Lecture 43

In this part 4, we are expected to conduct the gender and performance data analysis. We are expected to analyze the data by performing the following tasks. First, we are supposed to import and merge the HR and performance data files and examine whether average performance ratings differ by gender and also visualize the data. Lastly, we are supposed to analyze the gender and performance data across job levels and make inferences and also visualize the data. In this part, we will start with part 4 of the case study, where we will talk about the consistency of performance evaluation. We would like to see whether performance evaluation is consistent, for example, across gender and so on. Now, this is a very important aspect. First, we will import the data sets and join them. We are supposed to use two data, HR data and performance data. Let's load them one by one. First is the HR data. We will import this data set. For reference, I will keep this command for future use. Let's see what is inside this data. Let's have a glimpse with the glimpse command. It contains again 1470 observations. First is employee ID, second is department. We have seen this variable. Next is performance data. We will load the performance data. Again, for future reference, I will just copy this command. Like we do, I will use the glimpse of this performance data as well. Let's see what is inside. In this, there are two variables. One is employee ID and their ratings. So, along with the ID, the ratings. Now, because we are going to use both of these data frames or data, we need to merge them. The next task is to join these data along the employee ID variable. That is simple. Let's create a new join data variable. You can study more about joins, but here I am going to use left join. This will combine the data along the employee ID lines without creating any duplicates. Even if I do not specify, let's say I do not specify this and it will be joined by employee ID only or if you want to specify, that also you can do. Sometimes it happens that you want to join by some specific variable. You can specify that employee ID. That also you can do. This is also an available option. Both will result in the same data. So, we have joined the data now. Now, the next set of analysis, this first set of analysis, we would like to see if there is any differences across genders in terms of performance rating. So, we will compare the performance rating across genders. That is the first step of analysis. So, I will use the join data. I have already created it and group it by gender. That is obviously the natural course of action here. So, join it by gender. You can see now my data is joined with gender. All I need to do is just summarize the ratings along the gender lines. So, now my job is simple. I will just summarize it, create an average rating variable which will hold the average ratings, mean of ratings, so to speak, and run it. Now, you can see here the average male rating is 2.92 and average female rating is 2.75. Now, the rating seems to be different. There seems to be some kind of differences in male and female rating, but if there is a systematic bias, that needs some more exploration. Let us examine this in more detail. So, let us assume that those with rating of 4 or more are high performers. So, let's create another variable which is high performer. In fact, we will create new data out of it. So, first, let me create this join data and in this join data, we will add a new variable. For that, we need to use this mutate function and let's call it high performer, and in this, like we have been doing earlier, we will make use of felse function, rating, if it is greater than or equal to 4, then 4, else 1, otherwise 0, and if I run it, I get the values. So, let's create this new data, let's call it performance data, and let's store it. So, now I have this performance data ready for me for subsequent analysis. So, create a performance data with objects classified as high performer. High performer with a rating of greater than 4 will be a high performer. So, now we have created the data that we need to analyze. From next set of videos, we will do a detailed statistical analysis and data visualization as well. Now that we have created this performance object, which takes a value of 1 if it is high performer with a rating of 4 or more, or 0 if it is a low performer, we are good to start with our analysis. First, we will do the gender-wise analysis of ratings and we will see whether high performers are more in male versus female category. So, first let us do the simple t-test. So, t-test of high performer. Now, this t-test we will do in a different manner now. So, we have been already doing this t-test. So, let's do this high performer. I will show you a different regression approach to t-testing. So, t.test and all I need to do is use this tilde and gender because I need the differentiation. It is the same thing that we have been doing. I am using a different regression approach to that and you can see the t-test results. You can see that it is the same approach. We can see the average rating for male group is higher than the female group and it is quite statistically significant. That means there is a significant difference in the ratings. So, t-test of means. Now, here we conducted the t-test of means, but please recall our data is of one zero form. So, we can also conduct the chi-square testing here. So, that is also very useful to see whether there is a different chi-square test. So, that is also quite simple chi-square test and all I need to do is just provide performance data, performance dollar. Now, I need to provide the gender variable and the gender is the differentiating variable and then provide the high performer variable that we have created. So, if I run this code just see the output. So, you can see here also I find the result to be very statistically significant. So, overall I can say there is a very statistical significant differences in the ratings given to male particularly male higher ratings are given female lower ratings are given, but we need to do some more analysis. As a first step we will try to visualize the ratings of male versus female on bar plot. So, first we will visualize the rating. So, let's use our performance variable. So, what we will do is we will provide ggplot. Now, here we need to provide our performance data which we are going to use and we need to specify our aesthetic object. So, here we are going to analyze the gender variable and fill as high performer. So, fill with high performer. Now, I can use the bar probably bar plot would be a good option. So, let's see what kind of diagram the bar plot shows us. So, as you can see also it would be great if I because there are two categories we get if I use this factor command that would make things more suitable. So, I missed one bracket which I will add. Now, that will be better because now I have added this thing. So, you can see the data visualized. You can see the composition clearly one the difference in numbers. So, it gives me some idea but because the numbers are absolute probably it would be better if I use the position fill argument. So, let me show you. So, this is the visualized performance. Now, to improve this graph probably I'll use few arguments. Let's try some of them. So, let me use a new argument position fill. This position fill may improve the diagram. Let's see dodge there is one more argument you can use dodge that also gives you so it creates a separate number. So, you can see. So, while overall it looks like we have more high performance in the male category. There is also another approach to visualize data through ratings. So, what I can do is instead of using the fill as high performer. I can use ratings also with rating. So, I'll just change this to rating. Let's see. So, we get a very nicely distributed graph. We can see lot of high performer in the male category particularly rating 4 is given a lot while the females are given 3 is a lot. So, extreme high performers 4 and 5 are more in the male category. Also, sometime it is misleading because of the different numbers to compare the composition of different ratings. So, one good way is to use the column approach. For example, here I will slightly tweak the data. So, I'll use column here. So, now but then I have to specify the Y values which is high performer and now if I run it they are stacked one to one and you can see the composition more clearly. So, now you can see in the male the composition of high performer is higher the same thing I can do with the ratings bit also. So, again instead of bar I can use the column object and but I then I need to provide the Y axis separately show you the composition. So, if you look at in terms of this thing you can see the composition clearly the rating 5s are higher in male the rating 4s are higher in male while the lower ratings are higher in female. So, this gives us a very clear idea that high performers there is a high performance in the male category probably there is some evidence of systematic bias. Maybe higher ratings are given to male colleagues. However, this kind of analysis is often fraud with omitted variable bias. For example, in the previous case we saw rather than it was the pay differences in new versus old it is the mix of employee job mix was changing similarly here it may be possible that the bias is more on the job level. So, the ratings are different at job level rather than the gender, but we will carry out this analysis in the next video. In the previous video we argued that there is one possible explanation to our results was that there is a bias across male and female candidates in rating assignment or there is one possible reason could be the missing omitted variable bias. For example, there would be possibly case that there is a rating differences or bias across different job levels. For example, hourly salary managers and one particular category may be the low rated ones are higher in female workers. So, for that let us start this exercise. So, we need to examine the differences in job level rating distribution by gender. So, we need to check the difference in job level distribution across genders. So, for the same let us start with the visualization exercise. Visualization of composition of male and female across different job levels. For that let us start with our good old ggplot. We need to provide a performance object. A is x x is equal to gender. Now, we will fill it with the job level to see the composition. This would be a better way to visualize and we will use bar plot for starters. Let us keep. Let us run this. So, let us this gives us some idea. In fact, I could have used position equal to fill also. So, like we see stack fill and so on. So, if you fill it, it will scale the entire thing. So, you can see in terms of composition you can see hourly is higher hourly is higher in the female while the salary and managers are higher in male. Now, this gives us some credence to that intuition that probably it is the case that these if these are low rated the lower levels like early are low rated by managers and salaried are more rated then we have some reason to believe that probably it's not the gender bias. So, for that let's do one more step goes one step further and visualize the performance of male and female across different job levels. So, what we'll do is we'll use this ggplot command performance performance data. We have now in aesthetics. We have X as gender variable and we'll fill the plots with factor high performer. This would be our plotting scheme. Now here we need to add some more information first and foremost. We'll use the geom bar geom bar object with position equal to fill to again standardize it to that scale of one so that we can compare but now we'll facet wrap and if you recall the facet wrap will help us by segregating the plots and in this case we want to segregate them across job level. So, let's do that and let's look at the plot now. Now here the differences are not very stark if you look at salaried the performance of female versus male very close distribution for manager a little bit higher in the managerial category a little bit higher in hourly also same so not as stark as we saw earlier. So, probably it is not the gender wise difference because gender wise there is a minor difference but not as stark as what we saw earlier. So, probably it is the composition of hourly manager and salaried which is causing this difference. So, in the next set of videos we'll conduct a more robust statistical testing to see whether there are indeed very significant differences across gender and across these different job mix levels in this final concluding video. We'll conduct the statistical t-test and chi-square test to examine whether there are significant differences in performance ratings across the job mix that is manager salaried and hourly levels. So, we'll start with the salaried and we'll reuse the same code. I'll not rewrite the full code. So, let's start with the salaried class and I have the variable which is performance now inside this performance variable we'll filter it out with job level equal to salaried and I'll store this in the object called performance filter. So, we have created this object so now this object is created. Now, the first step is t-testing. So, let's start with the t-test and for t-test as you have learnt we can simply do this high performer object. This high performer object will be segregated across gender variable data is performance filter and if I conduct this t-test the difference is not statistically significant. You can see the p-value is turning out to be insignificant. So, this is not a very useful result or not useful as in it says that there is not significant difference across male and female. We can also apply our chi-square test. For this chi-square test I need to use the performance filter object dollar gender because across gender we have to see and our object is high performance. So, let's see yep no difference. So, we can see there is not significant difference as per this test also. Now, I'm not going to write the full code again I'll just copy paste we have done it for salary. So, let's do it for other also. So, next is manager. So, let's do it for managers. Now, for managers we'll have the filtering variable as manager. Let's do that. First, let us do the t-test not significantly different. Chi-square test not significantly different. So, across managers also there is not much difference but that the difference has to come from somewhere. If you recall there was difference in the performance. So, there has to be somewhere this results should lie. So, let's try the last one which is hourly. I'm hoping given our overall result there has to be some positive. So, with t-test yes. So, you can see it is 2.45% p-value that means at 95% this is significant and similar significance we are obtaining here also. So, now this ties up our overall results. Let me summarize it for you. So, first we found that across the female versus male there was a performance evaluation difference which gave us an impression that in the male category there were more high performance probably there was some systematic bias in rating assignment. However, when we analyzed the proportion of female versus male we found that relatively the hourly workers are more in the female category while manager and the salaried are in the male category and as it turns out here there is a very systematic kind of difference in performance who are in the hourly wage. So, in hourly level there is a significant difference in the across gender. So, it seems that while at managerial and salaried level there is no performance evaluation differences in gender wise but at hourly level there is a significant difference. So, this is what we conclude in this part. In this part 5 we are expected to conduct location and accident analysis. We are expected to analyze the data by performing the following tasks. First we are supposed to import and merge the HR and accident data files and examine whether the accident rates have increased from 2016 to 2017. Then we are supposed to visualize the data. We are also supposed to examine whether excessive employee overtime has any relationship with the accidents. Using various descriptive statistics, visualization techniques and logit regression model we are supposed to examine whether employee engagement has changed over the years and if it has any relation with the accident. And lastly we are supposed to conclude our findings with sharp and brief inferences. In this part 5 we will examine the employee safety related data. So, we will look at employee safety related aspects. Now, this exercise requires us in delving two data. One is HR underscore two CSV this data. So, let us import this data. Let's copy this. So, this is first data. So, let's see what is inside this. So, let's use glimpse command HR underscore two. So, again there are 2940 observations. There is a year column where we can see there are two years employee ID, their location and their overtime hours. So, from this we will get the overtime hours and we will also see if the overtime hours have some relationship with accident. The second data file that we are going to examine is accident data. So, we will import this data file. Let us copy this command for future reference accident data. So, we will use this. Let us again run the glimpse command and see what is inside this accident data. Again, three columns year, employee ID and accident type, mild and so on. So, accident type is provided. Now, as we can see year and employee ID are the two keys for merging the data. Let's see how to merge the data. Again, left join. Let's call this data HR joint the resulting data. Again, we will use left join. This is a very useful command when you want to merge two data frames for their intersection. So, it's a very useful command as you can see accident data. Now, I will provide the two keys to merge the data by equal to C. Now, one is employee ID the other is year. So, when I merge this so, this is HR two actually. So, when I merge this let us see the glimpse of the resulting data frame and it is HR joint. So, now the resulting data again it has 2940 observations, five columns now. So, we have year and employee ID intact but along with location we have overtime hours and accident type. So, now we will start with our data examination. Now, as you can see in accident.type there are some NA observations and some mild and others. So, what we will do is we will put all those who did not have accident which means NA as 0. So, these guys did not have accident while others who had some mild or any kind of accident we will put them as 1 which means they had accident. So, let's modify our data little bit HR underscore joint. So, this is our original data we would like to mutate, modify and create a new variable had accident. So, this had accident will have values if 1 that means the employee had accident if it is 0 that means they didn't have accident. So, I will use this is.na accident type. So, now accident type and if it is 0 0 in case it is NA, 1 if it is not. So, that's the way. So, you can see here for each NA we have a 0 because now with 0 lot of x analysis regression everything is possible with NA you may not do that. So, and as of now we have not assigned it to any data. So, let's use this assignment operation to create this basically this will have the effect of creating a new column in my original HR joint data. Let me print it and let me show you had accident this column is there. Now the first question that would like to answer is whether if there is any increase in accidents from 2016 to 17 or decrease or anything like that. So, let's analyze the trend in accidents and that is simple. We will use our data that we have created already HR joint. Now inside this data we need to group by year. So, that by now you would have understood that makes our job very easy. We'll just group it by year and then we'll use the summarize. Now all I need to do is create an accident rate variable and assign it the mean summary measure. So, I'll just add a simple descriptive which is mean and this would be it. So, you can see here if I look at year wise accident rates it's approximately 0.085 in the year. Now because our variable has 01 kind of form. So, we can interpret in sort of fractions. So, 0.085 rate in 2016 in terms of fractions and 0.12 in 2017 which means there is a clear cut increase. Now we would not be very satisfied at this stage probably in a convention that we have been doing would like to do some kind of statistical test. So, we would like to statistically test this difference in accident across 2016 and 2017. So, let's start with the typical t-test and this is very simple. We'll use this head underscore accident data that we have created. Head accident variable year. So, year is our segregating variable and now HR joined is the name of the data. So, that's pretty simple. We'll just run this t-test and you can see here the difference mean values we have already calculated the same mean we are seeing here but more importantly the p value is even less than 1% which means the difference is very significant statistically significant. So, first important result we had for this t-test approach. Now you would also like to have chi-square testing like we were doing chi-square test to just check the robustness or sort of verify get a second opinion of sort in our result. So, I'll use this chi-square test again that we know. Now we can use that because our variable is 0 1 form it's not exactly a typical numeric it's 0 1 form so we can apply if it was not we probably wouldn't have been able to but now we can do so dollar here we can apply this HR joined. Now you can see the p-value again coming out to be very significant which means there is both these tests suggest that there is a clear cut increase in the accidents in this year. So, we in this video we loaded the data we examined the accident and we found there is a very significant increase in number of accidents in year 2016 to 17. We'll do the further analysis of this data in next set of videos. In the previous video we discussed the increase in accident rates over the year 16 to 17. Let us also see in this video let us examine this data in more detail and see identify the job location year wise patterns in accident. So, we'll examine the year wise and location wise patterns. So, first let us go back to our data that we created HR joined. Now the question we have we would like to examine location and year wise pattern. So, we need to group it back location as well as year. So, you can see it has grouped the data location as well as year. Now we can appropriately summarize our data. So, when we use the summarize command now and I can create a variable accident rate. Let's say I can create this variable and summarize it with the mean command which has had underscore accident. Now if I summarize it I'll actually get my data but I can rather create new variable for future reference. So, accident rate let's call it accident rates. Let's create the data and let me print this data now. So, let us examine the data that we have got in more detail. So, look at East Valley. So, here from 2016 to 17 from accident rate has increased from 11% to 14%. Northward 6% to 12%. Quite sharp increase. Southfield 7 to 13. 7.6 to 13 and West River 8 to 11. So, we can see across all the locations there has been a significant rise in the accident rates. So, it seems there is some kind of pattern. Let us also try to visualize this data. Let's see if we can draw some insight by visualizing it. So, in this question we'll try to visualize the accident data. So, typical scheme we'll use the RGG plot for this kind of thing. So, we have GG plot. We'll provide accident rate data that's for this very purpose we have created the data. We need to supply aesthetics. Now in aesthetics notice I am using factor as here. So, I don't want to R let treat here as numeric variable. I want it to treat as factor two categories and then accident rate. So, accident rate variable and here I should have used accident rate actually small r. Now it will be fine. So, I prefer this kind of spellings. Now the next thing I need to specify geometric object if you recall. So, I am using geom call probably that geom call is a reasonable object and aesthetics I need to provide some kind of color filling. So, I want it to segregate with here. That's why I am using factor here. So, filling is good. It would look good the graph. Next facet wrap command. So, facet wrap will ensure that I want to plot. So, location wise I want to plot it location wise. So, this will increase the sort of aesthetics of my plot. So, let us draw it. So, you can see a very nice plot across there has been created and there is a very clear-cut pattern. If you look at all the four locations East Valley there is a rise Southfield there is a rise Northwood West River for all the locations there is a clear-cut rise in the accident from 16 to 17. So, this graph gives a very nice picture and from which we can draw lot of insights. Now one potential reason in the increase in accident rates could be the increase in overtime hours. So, probably we would like to examine overtime hours from location wise and see if there is a significant difference and we would like to do this exercise location wise. So, we will examine overtime hours location wise. So, for example, the first location is Southfield first we will start with Southfield and we will use our HR joint data. Now I will filter out with location. So, I need to specify the location which is Southfield. Let's see if I have run it correctly. Let me print this. So, I have just I have done it correctly Southfield I have categorized. Now, let's see if let's do a simple summary and see if Southfield has increase in this measure. So, we will group it by the year we would like to examine the overtime hours. So, by year and then use this summarize average let's call it average overtime and take it to the next line. Use the space here. Use the mean of overtime hours. So, we need to do it group by and let's see. So, we can see from 16 to 17 there is a very clear cut increase in overtime hours. Now, we would also like to add some kind of statistical test for this result. So, because the data is numeric not that one zero kind of thing. So, we have to rely on t-test. So, let's do that. So, t.test and we have to check whether overtime hours and segregated by year and data equal to Southfield. So, data equal to Southfield. Let's run it. Let's interpret the result. You can see the mean we already saw. So, obviously the mean is higher but is it statistically significant? It's like a cut-to-cut case. You can see p-value is close to 11%. So, it's not significant at 90% level but there is a strong signal that the overtime hours have increased. Let's do this exercise for other localities also. So, for other localities, I'll not rewrite the code. I'll just reuse the same code that I have already written. For example, Northwood. Next locality is Northwood. So, I'll just copy paste the name of the location and put it here. So, let's run it. So, there is a difference approximately 0.5. Let's see if it is statistically significant. No. So, as we can see the p and t-values, the difference between 2016 and 2017 overtime hours is not significant. So, let's pick another location. The next location we can take is maybe East Valley. So, we can take East Valley. I'll just copy paste the name. Now, this name has a space in between. So, for variable naming, I can't use it. I need to modify it a little bit. I'll put an underscore which is an acceptable name in our convention. So, I use this East Valley to place here also and here also. Let's see what we get. So, again the difference is very minor. So, I don't expect it to be statistically significant. You can see with t and p-values, the result is not very useful. Or rather, I should say it does not indicate any significant differences across the years 2016 and 2017. The last one is West River. Sorry, this was East Valley. This was the third one. The last one is West River. So, if you look at this, let me just copy paste it. Again, there is a space in the name of the data. So, I need to add that underscore to make it acceptable to R. Now, I'll just copy paste the same name here and here. Let me run it. So, again the difference is not very big. So, I don't expect it to be statistically significant. As you can see here, the p-value is quite small. The t-value and p-value indicate that the difference is not statistically significant. So, we can say there is only one location which was the first one. Southfield, where there was a statistically significant difference and the t-test also confirmed the same. So, that is our takeaway from this exercise. In the previous video, we have examined the overtime data and accident data. Let us now examine the relationship between engagement and accidents. And for this exercise, we would need to use another data, which is Survey 2. So, first let us examine the relationship between accidents and engagement. So, we'll analyze this and for this we need two databases. First, we need to add this Survey 2 data. So, we need to use this Survey 2 data. We'll import this. Let's copy this for future reference in our code file. So, this is a useful practice. Copy it for your future reference so that you don't have to remember the file name and location. Now, let's see what is inside this data. So, this carries again the year, the employee ID and engagement. The next step would be to first merge this Survey 2 data. So, for that we need this left join command. We have already created this HR join data and we also have this Survey 2 data. So, we'll merge them. We need to be just mindful that we are merging them by two variables, which is one is year and another is employee ID. These are the two variables. So, let us create a new variable. Let's call it safety variable. So, we'll use it. Now, first thing, we will again create that disengaged variable that we have created earlier also. We recall that. So, that variable was basically if the engagement level is less than 3, then we call them disengaged. So, this would require mutate function and we'll create this disengaged variable and similar exercise. It's very similar exercise. If engagement level is less than equal to 2, then it is 1. That means employee is disengaged and 0, then engaged. Now, we'll assign it again in the same variable. So, if I print it, you would notice that there is one more variable disengaged is created now, which will take a value of 1. If engagement score is less than equal to 2, that means less than 3. Otherwise, it will take 0. 0 means he is engaged. Also, for reference, I'll create one more. I'll modify my year variable. That is also needed. So, what I'll do is I'll modify the year because I need it in a factor form for analysis because every time I keep repeating this, I should rather create this factor here. So, this would be useful. Now, we are ready. Let us visualize first the disengagement level. So, let us visualize the data engagement across location. So, for that, we'll use our ggplot command ggplot command and what we'll do is we'll use our safety data safety data in x-axis, I want x as year. So, I'm specifying x as year and fill as factor disengaged. So, this is first. Now, I have created the plot. Now, next thing I'll do is I'll create zoom bar. So, I'll probably use zoom bar and position equal to fill. This will create a plot for me. But one more thing, I would like to segregate this thing with facetrap. So, I'll use facetrap because I want a more detailed plot. So, I'll use facetrap and according to location. Let us use the full code. Let us run it. So, let us examine these plots. As you can see, if we move from 2016 to 2017, the proportion of disengaged to engaged is almost same except Southfield. So, in Southfield, we can see that disengagement score has increased actually quite a bit from 16 to 70 and this is also the place where accident have also increased. So, probably there is some connection here between the disengagement and accidents. So, we'll explore this aspect in more detail. Probably, we would like to conduct some kind of statistical test. So, let us conduct one statistical test and because we are fixated only on one location. So, probably I'll create a subset of data, safety underscore South. So, I'll use the safety underscore Southfield and I'll filter out my data. So, for that, that is simple. We have already done that. So, I'll use my safety data, safety. I'll filter out by location Southfield. So, I'll create this data and let's see if it has worked. So, this is my Southfield safety data where only location that is there is Southfield. Now, we are good to go. So, we can do the statistical test. So, we'll start with statistical testing and because we have created our variable in 1-0 form, the disengagement variable. So, statistical testing in disengagement variable. So, I can use both the t-test. So, let's start with the t-test. We want to see whether disengagement has increased over years in Southfield. So, let's start with t-test and disengaged. Now, the variable name is disengaged and we want to examine across here specifically for the Southfield location because visually it seems that there is some increase in disengagement. Name of my data is safety South actually. So, I should use that. Let me run it. Let's analyze the data. So, in 2017, the disengagement has increased. Clearly, we can see it was 0.18. Recall, 1 is the disengagement. Those who are disengaged. So, the proportion has increased actually and it is statistically quite significant. In fact, it is less than 1%. So, the significance level is actually 1% which means 99% confidence. So, the result is very significant. Also, we can just test the robustness of this result with chi-square test. That also because it is 1-0 form. So, we can conduct our chi-square, typical chi-square test also and here we need to have that variable safety South. We have the data which is disengagement variable and we would like to segregate it across the years. So, let's do that. Let's run it and again very similar result is obtained. So, chi-square and t-test they are in agreement. P-value is significant for chi-square as well as for the t-test. So, we can conclude that there is quite significant difference in disengagement across 2016 and 2017 for this location Southfield and before concluding analysis as a precautionary check, we will for other locations also we will check that whether there is an increase or decrease in disengagement. So, that we will do in the next video. In this video, we conclude by saying that there is a quite clear increase not only in terms of accident but also in terms of disengagement level. So, there seems to be some relationship between disengagement and accident levels. We have more to say. We will examine this in more detail shortly. So, before culminating this exercise with the regression modeling, we would like to see whether in other locations also there has been increase or decrease in disengagement across years. So, let's create a variable for other locations disengagement levels. So, what we can do is we can just filter out the data. So, safety variable we have already created. In the safety variable, we are interested in filtering filter location. Now, in this location, except south speed, we are interested in other. So, in one go, I am filtering all. So, let's call it other underscore location. Now, two tests we are going to do. First is the typical t-test. Let's start with the t-test of other locations. For that, it's simple. We'll use this other underscore. So, t.test Now, we have this disengage variable disengaged and it has to be examined across here and the data is other locations. So, let's see. Almost similar. So, I am not expecting any significant p-value. So, as we can see, both of them are similar. So, there is no significant increase. We can cross check it with the chi-square test. We can cross check this result. All we need to do is other location dollar disengagement and we need to segregate them across here. So, dollar here. Run it. So, you can see it's not significant. So, again, our hypothesis seems to be there that there is no difference in other locations. The main difference is happening in the south field. So, now, our final focus of analysis will be south field location where we'd like to see what kind of relationship in accident and engagement and over time is there. So, first, let's do a simple correlation test and we'd like to see the correlation in south field with accident and disengage. So, let's see this correlation. South field accident and disengagement. So, let's see. Although disengagement is 1-0 kind of variable, but let's see. Okay. So, there's a very significant correlation of 23% and the correlation is quite significant. So, it means there is some relationship with accident and engagement. The second thing, we'd also like to see if there is some relationship with over time. So, that also we can test here and no, it's not significant. So, not a very useful. So, over time seems to not be a very useful variable but we still because we are doing the analysis in the multiple regression analysis that we are going to do next, multiple regression analysis, we'll still use this data. So, let's call it save our output in the model multiple multiple. It's called model multiple. This is where we'll save our output. Linear modeling. Now, first variable is had accident. So, we'll use this had accident variable which we have created. Again, here we have already in the factor form. So, not to worry. Again, then we have disengaged variable disengaged variable plus over time r. So, over time underscore r that also we have created and data is safety south. Just check the data if my year variable is in. We just do a glimpse of this. Safety south. So, I just wanted to confirm if my year variable is in factor form. So, you can see it is factor. So, we are good to go. So, one way would be to analyze this and just run the summary command and see what variables are significant. Model underscore multiple. Let's do this. Now, let's interpret the output. So, here we can see the disengagement variable is very significant. So, we can see over time r is not a very significant variable. So, we are going to remove it. But disengagement is very significant. This is causing the accident. It is playing a major role. One way to improve this exercise is to run a second version. Remove the less important variable which is over time r and also interact here with disengagement. So, if there is any changes in disengagement, that will be highlighted. So, that we can do. Let's interpret the result now. So, let us interpret these results. First and foremost, the reference category is 2016. As we can see, this is reference year. First and foremost, we can see from 16 to 17, there is an increase. So, we can clearly see 16 to 17, there is a significant increase in accident which is there. More important result is that disengagement variable has a very significant relationship. So, this disengagement variable. Now, this is for disengagement for 2016. There also it has a very significant loading for accident. 2017 is not significant. That means whatever was in 16, the same level, the same kind of relationship can be assumed in 17. So, disengagement level has a significant relationship with accident. It remains significant. So, we can say that whatever the relationship was there in 16, the same carries on 17. So, there is that. And in general, apart from that disengagement variable also, there is a kind of increase yearly trend also in increase. So, that is also captured here. So, there may be other factors also apart from disengagement level which are causing increase from 16 to 17. To summarize this lesson, first we examined the recruitment source data. We found that those coming from such firms are performing poorly on sales quota percentage achievement and also having higher attrition rates. In contrast, those coming from NA sources, most likely these are lateral hirees with sources like LinkedIn or online direct mail application are doing well on their sales quota targets and also have lower attrition rates. Then we examined the employee engagement data. We found that engagement levels of sales department employees are quite low as compared to other departments. One possible reason of this could be low vacation days as the number of vacation days are significantly lower from this department as compared to other departments. In the next part, we examined pay fairness across the job mix and across departments. We found that the pay of new hires is more than old employees. When we analyzed across job mix levels, for example, hourly, salaried and managerial levels, we found that the new hirees are less likely to be hourly workers and more likely to be salaried and managerial employees. So, the difference in pay is not on account of old versus new bias, but simply because the composition of new employees is tilted more towards salaries and managers who have higher salaries and less in case of hourly wages who have lower salaries. We also examined the pay differences across departments. We found that the pay differences are only significantly different for new and old employees in the engineering department, but the pays are not significantly and statistically different across sales and finance department. For these inferences, we employed linear regression analysis and t-test of means. In part 4, we examined the performance ratings across gender and department. We found that there is a significant difference in performance ratings across male versus female employees. Initial evidence suggested that male employees have higher ratings than female. Subsequently, we analyzed the male versus female performance evaluation across different job levels, for example, hourly, salaried and managers. We found that the systematic bias or difference is only found along the hourly wages. In contrast, the salaried and managerial levels, there is no systematic or statistically significant bias or difference in the results. In part 5 of the case, we examined the relationship between employee safety, disengagement and vacation days taken. First, we found that there is a significant increase in accident rates in the Southfield locality and there is a considerable increase from 2016 to 2017. We found that vacation days taken and disengagement levels may have some role to play in demotivating the employees and causing accidents. In general, there is an increase in accidents from 2016 to 2017 which needs further examination.