 back to a new session on dentistry and more so today we have a statistics topic that is tests of significance so one video I have covered regarding the tests of significance where I had mentioned about the various tests and how the test should be applied on what condition the scenario of parametric test and non parametric test so this is extension of that particular video because in this video I'll be explaining about each test how a test should be done and and the way we do a test on the mathematical style and based on the hypothesis so let's move on to the topic so we starts with a hypothesis so hypothesis is nothing but an assumption so any research we start with a hypothesis and that should be null hypothesis as the word suggests it is null hypothesis hypothesis is nothing but an assumption a projection of data or the idea of the researcher about the parameters under study for an example a hypothesis is the mean pulse rate among the two groups are same or there is no significant difference between their pulse rate so today if we are conducting a study on two different groups regarding their pulse rate and we are postulating that or we are hypothesizing that there is no particular difference between these two groups suppose we might introduce a new trick into one group to control the blood pressure and by pulse rate so null hypothesis states that this particular trick has no effect because it cannot produce any effect why we do that this is how we are supposed to start a study we should keep a null hypothesis and we are doing the study to reject the null hypothesis so what we are trying to do with our studies we are trying to reject the null hypothesis and to accept a alternate hypothesis stating that there is a difference between this pulse rate between the groups or there is an effect of that particular trick in reducing the pulse rate or blood pressure whatever so any study will be starting with a null hypothesis and our aim in the study is to reject the null hypothesis so null hypothesis is an idealistic situation against which our study will be done okay so it conveys a meaning that there exists no difference between the different samples so we are doing the study to reject the null hypothesis so how do we do rejecting or how do we conduct a proper hypothesis testing is by test of significance so we can reject a null hypothesis or accept the null hypothesis based on the test of significance so if we reject a null hypothesis it means that there is a significant difference between the group or the particular drug has an effect or particular intervention has an effect or there is some difference due to a particular causal factor in the outcome if we are accepting the null hypothesis and stating that there is no difference means both the groups are same the intervention has no effect or the new drug has no effect so likewise so we always try to reject the null hypothesis the next concept is level of significance or P value this is the most confusing part or most intricate part in statistics that is the P value concept so P value P means probability value so it is the probability of null hypothesis being true so we can accept or reject the null hypothesis based on the P value so ultimately we reject our null hypothesis or we accept the null hypothesis based on the P value so how do we get this P value by doing the test of significance so it is a function of the observed sample that is used for testing the hypothesis okay so P value gives a ultimate result whether to accept or reject the null hypothesis so practically we keep P value less than 5 percentage as significant the ultimate P value what we get after our test of significance is less than 0.05 or less than 5 by 100 that result will be significant so in another way P is equal to 0.05 implies we may go wrong 5 out of 100 times by rejecting null hypothesis so we can attribute significance with 95% confidence so only there are chance for five times being wrong so either we should accept or reject null hypothesis based on the P value but we can go wrong only five out of hundred if it goes six out of hundred we cannot say that there is a significant difference and we need to accept the null hypothesis if it is less than five by hundred that is less than 0.05 we can reject the null hypothesis if it is any value greater than five or 0.05 we need to accept the null hypothesis I hope that concept is clear P value concept P value is nothing but the probability of null hypothesis being true so finally how do we get P value means by doing test of significance that is coming in future slides so what's the video at till the end because there are lots of calculation and mathematics coming so we'll get a very clear idea how we do this test and over test or guys for test so how do we do a testing of a hypothesis these are the basic steps of a hypothesis testing that first we should set up a null hypothesis that we have already seen what is null hypothesis and how to keep a null hypothesis then we have to define our alternative hypothesis that will be exactly opposite of null hypothesis this will be denoted as H0 and HA then the crucial step that is the test of statistics so any statistics based on the variable number of groups and other parameters which I mentioned in my previous video about test of significance you need to use t-test this x square is chi-square test z-test ANOVA test Wilcoxon test or man with new test so any test let it be any test you have to find out the P value then you need to determine the degrees of freedom that is a different concept so these steps you need to remember now hypothesis alternative hypothesis then the test of test at 6 then a degree of freedom then you have to set the P value okay so there will be a P value table for each test so t-test one table is there chi-square test one table is there and z-test table is there so that is a probability value for a test statistics and based on the degree of freedom you will understand in the next slides what is exactly what I'm talking about then you have to see the P value from the relevant table and based on the table and your test value we need to accept or reject the null hypothesis once you see the example we'll get a better idea so after doing a test of significance what we are getting is we are testing it that the research or alternate hypothesis against the null hypothesis this research is nothing but alternate hypothesis so we are checking whether the difference we are getting is real or it by chance that is a P value if it is less than 0.05 you can say that it is a real difference and if it is not less than 0.5 you can say that it happened by chance so these tests we have seen like few tests I'll be explaining in detail in this video chi-square test and standard error of two proportions student T test paired and ANOVA so let's see how we conduct a standard error of difference between proportions okay so we have two proportions that is qualitative data between so data also I had explained in my previous video two groups so we have a two groups with more than 30 samples so this is a formula standard error proportion of one and standard error proportion of two so this formula we have to apply so all this will be done by softwares and today's scenario there is no manual calculation but this is a theoretical part so we have to this is a z test we are doing so z value we have to calculate P1 minus P2 divided by standard error of P1 minus P2 if z value is greater than 1.96 and it will be significant if it is less than 1.96 it is not significant because that is a table value so z table is there so z table 1.96 if you are getting it will be significant greater than 1.96 less than 1.96 it won't be significant okay P value will be more than 0.05 so let's see an example you will get a better idea where the cure rate of typhoid fever after treatment with syprofloxacin and syphetroxone where they call as 90 percentage and 80 percentage among 100 patients treated with each of the drugs so how can we determine whether cure rate of syprofloxacin is better than syphetroxone so we need to keep the null hypothesis that is there is no significant difference between the cure rate of two drugs then alternative hypothesis we are saying that syprofloxacin is 1.125 times better in curing typhoid fever and then we are to third step is we have to do the test that is z test we are doing so we calculate the z test we get the z value so we have P1 minus P2 this standard error thing so 90 minus 80 divided by we get ultimately we get a score of two since that is two it is greater than 1.96 hope you remember this if it is greater than 1.96 we will reject the null hypothesis if it is less than 1.96 we accept the null hypothesis okay so we get score of two that is greater than 1.96 so it is significant and what we are doing is accepting or rejecting so we reject the null hypothesis what is the null hypothesis there is no significant difference between the two cure rates of two drugs and we are accepting the alternative hypothesis that syprofloxacin is 1.125 times better in curing typhoid fever that the syphetroxone this 1.125 we get from the data from the assumption after a particular review of literature we have we can keep an assumption so it need not be same for every study it might change sometimes we don't keep exact value so anyway that doesn't matter the thing is the test value should be greater than the table value this is a table value okay so if it is greater than the table value we reject it what we reject we reject the null hypothesis and we accept the alternative hypothesis or research hypothesis okay so let's see what is chi-square test chi-square test there are few prerequisites like sample must be random and there should not be any zero value so what we do is we should create a contingency table okay and we should determine the expected value then we should minus observed minus expected value there is a formula for expected value rho into rho total minus column total divided by total so this is observed value expected value square it divided by expected value then we finally calculate the chi-square value and we see an example a study done in a hospital where cases of breast cancer were compared against control from normal population against the position of family history of carcinoma breast so hundred in each group were studied for presence of family history 25 cases and 15 controls okay so let's see the significance of family history in breast cancer so we have 25 by 15 times more common cancer in breast that family history is 1.66 times so this is how we got that 1.15 of that particular previous 1.125 times so this is how we got this exact value so that doesn't matter yet okay so here we get 1.66 times more common carcinoma breast so we are testing is it a risk factor in population so we are applying the test of significance by chi-square test this x-square denotes chi-square so first we are keeping another hypothesis saying that there is no significant difference between incidents between cases and controls and alternative hypothesis we are stating that family history is 1.66 times more common in carcinoma breast so third step is we are conducting chi-square test so this is a contingency table cases controls present absent so 25 75 15 85 so total 100 we have so this is the case this is the cases among this is a risk factor among cases risk factor among controls and there's no risk factor among cases and there's no risk factor among controls so we get this table then we calculate the expected value the raw total into column total divided by grand total so 100 into 40 by 200 is easy 100 into 40 by 200 so you have to see this L shape L shape everywhere you keep L shape you get the expected value it's easy actually so then you have to minus observe value minus expected value you get 5 then square it then divided by expected value ultimately you get chi-square value that is 3.125 okay now you have to calculate the degree of freedom in Z test there is no degree of freedom in T test I know what test and chi-square test you have degree of freedom now that is a different concept I'll explain in another video so it is a formula raw minus one column minus one multiplication so you have a 2 by 2 contingency table so 2 minus 1 2 minus 1 so you get 1 into 1 that is 1 so this is the table I was talking about so every test let it be T test chi-square test I know what test there is a fixed table for each degree of freedom and for the P value so this is a significance value okay so if you're keeping 0.05 with a degree of degree of freedom one the critical value that is x square value is 3.84 so the chi-square value after our test is greater than this one we reject the null hypothesis and if it is less than this value we accept the null hypothesis okay so if you're keeping a significance value point zero one it should be 6.64 so let's see our x square value is 3.125 okay but the table value is 3.84 so what we are doing is it is less than the table value so we need to accept the null hypothesis we cannot reject it because our test value is less than the table value at the degree of freedom one and significance levels 0.05 okay so we need to accept the null hypothesis and confirm that there is no significant difference between incidents of family history among cases and controls so there is no rule for family history in causing carcinoma breast so this is how to chi-square test now let's see what is student test there are two types unpaired unpaired T test so almost same the steps are same only thing the T value calculate first null hypothesis alternate hypothesis then the T value this is two groups other mean group one mean minus mean group two mean then this standard error of group one minus group two so if we have combined standard deviation so we have to use this formula so formula is different for different scenario so let's see what is the chest circumference in 10 normal and malnourished children of same age okay so we have 10 people's normal malnourished chest circumference so what we are finding out is whether the mean chest circumference is significantly different in two groups okay so here the table value for 18 degree freedom at 0.05 is 2.02 okay so the table which is which was there in chi-square test similarly one table is there for T test okay so that table is not here so anyway that table value is 2.02 so why we are saying that degree of freedom 18 is here 10 number here 10 number so it is n1 plus n2 minus 2 okay so 10 plus 10 minus 2 it will become 18 so let's see this mean of first sample standard deviation and we multiply it with standard deviation and this degree of freedom this is degree of freedom 10 minus 1 so by substituting we get value of 2.03 centimeter and then T value this is a standard error we are calculating 2.03 then we are substituting with this one mean value and ultimately we get a T value of 6.75 okay you remember the table value was 2.02 okay table value was 2.02 at degree of freedom 18 and significance level 0.05 so the present value is 6.75 which is at 18 degree of freedom and 0.05 we compare it with value 2.02 so the test value what we get is very greater than 2.02 so what we do we reject the null hypothesis because it is very greater so we reject the null hypothesis and stating that the difference in the main chest circumference value between normal and malnourished group is statistically significant okay so we reject the null hypothesis and accept the alternate hypothesis this is how we do T test of different group if it is same group before after observation we have to do a pair T test so this is before treatment after treatment the same scenario but here we have degree of freedom 9 because the same group of people only 10 patients in the another example we have two groups so n1 plus n2 minus 2 because of two groups here n minus 1 so 10 minus 1 we get degree of freedom 9 and at significance level 0.05 our table value is 2.2 okay so what we are finding here is whether the drug is significantly affecting reducing the anxiety score okay so before treatment we take an anxiety value after the drug we are taking anxiety value whether it is effectively significantly reducing it or not so the same example we have before treatment value after treatment value we minus it see the mean value we take the mean value each value will be deducted from mean value so this is the difference in mean value then we square it we add up all the square value then we substitute it before that we find out the standard deviation by this formula x minus x bar square by n minus 1 then we calculating the t value and standard error will be standard deviation by root of sample size we get 1.43 so t value will be x bar is standard error so we get 0.09 okay so our degree of freedom is 9 so our t value is very lesser than t value is very lesser than the table value at a degree of freedom 9 because the table value is 2.21 what we get is 0.09 so we cannot reject the null hypothesis instead we have to accept the null hypothesis okay so we accept the null hypothesis and conclude that there is no statistically significant difference in the anxiety score before and after treatment or in other words we can say that the drug is not effective and difference might have occurred because of chance okay so ANOVA also we apply it for more than three groups if we have more than two groups it let it be three four five we can do ANOVA the steps are same we have to see the null hypothesis alternative hypothesis then we have to calculate the ANOVA value then degree of freedom compare it with table value if it is greater than the table value we reject it if it is lesser than the table value we accept it so in ANOVA we have to see the variation between the groups and variation within the groups so then we have to see the f value so this is the f value in ANOVA just like t value and t test so this between value and within group value so we get this value and if that particular value is greater than the table value we reject it so this is a basic steps in tests of significance most commonly the z test which used for proportion then the chi-square test which used for again proportion but different groups like contingency table so then we have t test and paired and paired t test and ANOVA ANOVA is not explained in detail but my idea is to express or explain the various steps involved in test of significance which are commonly the seven steps first we need to keep an null hypothesis that is no difference between the group then we have to define alternative hypothesis so our aim is to reject the null hypothesis and accept alternative hypothesis so the third step we need to calculate the test by t test chi-square z test then degree of freedom then you have to see the p value based on the degree of freedom you have to compare it with the table value if it is greater than the table value at corresponding degree of freedom and the significance level we need to accept or reject the null hypothesis so that's all about the test of hypothesis so that is covering null hypothesis alternative hypothesis p value and t test chi-square test ANOVA and z test okay I'll come up with more videos related to biostatistics thank you