 तो बताया, power of the test के अंदरी के एक हमारा distribution है, नाला hypothesis के लिए, और उसके अगेंस्ट एक हमारा distribution है, अपने alternate hypothesis के लिए. और जो over lapping basically है, वो हमें बताती है कि जितना जाडा over lapping होगा each other distribution के अंदर, उतना ही जाडा beta और alpha यानी type 1, type 2 error के चांसे जाडा होंगे. जैनी वो, अगर हमारा distribution सांपस साइस जाडा है, तो more likely हमारे, जो distribution है, वो over lapping नहीं बनते है. और हमारे distribution आजे बनते है कि वो over lapping area कम से कम होता जाडा. तो if there is no over lapping area, means two distributions are independent and we can make a right decision. तो 95% confidence interval, if they do not overlap, we can conclude that the means come from different population and therefore they are significantly different. तो अगर हमारे distribution over lapping नहीं करते है, we can conclude that we will reject the null hypothesis and our error chances are also less and our power is also more. और ये कैसे होगा, हमारा सांपस साइस जब एंक्रीस करेगा. ज़से ज़से हम सांपस साइस एंक्रीस करते जाते है, we are approaching normality. और हमारा नहीं करते है, हमारा साइस करते है, our distribution is more normal, more homogeneous and so on. तो फेस वेजा से हमारी over lapping कम हो जाते है, and our power is also increasing. सांपस साइस बेदे दे रिसल्स of a study or statistically significant can depend on the sample size. अगर परस करेगे एक रियल अपका एकजिस करते है, for example, males or females are really different on some activity level in the population. अगर अगर अपने सांपस साइस परस करेगे 10 का या 20 का द्रोग किया है, लेकि उस श्माल सामपल में चुके वो दिस्टीबूचन बहत फलातर बनेगा, दीता के चांसे जाडा हो जाएंगे, अरर के चांसे जाडा हो जाएंगे, अफिर हमारा दिस्टीएन गलत होगा, यह अगर हमारा समवाल सामपल साइस है, तो वरा दिस्टीबूचन अज़े बन जाएगा, जिसके अंदर हमारी अरर के चांसे जाएंगे, यह नहीं, हमारा अकष्टल हमें पता है, के पापूलेटिशन में, अगर हम सामपल साइस इंक्रीस करते जाते है, तो even small differences भी हम दिटेक्त करते है, जस आभी फस करे मेरी स्थुडने रीषाच की, और जम हमने देखा, तो उसके गर्ज और भोएस के सामपल में, सोचल मीट्या यूज में, हाडली दो पौएंट्स का फरकता, अगर उनका जो ताईम है, सोचल मीट्या को यूज करने का, वोस 3 आवर्स, तो गर्ज का ताईम 3.15 आवर्स था, याब less than that था. लेकिन जब हम सामपल साइस इंक्रीस करते है, तो even हम small differences भी दिटेक्त करते है, चस कु कि भगर हमारा, एक और रव कर ड्यबुषन में, वो हम सीवाड़ सीवाड़ा पाटेसपभनस को एलाव करते है, तो हमारी नालःा पोतिसिस जो जो जो जो जाती हैं. तो बेसी कि लिलि गई ते डर्य खेल यूग, के हमारी सिथनिप्किखिंस जो है, सामपस साईसे, जब आम कन्कुट करते हैं के रिजाल सगन्टिकन्ट हैं वी वो रजक्त नाला आपोटिसिस, it is directly effected by the सामपस साईस. So increasing the सामपस साईस, most likely you will detect even the small differences and you will end up at a right decision. Lakin with a small sample, there are huge chances of committing type 1 error because you will actually not be able to detect the real differences in the population because of the small sample size. So a larger sample size tends to yield a statistically significant, by the way, this is one thing that we calculate the power of the test, the power of the test means how many samples we need, i.e. how many samples we need to detect the effect of the population. Chaya boh th tiny bhi effect ho, phir bhi muslim first karni effect size boh small hai, to aap ho kainge 500 ka agar data leinge to wo effect detect ho jaega. So a larger sample tends to yield a statistical significance. So agar aap ko lage ki hamara statistical significance result aaye aur ham naalā hypothesis ko reject kharin aur apne alternate hypothesis ko liye evidence dhunde aur effect talaash kharin. On the other hand, if the sample size is too small, an important relationship or different can be undetected, just main abhi baat hiye ki sometimes differences are there, you can see them, lekin small sample kyo jaise aap ho sko detect nahi karpate. In this case, power of the test will be too low. So small sample agar aap leinge, differences detect nahi karsakenge, jis ka matlab hai ki hamare power of the test lo ho jaegi. Power kya hai? Detecting, rejecting the naalā hypothesis when it is actually false. So sample size given that power is the ability of a test to find the effect that genuinely exist and the effect is found by having a statistical significant results which is p smaller than 0.05. Hence there is also connection between sample size and the p-value associated with the test statistic. Abhise bohse baat karte hain ke p-value is kind of misleading, kyo kye ham kate hain ke ji aap jab spaces me ham results run karenge to ham kate hain p-value if it is smaller than 0.05, toh amare results significant. Yadir ke hamne bohda fa distribution banaya hai. Aur hamne kaha hai ki agar hamare results isme aajate hain which is alpha level. Agar hamare p-value is smaller than 0.05, toh amare results are smaller than 0.05, toh amare results significant. Aur iska matlab hai ki results significant aur yaha fall kar rahe hain toh ham naalā hypothesis ko reject kar denge because this is a rejection region. Lekin chuke ye sample size se directly related aaska matlab ki agar ham chota sabi tiny effect hai toh aap usme sample size increase kar ke usko detect kar le, p-value significant aajayi aur aap ka naalā hypothesis reject ho jaga. Isli aap aane must kar diyao hai ke jab aap p-values report kar hain toh you definitely have to report effect size also. Ke agar aap ne sample size 500 ka le liya aur tiny effect bhi detect kar liya aur aap ne kaha mere results significant hain toh you will not only reporting p-value which is 0.05 less than ho nahi chahiye, balki you will also be telling that effect size is very small, medium or large. Ye ke example dva ke study got 2 groups of 10 heterosexual young men and got them to go up to women that they found attractive and either engage them in conversation which will be group 1 or sing them a song which will be group 2. So researchers may hear how long it was before the woman ran away imagining the experiment was also repeated using 100 men in each group. So 2 groups banaye aur dono me women ko attract kar nahi, ek ne usko conversation mein engage kar nahi aur ek ne usko gana gaa ke until aap ka jo hain wo the women will run away aur gayi. Good bye. Isli aap eksperimen kiye aur ek group ke andar, dono me 10 men liye hain. Lekin jo ek group hain usme ono ne up to 100 tak subjects ko try kiya hain aur ek group me ono ne just 10 subjects ko hi try kiya. So results showed that in both cases the singing group had a mean of 10 and a standard deviation of 3 and the conversation group had a mean of 12 and the standard deviation of 3. So dono groups me almost mean or standard deviation equal. The only difference between the two experiment is that one collected 10th scores, yani ono ne 10 logon se baat ki aur engaged content. So results showed that in both cases ono ne 10 logon se baat ki aur engage kar nahi ki koshish ki aur other group ne 100 logon ko engage kiya aur ono ko baat kar nahi ki koshish ki. So differences of the sample size and in next slide the confidence intervals become much narrower when the samples contain 100 scores than when they contain only 10 scores aur yani piche bhi draw kar ke deka hai ki jab humara sample size increase karta hai to humara distribution overlap nahi karte aur uska matlab hai ki humara independent aur hum se hi decision ke upar poachne. Ye example isme hi devi hai. Basically these standard error bars aur hum ketein ki in dono ko overlap nahi karna chahiye. So iss ke andar jaha pe humara 10 ka data hai ab dekhne ki humari bars overlap kariye. So iss ka matlab ki yaha pe significant results nahi hai. Hala ki dono me 10-10 logon se men thelekin usme ono ne 100 logon ko engage kiya tha aur usme ono ne 10 ko kiya tha. So iss distribution ke andar overlapping nahi hai. Right? Yopar jaara aur ye niche. Iska matlab hai ki yaha pe results significant hai. So you can see even if mean of two groups is same and the standard deviation is also same but still by just increasing the sample size we approach significance and here we got non-significant results. So this is how sample size works and that's why sample size is important. Take home message is ki we should take larger sample lekin we also should report the effect size as well. So the sample size affects whether a difference between samples is deemed significant or not. Right? Ja saham ne abhi dekhah abhi ki humara decision ko effect karega ki wo significance hai ke nahi hai. In large samples small differences can be significant or small samples may even real differences can be non-significant. Even a difference of practically zero can be deemed significant if the sample size is big enough. Ja saham ne abhi example bada hi ki bada tiny sa difference doh group meta lekin increasing the sample size made that difference significant. So sample size is directly related to a significance of the results for the decision or when we say that the hypothesis is rejected or accepted. So that's why we increase the sample size but also report the effect size.