 तो आनलिशिःएश लवेरिन्ज बने बात की के, वि have to go through notational systems step by step and we have to calculate the total variance and then divide that variance into smaller parts and see and then we have to calculate the effer ratio. अब आन विरिन्ज बात स्थब करते दिक्ते हैं के कि से हम effer ratio क्याइट करते हैं कि. तो सब से पहले यह में एक सामपल ग्रवेट्र की बुक में से ही ली है, it's easy one, smalls that are a small sample. तो वि have the same telephone condition is our independent variable, जाँप है मारे पास 3 लेवलग हैं, no-treat में, no-phone, number 2 में हैं, our hands held phone and number 3 में हैं, hands free phone. और मारे पास 3 गुप्स में 5 पाश लोग हैं, जो हमने रेंडम ली असाणिएं की हैं, 3 गुप्स केंडर, तो आप देख सकते हैं कि no-phone केंडर, so more score का मतलब हैं, better performance in the driving simulator. तो हमारे पास, scores हैं, 5 पाश लोग हैं, हमारे तीनो गुप्स केंडर, 1, 2, 3, 4, 5 और उन पाचो लोगों का, driving performance, driving simulator के अपर performance score हैं, so no-phone केंडर अप scores देख सकते हैं, तुस्तरे में भी और तीसे में, so in this, at first, what we have to calculate हैं, हमने basically, we have to calculate the sum of square, i.e. s-s calculate करना अथ. In this slide, the letter K is used to identify the treatment conditions that is the number of levels of the factors. तो, हमारे पास यह हैं के, इसका मतलब हैं के हमारी कंडिशन्स कितनी हैं, का हमारी तीन कंडिशन्स हैं. This means that our conditions are three conditions. यह केपिटल एन का मतलब हैं के हमारा सामपल साइस कितना हैं, total three groups में, तो वो 15 हैं, g means that our total कितना हैं, i.e. summation x. अगर इन 15 की 15 values को जमा करें, performance के अपर, तो वो हमारी कितनी हैं, यह सुसको g, यह हम summation x भी कै सकते हैं, which is equal to 30. तानी करने के बास, तो वो हम ने और दी किया हैं, अपका T1 जो हैं total of group 1 हैं, यह अप इन 5 values को जमा करें, तो 20 आता हैं, T2 का मतलब हैं, यह इन 5 values को जमा करें, तो 5 हैं, यह 5 हैं. तो आपने ss कलकलेट करने हैं, ss का formula यह यह याद रखें किस का मतलब हैं, कि सममेशन, x minus, mean, where. इसको में मिता के तोबारा लिएत में, ता के clear हो जाए, ss is equal to summation x minus, mean, where. आप आप भी आपने n से divide नहीं करना, बलके सिरफ आपने, हर x में से, उसका mean minus करना हैं, और उसको square करना. मसलन, इसका mean जो है मारे पास आया है, 4. वो कैसे 4 आया हैं, हमने इन सारो को जमा करें, पाच पे divide किया, तो mean is 4. आप आप आपने हर value में से 4 minus 4, और उसको square करनेंगे, तो it will be equal to 0. आप आपने सारो को किया, तो आपका ss 1 6 आगया, ss 2 6 आगया, ss 3 आपका 4 आगया. तो हमने हर x में से, mean minus कर के square किया, और हर group के लिया हमने sum of square, तो sum of square basically is a variability, आपका spread आपका, किया आपका, हर score में से कितना पर है, और फिर आपने n1 दे दिया, और फिर आपने mean दे दिया, यह हमने basic calculations करनेंगे, में हमने कालनेंगे यह समेशन x by n किया है, और हमने ss निकालनेंगे, यह हमने x minus mean यह लिख कावायध, विसको में दुबारा लिख की है, यह हमने calculate की है, इस में हम, आप के लाई टेल यह एक जाकली, जो हमारा पीश हमने calculation table में की है, नमबर वन analysis of sum of squares, सब से पेला step हमने, वन सम of squares निकालने है, ये वेर्यन्स आपने तोटल भी निकालना है, आपने विदिन भी निकालना है, और आपने बिट्वीन भी निकालना है. उसके बाद है, each of the two variances in the IFRESHOW is calculated using the basic formula for the sample. आपने वेर्यन्स निकालना है, between groups ता और जो मने काता, within group का, तो, to sum up all these, number one, we will calculate SS, i.e. sum of squares. Number two, we will calculate the degrees of freedom for each group, because we have to divide SS on degrees of freedom. And number three, we will calculate the IFRESHOW, in which we will calculate the between variance divided by within variance and calculate the simple IFRESHOW. So, how do we calculate degrees of freedom? We have to calculate three types of degrees of freedom. First, we have to calculate for between, then we have to calculate for within and then we have to calculate for total. So, for your between groups, the meaning of degrees of freedom is, we talked in the T-test that the meaning of degrees of freedom is N minus 1. i.e. we keep one self-free, so we can reach to the true conclusion. So, for our between groups, for degrees of freedom, the number of groups, we will do one minus out of them. We have three levels of driving, if we do one minus out of them, then our between group degrees of freedom will be true. And after that, for within group variance, degrees of freedom is N minus K. Our total is N15 and our group is 3, so for within group variance, degrees of freedom will be 12. And total, if you have to calculate, then total always is N minus 1. If we have 15, then our total, for sum of squares, will be degrees of freedom and will be 14. So, we will get three types of degrees of freedom and three types of sum of squares. And then we will divide the variance between the variance within. So, our F ratio is coming to us. So, let's do one by one step by step. So, the first step is to calculate sum of squares which is within sum of squares. So, for within sum of squares, you have already taken out your group. Now, what we will do is, we will add three of them. 6 plus 6 plus 4 is equal to 16. So, next we will take out total sum of squares. Total SS. And we have given the formula for taking out total SS which is summation X square minus summation X whole square over N. We have summation X square. If you take a look at the data, it is equal to 106. And then our summation X total is 30. So, 30 whole square for N we have 15. So, if you solve it, then your answer will be 46. You can get the calculator and can calculate. So, now take out your between SS. Between sum of squares. And taking out between is the easiest because if you do within minus out of total, then your between will come. Because total variance is 46. And within 16, so simple of 16 you have to do minus out of it. And the rest will come between sum of squares which is equal to 46 minus 16 is equal to third. So, this is our first step. The second step is we have to calculate degrees of freedom. And degrees of freedom I have told you that you have to take out within, between and total. So, for within I have told you that your formula is N minus K which is equal to N. Our group is 15, our group is 3 which is equal to 12. And for between degrees of freedom formula is K minus 1. Our three groups are 3 minus 1 is equal to 2. And for total I have told you that we have total N which is equal to 15 minus 1 is 14. This is our second step. Our third step is we have to divide with degrees of freedom and take out within variance which is called mean square. Mean square or you can do this also, variance. So, to take out within variance you have to divide with degrees of freedom which is called SS within. This is also within. How much is our SS within? We took out the SS within 16 and we took out 12 degrees of freedom. So, 16 divided by 12 is equal to 1.3. Now, we will take out for between. Between SS or between sum of between variance. And you can call it mean square between. And you can write variance between SS also. So, how much of between did you take out? Between SS we took out this one 30. And we took out between degrees of freedom 2. So, 30 divided by 2 is equal to 15. So, now we have both the variance. And our F ratio that is equal to between variance divided by within variance. And we took out between 15 and we took out within 1.3. So, if we calculate this, how much of our F ratio will come? Almost, we will calculate this and see in the next page. So, this is step by step. Step 1, you will calculate sum of square, i.e variability in the data. Then you will calculate the degrees of freedom for all three. Sum of square for all three. And then you will calculate variance actually for between and for within. And then you will take out F ratio on the fourth step. Which is your between variance divided by within variance. And once you calculate it, just like we did in the T test. That our calculated value is there. And we have to compare it with table value. Just like we did. We will compare it here too to draw a conclusion. What will come out? There are significant results. If you remember that when our calculated value is greater than table value, then our results will be significant. And if our calculated value is less than table value, then our results will be non-significant. So, this is our summary table. This is also an example from the book of Gravator. So, you can see that we took out SS on the first step. Sum of square and you know how to take out X minus mean square. Then we took out degrees of freedom. Divide by degrees of freedom. M stands for mean square. And we took out F ratio. Between variance divided by within variance. Which is equal to 11.28. This is 28. So, this is our table actually. And we split the variance. We told it exactly where and where. Total variability is so much. And then it goes between. And then it goes within. Isn't it amazing that in driving performance, because of any particular variable, there is so much change. And you want to see other factors also, which are random, which are noise, which are within factors, which are error variance. We separate them. And we see the effect of treatment, that how much our dependent variable is coming. This is your F table. It is available in any stats book. As I showed you the table of T. So, you have to see degrees of freedom between group, which is numerator. This is between group's degrees of freedom and this denominator is our error variance. Within group variance's degrees of freedom. Our two is between group's degrees of freedom and our 12 is for within. So, we have two values. The first value is our 3.8 at alpha 0.05. And our 6.93 is at alpha 0.01. That is, our results are significant. If our calculated value falls in this region, then we will claim that our results are significant. So, our value is 11.28. The calculated value is even far above. So, our results are highly significant. We can say that our results are significant at alpha 0.01. Because our calculated value, 11.28 is greater than your table value, which is 6.9. So, our results are significant. Significant results means that we will reject the null hypothesis. And null hypothesis is that three groups will have equal performance. But no. By using phone and not using phone, your driving performance is significantly different.