RM&PR | RESEARCH METHODOLOGY & PROJECT REPORT | TWO WAY ANOVA EXPLAINATION | @shivanipallela⁩

Added: 2026-05-28

[00:00:02]Hello all, welcome back to our channel.

[00:00:04]So, students in this video we will discuss the topic explanation of two-way ANOVA, which is having in your unit four in MBA statistics for management, okay?

[00:00:15]In previous video we have already learned the one-way ANOVA, right? So, in this video we need to going to learn the two-way problematic explanation of two-way ANOVA, okay? In two-way ANOVA, there are total eight steps you need to do it, okay? How you need to recognize whether it is a two-way ANOVA means one-way ANOVA is nothing about the single variable, okay? But here, along with the two variables they have given, brands they have given, and also the samples also they have given, okay?

[00:00:49]Brands they have given, samples also they have given. Two variables you are having. In that cases, you need to assume that you need to do the solution in two-way ANOVA, okay? So, there are eight steps, no? The step number one you need to do it is you need to allocate a table, okay? So, X, Y, Z, sorry.

[00:01:14]You need to assume A as X, B as Y, C as Z. Your wish, any names you can put it on this, okay? And uh what they have given? A, B, C, D, no? A, B, C, D they have given, right? So, what you need to do is you need to add row total and column total also, okay? So, what they have given? 9, 12, 9, 12, 11, 10, 10, 15, 12, 11, 12, 14. So, this is the data whatever they have given in the question. Now you need to do it row total and row total square, R and R1 square. Now you need to do column total and column total square also. Okay? So, row total how you will do? 9 + 12 + 10 + 11 is equal to 42. 12 + 11 + 15 + 12 is equal to 50. 9 + 10 + 12 + 14 is equal to 45. Okay? Now you need to do it square. 42 into 42, 1764.

[00:02:32]15 into 15, 2500.

[00:02:36]45 into 45, 2025.

[00:02:40]So, row total you have done. Row total square also you have done. Now come back to the column. So, column total 9 + 12 + 9 is equal to 30.

[00:02:51]12 + 11 + 10 is equal to 33.

[00:02:55]This will be 37 and this will be your 137.

[00:03:00]Okay? So, 37 sorry, 37 and here also you will get 37. Okay? So, 30 into 30 you need to do it, then you will get square.

[00:03:10]33 into 33, 1089. 37 into 37, 1369.

[00:03:15]37 into 37 is equal to 1369. So, in first step you have done row total and row total square, column total and column total square you have done. Now come back to the step number two. In step number two you need to calculate GT, that is called grand total. What is the formula of grand total means whatever the row total or column total you have, you need to take it. Okay?

[00:03:42]What is the row total?

[00:03:45]Row total should equal to column total.

[00:03:51]That is, when you add 42 + 50 + 45, what you will get? You will get 137.

[00:04:01]Okay? So, when you add 30 + 33 37 37 also, you will get 137. So, GT is equal to 137.

[00:04:11]Okay? You need to add You need to add column total and row total. It should get equal. That is called grand total.

[00:04:20]Now, you need to calculate in the step number three is CF.

[00:04:25]That is correction factor. So, what is the correction factor formula? GT squared by n.

[00:04:33]So, grand total how much we got? 137.

[00:04:36]So, 137 squared by n. N is nothing but number of observation. 1 2 3 4 5 6 7 8 9 10 11 12. So, 137 into 137 divided by 12 you need to do it. Then, you will get 1564.

[00:04:51]That is your CF. Correction factor is 1564. 137 into 137 if you will do means, 18769 you will get.

[00:05:02]From that, you need to divide it by 12.

[00:05:04]Then, you will get correction factor.

[00:05:06]This is step number three.

[00:05:08]Okay? So, step number four is step four.

[00:05:15]Calculation of TSS.

[00:05:19]What is the calculation of TSS formula means? Whatever the number of squares, n squares minus CF.

[00:05:28]So, what is the n's you are having, ma?

[00:05:32]See in the question, you are having 9 12 and 10 11 12 10 10 15 12. For all that, you need to do the squares. Okay? How you need to do squares? 9 squared + 12 squared + 10 squared + 11 square plus 12 square plus 11 square plus 15 square plus 12 square plus 9 square plus 10 square plus 12 square plus 14 square minus CF you have got 1564 no So whatever the data you are having you are just doing square. 9 into 9 81. 12 into 12 144. 10 into 10 100. 11 into 11 121.

[00:06:16]Like that you need to substitute it and from the final answer you deduct the correction factor. Okay, what's the answer that you correction factor minus is there you will get the the answer 36.92.

[00:06:30]The SS answer is 36.92.

[00:06:34]Just substitute the answers, okay. Now step number five.

[00:06:40]In step number five SSB you need to calculate. Sum of squares between samples. What is the formula is nothing about the What is the row total square?

[00:06:51]R1 square by n plus R2 square by n plus R3 square by n minus CF. What is the row total of we are having first one row total you what how much we have got? 42 50 45. How many columns you are having in a row? Four columns you are having in a row. So how you need to do? 42 square divided by four plus 50 square divided by four plus 45 square divided by four minus 1564.

[00:07:29]Correction factor is 1564 no? So the final answer you need to write it, okay.

[00:07:33]So I'm writing the final answer. 42 into 42 divided by four. Like that you need to do it, okay. So you will get the answer 1572.25 - 1564.

[00:07:47]Then, your SS B answer is Your SS B answer is 8.17. Just I'm making it substitute just like that. I'm not doing anything. Just I'm doing the substitution. So, this is called sum of squares between samples. Now, step number six. Now, you need to calculate SS C. That is sum of squares between columns. Okay? So, between columns, what is the column total you are having? 30 squared divided by three. Why I'm making divided by three? 30. Okay? How many column rows you are having? 1 2 3. 33 squared divided by three. 37 squared divided by three. Like that you need to do it. Okay? So, 30 squared divided by three plus 33 squared divided by three plus 37 squared divided by three plus 37 squared divided by three minus CF. Okay? So, the final answer how much you will get means 157 uh 5.66 minus 1564. This is the CF answer. Then, SSC answer will be your 11.58.

[00:09:05]You will get it. Okay? After doing the calculation.

[00:09:09]Now, step number seven.

[00:09:11]In step number seven, ma you need to calculate SS E.

[00:09:18]To calculate SSE, what will be the formula is TSS minus Okay? TSS minus SSB minus SSC. What is the TSS total? 36.92.

[00:09:34]SSB total is 8.17 minus SSC total is 11.58.

[00:09:42]36.92 minus 8.17 minus 11.58 if you will do means what will be the answer? 17.17.

[00:09:50]Now the last step is step number eight. That is called ANOVA table.

[00:09:59]Okay?

[00:10:01]So in this step number eight, you need to draw a table. Okay? So in this table, what is you will have means SS C the first thing you will have sum of squares between columns, sum of squares between One minute. Sum of squares between rows and sum of squares between TSS. Okay? So SSE.

[00:10:32]For these three you will have So what will be the answer of SSE? What is the answer of SSE we have got? 11.58.

[00:10:40]SSB answer is 8.17.

[00:10:43]SSE answer is 17.17 we have got.

[00:10:48]Right? Next we need to find out the degree of freedom. Degree of freedom is C minus one. Columns, how many columns you are having? 4 minus one is equal to three only. Now here R minus K. R minus K is equal to how many rows you are having? Three. How many K you are having means one. Means what is the particular thing about the thing here you are having means one. So 3 minus one is equal to two. Okay? Now what you need to do is row into column. So three you have got, two have got. 3 into 2 is equal to 6.

[00:11:23]Now what you need to do? 11.58 divided by three, 8.17 divided by two, 17.17 divided by six. When you do all the divisions, means you will get three Here, I will explain it in the book only so that you will be able to understand it more, okay? See here.

[00:11:41]Degree of freedom. When you watch on one-way ANOVA, afterwards when you see this, this will be useful. So, 3 2 6 you have got. 15 18 Sorry, 11.58 / 3 if you do means 3.86.

[00:11:54]This you will get 4.09. This you will get 4 2.86. Now, you need to calculate this one.

[00:12:01]3.86.

[00:12:03]The last number is 2.86, no? With that, you need to divide it, okay? 4.09 / 2.06 2.86. Now, again you need to do it.

[00:12:14]1.37 35 you will get. 1.47 you will get.

[00:12:19]Whatever the final answer you are getting, that will be your F ratio, okay? This column is not needed in your examination. So, just this understanding the table is very much important. Now, you have got the answer 1.35 and 1.47.

[00:12:36]So, this is will be your two-way ANOVA calculation. I hope that you have got clarity. If you're having any further doubts, let me know in the comment section. See you all in next video.

[00:12:46]Bye-bye, everyone.