SPSS Tutorials: Three-Way Cross-Tab and Chi-Square Statistic for Three Categorical Variables

welcome to the methodology institute's spss video tutorial series sponsored by the Elysee Annual Fund this tutorial follows on directly from the previous video in which we were using the crosstab function and SPSS to examine a relationship between two categorical variables with the difference being that in this tutorial we'll examine the relationship between the same two variables with the introduction of a third control variable and in order to do this we will need to generate and interpret what's known as a 3-way crosstab or 3-way contingency table and again we will also be looking at the chi-squared test statistic the first two variables we'll be working with today are described fully in the previous tutorial and those variables were firstly a binary categorical variable which recorded whether or not respondents were interested in politics in this week we do desire explanatory variable and secondly a categorical variable which recorded respondents willingness to attend the peaceful demonstration or protest and which was treated as a response variable and so in this tutorial we will still be examining the relationship between these two variables however we're going to do this will taking account of a third control variable and this is the variable in our dataset named gender and we can see how this additional variables being coded if we click on the right hand side of the box in the values column and this shows us that female respondents in our dataset have been assigned the value 0 whereas male respondents have been assigned the value of 1 but any respondents who for whatever reason did not answer the question have been assigned the value of minus 98 okay so we can now click Council to come out of the value labels box and we're ready to go ahead and run the analysis and for this we need to select the analyze drop-down menu and then under descriptive statistics select cross tabs so from the first cross tabs tutorial you'll probably recall that it's my preference to select the explanatory variable for the rows and the response variable for the columns and so explanatory variable was how interested are you in politics with two response categories and that's this one here so the first thing we can do is select that with the left mouse button and then use the arrow at the top here to move it across into the rows box now our response variable was this one here would you ever attend a peaceful demonstration or protest so we can select that variable again with the left mouse button and this time use the arrow here to move it across into the columns box now lastly we need to select our third control variable and that was respondents gender this one here so we can select that and the control variable goes in the layer box this one at the bottom so we use that hello to move the variable across and so there are two more options we need to select before we can run the analysis but the first of which is to specify that we require the chi-square test statistic which we do by clicking these statistics box at the top right and then selecting chi-square and click and continue and the second option we need to select is for Robeson's jism and this means that each category for our low variable will then be broken down according to the response categories for our column variable with the cells in each row adding up to 100% so to request this option we just need to click on these cells box on the top right and then select row percentages and click continue we can then proceed to run the analysis by clicking ok so now we can have a look at our output for the three-way crosstab and chi-square test and as usual for this function SPSS the first table that we get in our output is just the case processing summary which shows the number of valid responses against the number of missing values and the total number of respondents so in order to see the 3-way crosstab itself we're going to need to scroll down in the output viewer window and I'll also just scroll across to give us a better look at the table as a whole and so when we introduce a third variable to our crosstab in this case the respondents gender we get what are known as partial tables and so in this case we have two partial tables the first for female respondents in our dataset and the second for male respondents and then within each of our partial tables we have a breakdown of answers to our response variable would you attend a peaceful demonstration or protest for the two groups in our explanatory variable those who are not at all or not very interested in politics or those who are quiet or very interested in politics and the key to interpreting a 3-way crosstab such as this one is to treat each partial table separately so for example the first partial table shows within this to protest amongst female respondents between those with higher and lower levels of political interest so here we can see that only 3.1 percent of female respondents who weren't very interested in politics have attended a protest whereas amongst those who were interested in politics 26.6% have attended a protest then turning to the second partial table for our male respondents we can see here that seventeen point six percent of those who weren't interested in politics had actually attended a protest compared to twenty six point two percent of male respondents who were interested in politics and so the general story across the two partial tables seems to be that both among male and female respondents those with higher levels of political interest are also more likely to have attended a protest or demonstration but the extent of the difference between those with low and high levels of political interest appears to be greater amongst female respondents than amongst the male respondents in order to confirm whether or not this relationship between interest in politics and willingness to protest is statistically significant for both the female and male respondents in our sample we need to look at the results of the chi-square test and so for our female respondents the value of our chi-square test statistic is sixteen point eight to zero that's at two degrees of freedom and with a p-value shown by SPSS in the last column as point zero zero zero which we of course would state as less than point zero zero one so amongst our group of female respondents we can interpret this test statistic of sixteen point eight two and its p-value of less than point zero zero one it's very strong evidence against the null hypothesis that amongst female respondents are two variables interest in politics and willingness to protest are independent or not associated in the population from which our sample data was drawn but if we then turn to look at the results of the Pearson chi-square test for our male respondents we can interpret the test statistic of 1.179 and it's p value of zero point five five five as insufficient evidence against the null hypothesis that our two variables interest in politics and willingness to protest are independent or not associated in the population from which the sample data was drawn and so in other words assuming that we're working at the conventional five percent significance level amongst male respondents we would fail to reject the null hypothesis that there is no relationship between interest in politics and willingness to protest within the population whereas amongst female respondents we could confidently reject the same null hypothesis as there is strong evidence that amongst the female respondents there is a relationship between interest in politics and willingness to protest at least at the 5 percent significance level and so in situations such as this we have what is known as a partial association and this would in fact bring us to the overall conclusion that when controlling for gender the relationship between interest in politics and willingness to protest is no longer statistically significant overall however a partial association remains for female respondents and so in conclusion the respondents gender does appear to have an impact on whether or not their level of interest in politics will affect their willingness to take part in a peaceful protest or demonstration so in this tutorial we've shown how to use SPSS to generate and interpret a 3-way crosstab and its accompanying chi-square test

Channel: Department of Methodology LSE

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Keywords: SPSS, SPSS Tutorial, software tutorial, data, data analysis, SPSS analysis, Methodology Institute, statistical software, SPSS Chi-Square, Three-Way Cross-Tab, Chi-Square, SPSS Three-Way Cross-Tab, Three Categorical Variables, Categorical Variables, SPSS Categorical Variables

Id: LUuLGLGI650

Length: 9min 3sec (543 seconds)

Published: Tue Jul 03 2012