one dependent variable and that's points the final question then is do we have any violations in our assumptions and at this point we're going to say no so here based on the information we have we've determined we have one or actually two to nominal independent variables to nominal independent variables one has multiple groups one has two groups okay so we would look at our table in our statistics guide and we would say ok what do we what will we move down the the row and we'd say ok we're looking for a analysis that we can analyze two independent variables next we're going to look at the dependent variable we have one dependent variable one dependent variable so we're going to look next down that down that call or down that row with what analysis can analyze two independent variables and one dependent variable and remember that dependent variables measured at the ratio level and we're not in both and we know both of our groups then are independent of one another that we're looking we're not looking at dependent data we're looking at independent data so what analysis can be used for the purpose of simultaneously evaluating the effect of two independent variables on one dependent variable if you said a two-way anova you're correct so in this scenario we'd use a two-way anova now I'm going to throw one little monkey wrench in there what if we go back to that dependent variable question we say well we don't have just one dependent variable the researcher decides they don't want to or he doesn't want to just look at course points he also wants to let's say look at perceived learning so we have two related dependent variables how does that change our analysis or what analysis would we use so we have two independent variables and two related dependent variables now looking at that table what do we use if you set a two way manova or a manova you're correct so now you have the tools to make a decision about a statistical procedure so this concludes this tutorial like I said at this point you not only know the factors you need to consider for choosing a statistical method but you also know the process of making a decision and choosing a specific statistical procedure to analyze your data

Channel: The Doctoral Journey

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Keywords: statistics, statisical procedure

Id: gABEOb4mV8Q

Length: 47min 27sec (2847 seconds)

Published: Fri Aug 30 2013