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

Ajouté : 2026-05-28

[00:00:01]Hello, all. Welcome back to our channel.

[00:00:03]So, students, in this video, we will discuss the problematic explanation of unit number four, one-way ANOVA. So, this is the first topic you are having in unit number four. In unit number four, there are two different topics, ma. One-way ANOVA you are having, two-way ANOVA you are having, okay? So, in this video, the complete concept of one-way ANOVA, how you need to calculate any of the ANOVA in one way in the examination hall. In this video, I will do the explanation, okay? So, by watching this video, you will be able to find out the solution for any type of one-way ANOVA question in your examination, okay? So, all you need to do is don't skip the video and watch till the end, okay? So, briefly, we will explain the topic point-wise, okay? So, in one-way ANOVA, ma, total there are seven steps you need to do.

[00:01:01]Only seven steps you need to do in one-way ANOVA. How you need to recognize the question whether you need to do it in one-way ANOVA or two-way ANOVA? They will not mention in the question, "Calculate one-way ANOVA. Calculate two-way ANOVA." Like that, they will not mention in the question. All we need to clarify, all we need to decide whether the question is one-way or two-way. How we need to recognize one-way ANOVA question means any single independent value.

[00:01:32]Here, they are especially saying on the thing of brands. In brands, A is there, B is there, C is there, D is there. All this four is depending on one variable, that is called brands. Means, in brands, there's only one variable, no? Means, single independent. That type of questions, when you are finding in the thing, you need to that the solution should be in one way ANOVA, which is seven steps. All you need to remember the seven steps, it will be easy. So, solution I'm doing.

[00:02:08]So, before starting one way ANOVA solution, the first two lines you need to write it, ma. Okay? That is H naught H naught H of zero is equal to null hypothesis, we will call it as a null hypothesis.

[00:02:26]In any question, this statement is fixed, okay? H1 is equal to alternate hypothesis. So, this two you need to remember in your solution, okay?

[00:02:37]Definitely, you need to write this statement, okay?

[00:02:40]This symbol is called this symbol whatever you're having, U1, U2, U3, U4.

[00:02:48]Just for understanding purpose, I'm making it as a U. Actually, this this type of symbol is called as a mean, okay? How many columns you are having? 1 2 3 4. So, mean one, mean two, mean three, mean four. In first statement, what you need to write it is H naught H naught means null hypothesis. Mean one is not equal to Sorry, is equal to mean two is equal to mean three is equal to mean four.

[00:03:25]Like this, you need to write it. When null hypothesis is there, that time this will be occur, okay? When alternate hypothesis is there mean one is not equal to mean two is not equal to mean three is not equal to mean four.

[00:03:44]Okay? This whatever the stuff you are having from here to here, it is same for any kind of question in your examination. What a lot of question I didn't occur to me This is fixed. This is same. Okay? Next step. Now, the steps will be occur.

[00:04:06]Okay? The first step what you need to do is here I'm writing step number one.

[00:04:12]In this step number one, you need to calculate the X1, X2, X3, X4 already they have given. This you need to assume that X1, X2, X3, and X4. Now, you need to find out X1², X2², X3², X4². See, in A category, B category, C category, D category is there normal four columns you are having. In each column, draw two two lines.

[00:04:44]Okay?

[00:04:45]In each column, draw two two lines. Just I will make sure I will draw the line so that you will easily able to understand it. Okay? So, This is X1, X1², X2, X2², X3, X3², X4, X4². X1 is 20, 19, 21 they only they have given. 20, 19, 21. X2 is 25, 23, 21.

[00:05:26]X3 is 24, 20, 22. X4 is 23, 20, and 20.

[00:05:34]Okay? Now, you need to find out the squares. 20 into 20 is 400.

[00:05:41]19 into 19 is equal to 361. Means it is nothing about the 19 into 19, 20 into 20. Like that, you need to do it in the calculator. 21 into 21 is 441.

[00:05:56]21 into 21 is 441. 23 into 23 is 529.

[00:06:02]25 into 25 is 625.

[00:06:05]24 into 24 is equal to 576.

[00:06:09]20 into 20 is equal to 400. 22 into 24 22 is equal to 484. This will be 400.

[00:06:17]This will be 400. 23 into 23 is equal to 529.

[00:06:22]Like this, you need to do it. If you are having three columns, only these three will come. If you are having only two, means these two only will come. Okay?

[00:06:30]Now, you need to take the total. X1 total, X1 square total, X2 total, X2 square total. 20 plus 19 plus 21 is equal to 60.

[00:06:42]Okay? X1 total is 60. X1 square total is equal to 1202. 1 2 0 2. Okay?

[00:06:50]X2 is equal to 69.

[00:06:53]X2 square is equal to 1595.

[00:06:58]X3 is equal to 66. X3 X3 square is equal to 1460.

[00:07:06]1460.

[00:07:08]X4 is equal to 63.

[00:07:11]X4 square is equal to 1329.

[00:07:14]Okay? So, this is the first step you need to do in any kind of question in one way ANOVA. Okay? You need to find out the square values. Okay? And you need to total up the X1 and X2 X like that. All the things. Okay? Now, step two, ma. Calculation of grand total.

[00:07:34]In step two, you need to find out the GT. That is nothing about the grand total. What is the formula of grand total is equal to sum of observations?

[00:07:44]Means in the question in the question what they have they have given X1, X2, X3, X4 they have given no.

[00:07:53]X1 total is 60. X2 is 69, X3 is 66, X4 is 63. You need to add X1, X2, X3 and X4 then you will get a grand total. X1 plus X2 plus X3 plus X4. Means X1 you are having 60, X2 you are having 69, 66 plus 63. Total if you will add it means 258 is your grand total. So this is the second step you need to do in your one way ANOVA. Now the step number three.

[00:08:29]In step number three you need to calculate correction factor.

[00:08:35]Calculate correction factor.

[00:08:42]What is the formula of correction factor is nothing about the GT squared by n.

[00:08:50]Okay, what is the answer of GT we have got 258.

[00:08:56]Okay, so 258 squared divided by n. N is nothing but number of observations. In the question 1 2 3 4 5 6 7 8 9 10 11 12.

[00:09:09]So number of observation is equal to 12 only no. N is equal to 12. So 12.

[00:09:17]So 258 into 2 divided by 12.

[00:09:22]If you do means 5,547 you will get the answer of correction factor. So this is the third step you need to remember it in your one way ANOVA. Now we'll come back to the step number four.

[00:09:38]Okay?

[00:09:40]Step four.

[00:09:42]In step number four, you need to calculate TSS. Calculation of TSS. TSS is nothing about the total sum of squares.

[00:09:55]How we will calculate this total sum of squares means just write the formula. X1 squared plus X2 squared plus X3 squared plus X4 squared minus CF.

[00:10:12]So, X1 squared total how much we got, ma? 1202. X2 is 1595. X3 is 1460. X4 is 1329. So, you need to add everything.

[00:10:24]Okay? So, this is the formula. So, 1202 plus 1595 plus 1460 plus 1329 minus correction factor. CF is nothing about the correction factor, no? What is the answer we have got in correction factor? 5547. That is 5,547.

[00:10:48]When you add all these numbers, you will get 5,562.

[00:10:55]Okay? 1202 plus 1595 plus 1460 plus 1329 if you add it means 1562 you will get.

[00:11:02]From that, 5,547 correlation factor you need to minus it. Then, TSS answer will be your Actually, when you add 1202 plus 19 this all if you'll add means but 5586 you will get. Sorry.

[00:11:21]5586 you will get. From 5586 you need to deduct this 5,547.

[00:11:28]If you deduct means 39 you will be getting the answer, that is called TSS.

[00:11:34]1202 + 1595 + 1460 + 1329 is 5586.

[00:11:41]From that correction factor 5547 you need to do minus, then 39 will be your answer of TSS. Okay? So, this is the fourth step. These are the fixed steps in any question, there is no change in the formula, there is no change in anything, okay? Step number five. In step number five, calculation of SSB.

[00:12:06]SSB is nothing about the squares between samples. Okay? That is called sum of squares between samples. Then, what is the formula of this sum of squares between samples means? Just write the write down the formula in an understandable manner, I am explaining it, okay? So, first you need to take the See here.

[00:12:31]What is the total of X1, X2, X3, X4? X1 total is 60, X2 total is 69, X3 total is 66, X4 total is 63. So, 60 squared First, what you need to do is X1 total is 60 squared divided by How many rows you are having? 1 2, sorry, 1 2 3, no? So, 60 is the X1 total, from that how many rows you are having?

[00:13:02]1 2 3. So, 60 squared divided by 3 plus X2 total is 69. 69 squared divided by 3 plus Again, third one is 66. 66 squared divided by 3 plus 63 squared divided by 3. From that, you need to do the correction factor minus CF.

[00:13:27]Okay? so 60 into two if you will do means 3,000 Sorry, 60 into 60 if you will do means 3,600.

[00:13:36]3,600 divided by three means 1,200 you will get it. For this you will get 1,587.

[00:13:43]For this you will get 1,452.

[00:13:45]From this you will get 1,323. Correction factor what we have got? 5,547. CF we have got No, already we have calculated 5,547. You add all these number from that deduct CF. So, when you add all these numbers means 5,562 will be your answer. From that correction factor if you deduct means what will be the answer of SSB? That is 15. Okay. So, here I'm not using the calculator. In the Just pause the video and use the calculator so that you will understand it, okay? So, this is the step number five. Step number six is Step six is calculation of SSW.

[00:14:30]Calculation of SSW. That is sum of squares within sample, okay? Within sample. Here the formula is TSS minus SSB. TSS answer how much we have got?

[00:14:46]39. SSB answer 15. 39 minus 15 you need to do. When you do that, 24 you will get. That is called sum of squares within samples, okay? So, this is the answer of SSW.

[00:15:03]This is the answer of SSB. This is the answer of TSS.

[00:15:09]Okay? So, this is the thing. Now, the last step, in step number seven, you need to draw the table.

[00:15:17]ANOVA table we will call it as a ANOVA table. ANOVA table. This is the last step. In this, you are having five columns, ma. The first column The first column is you are having source.

[00:15:35]Second column you are having sum of squares.

[00:15:40]Third one you are having degree of freedom.

[00:15:44]Fourth one you are having mean square.

[00:15:47]Fifth one you are having F ratio. Okay.

[00:15:50]In this, this columns names is also fixed in any question. In this, you need to take it as a between samples.

[00:16:01]Between samples and you need to take the within samples.

[00:16:06]Within sample is SSW.

[00:16:10]SSW answer is 24.

[00:16:13]SSB answer is 15. So, SSB answer is 15.

[00:16:18]SSW answer is 24. So, 15 24. If you add 15 + 24, what will be the answer? So, 39 will be your answer. Degree of freedom is nothing about the For SSB, K - 1 you need to do it.

[00:16:34]Okay. What is K means how many columns we are having in the question? Four columns. 4 - 1 is equal to three.

[00:16:42]So, this formula is n - k. Total number of observation is 12. From that, columns is four. 12 - 4 it is eight.

[00:16:51]So, this formulas is also fixed in any question, okay? So, 3 + 8 11 is the answer, okay? Total of the level. Now, what you need to do is 15 / 3. 24 / 8 you need to do it. 15 / 3 is equal to five. 24 / 8 is equal to three. Okay. 15 / 3 is equal to five. 24 / 8 is equal to three. In the F ratio, what is the answer we have got here? 15 five. Here you have got three. So, first thing five by three you need to do it. 1.6 you will get it. Here three you're having as it is. Here you're not having any value.

[00:17:32]So, keep it nil.

[00:17:34]Okay? So, five by three is equal to 1.67.

[00:17:38]Okay, you will get it. Now, F ratio how much you have got? F ratio is equal to 1.67. That's it. So, like this you need to solve the one-way ANOVA in your examination. I hope that you have got clarity. If you're having any further doubts, let me know in the comment section. And remember the formulas especially, okay? All the very best for your examination and the preparation.

[00:18:01]See you all in the next video. Bye-bye, everyone.