Tiêu đề P value Significance .pdf ✅

abc methodology & of research biostatistics o thesis that reflects the conservative position of no effect or no difference or no association in to baseline. Usually the researcher has reason to believe that• some effect or some or some association exists there beenuse of which he been motivated to (fcreocc to collect sample nnd to measure outcomes in sample with the hope of finding di Ille enough to be able to reject the null hypothesis. ill h hypothesis is "drug A is better thnn drug B"; to prove this research hypothesis there If drug A decrease death rate by 10% it needs to be tested as better doing statistical test, If e.g. A decrease denth rate by 9 % it also needs to be tested as better doing statistical test and so on. But if we approach vin only one test is enough to come to conclusion. (Ho) covers all possible exceptions to the research hypothesis (alternative hypothesis). H and alternative hypothesis (HA) all possible states of the world is entertained. These two HA) are mutually exclusive and exhaustive. Either Ho is true or of HA the is statistical true. The test hypothesis owever according to the we can logic thflt we dream to test is the HA. H do this directly rather we do it indirectly via testing of Ho. You can reject the Ho , it will with only one alternative; that is to accept the HA. If you fail to reject the Ho in that case you method of disproving the Ho. If we can disprove & reject the null hypothesis then automatically the HA (research hypothesis) stands as true. If can't disprove & can't reject null h\T0thesis then automatically the HA (research hypothesis) stands as not true. statistical technique enables us to reject null hypothesis but do not provide ways to directly accept a research Therefore, research hypothesis is to be converted into null hypothesis to make that it testable research because the only way to test a research hypothesis is to eliminate all alternatives of all hypothesis hypothesis. Null hypothesis stands for all of these alternatives of research hypothesis. So testing is done indirectly via null hypothesis. "l)uring writing of protocol / thesis / research report, it is preferable to write research hypothesis (alternative hypothesis). Null hypothesis is usually avoided because stating hY)0thesis in null hypothesis form creates an unskillful amateurish impression" Analogy tonull hypothesis: In legal system & judicial practice, an accused person is assumed innocent until proven guilty. An accused person is always brought to court with a hypothesis that "accused is guilty". When this accused person stand before court for trial; jury board start with null hypothesis assuming him innocent and states that 'he is not guilty'. Now court asks the prosecutor to provide evidence against this null hypothesis (Ho). Prosecutor collects witness & evidences against the Ho over the years and tries to reject null hypothesis of jury board. If jury is satisfied with evidences & arguments provided by prosecutor against Ho, null hypothesis is rejected and alternative hypothesis is accepted stating that accused is guilty; so accused person will be punished. If prosecutor fails to provide sufficient witness & élådences aganist Ho; null hypothesis is retained stating that accused is not guilty and the accused is acquitted. Probability and P-value in relation to hypothesis testing: For testing of any research hypothesis, the statistical convention is to begin with the null hypothesis (Ho) which states that, there is no difference between two or more sample statistics or between sample statistics and population parameter. Suppose our research hypothesis is "diabetes mellitus (DM) causes hyoertension (HTN)". A study is carried out on 50 diabetic and 50 non diabetic individuals. Participants in both groups are assumed to be otherwise highly matched except for the DM. Mean blood pressure (BP) Of diabetic and non diabetic group found to be 130 mmHg and 120 mmHg respectively. This apparent difference of 10 mmHg tends to prove that DM causes HTN but this needs to be tested through hypothesis testing.
abc methodoloq & of research biostatist cs To Ho. researcher states that, DM does cause HTN or there is no difference of blood pressure between diabetic and non diabetic che observed difference of (10 happened to occur purely due to by chance or sampling error. This is the fact in mmHg) h the null of no difference between groups is true, the observed difference every between Silently in if will always be explained to be due to by chance or sampling error without any cause. corner of mind researcher also cultivate the alternative hypothesis (HA) which states that diabetic DM groups. NTN or really there is difference of mean blood pressure (IBP) between diabetic and non the observed difference of BP (10 mmHg) between diabetic and non diabetic group is not due to by chance In result this (event). study blood Now pressure difference of 10 mmHg between diabetic and non diabetic group is the occur under null researcher will find out the probability of this result (10 mmHg difference) hypothesis (when Ho assumed to be true) due to by chance probability found to be low, it be (sampling error). If this difference to occur under concluded that there is less chance of this result 10 mmHg will be null due to by chance (sampling error) without any cause. so null automatically alternative regarded hypothesis to be false and it will be rejected. When null hypothesis gets rejected gets accepted to conclude that really there is significant of mean blood pressure difference between diabetic and non diabetic groups; that means the result 10 mmHg) will be proved (difference of to be significant. Therefore, it will be concluded that DM causes the mean blood pressure in diabetic since reverse (diabetic 120 mmHg, non diabetic group is more than that of non diabetic group. If this data were 130 mmHg) difference (10mmHg) between significant; in that case it would be two groups was concluded that DM reduces blood pressure. Alternatively (sampling error) if the probability of this result (10 mmHg differences) to occur under Ho due to by chance mmHg difference found to be high, it be concluded that there is high chance of this result of So null hypothesis to will occur under null hypothesis due to by chance (sampling error) without any cause. be regarded to be true and it will be accepted (fail to reject) to conclude is in fact no difference that there difference of 10 mmHg of mean blood pressure between diabetic and non diabetic group; the observed means has happened purely due to by chance (sampling error) not due to DM, that concluded the that, result DM (difference of 10 mmHg) will be proved to be not significant. Therefore, it will be does not cause HTN. So in hypothesis testing probability (P) is defined as Chances of occurrence of an event due to by chance (sampling error) under null hypothesis. P-value is the quantitative estimate of this probability of by chance and it ranges from O to 1. P-value zero means, no chance of the event (observed result) to occur due to by chance (sampling error) under null hypothesis, when null hypothesis is true. P-value 01 means, 100% chance of the event (observed result) to occur due to by chance (sampling error) under null hypothesis, when null hypothesis is true. P-value 0.5 means, 50% chance of the event (observed result) to occur due to by chance (sampling error) under null hypothesis, when null hypothesis is true. P-value 0.05 means, 5% chance of the event (observed result) to occur due to by chance (sampling error) under null hypothesis, when null hypothesis is true. So, P-value simply represents the magnitude of the chances of by chance for an event (result) to occur under null hypothesis, when null hypothesis is true. The more the p-value, the more the chances of bychance (sampling error) and the less the p-value, the less the chances of bychance (sampling error) Roughly speaking, p-value represents the probability of Ho to be true. It expressess the weight of evidecne in favor or against the null hypothesis (Ho). If p-vulue is low, it goes against the null hypothesis; if p-value is high, it goes in favour of null hypothesis. Remember, even a very low p-value indicates that there is some probability of Ho to be true. * By chance, sampling error, sampling variation, random error and random variation are synonymous. 198 Low P.value (Pso.05) Less chance of the result Ho due to to by chance/ sampling occur ermr under Strong evidence against H Ho re•ected HA accepted Result is significant STATISTICAL SIGNIFICANCE abc o' methodolo research High P.value (bo 05) Ho due to by chancel sampling error Weak evidence against H0 0 accepted (failed to reject) Result is not significant to occur due to by chance (sampling error). Significant means, result is due to by chance due to some obvious extraneous causes. Not Significant means, result is likely occur to by chance or sampling error. Therefore, 'by chance' pleads to conclude the result not significant & 'not by chance' pleads to conclude the result to be significant Estimation and Hmthesis testing are to evaluate the statistical In significance fact these tools are used to estimate the chances ofby chance or sampling error behind sample result & to say how well the sample approximate the true value. so the essence of statistical significance test is to estimate the probability of the observed result to occur due to by chance or sampling error. Ifthe magnitude to of be true (significant) and if the magnitude of by the observed result to be true; so the observed is low, observed result is certified is high. there is no evidence in favor is certified to be not significant. It is the point of demarcation between chances ofby chance (not sampling error) (sampling error) and not by chance for an observed result to (rcur. It is the line of demarcation where we accept (fail to reject) or reject null hypothesis. Level of significance is expressed as percentage e.g. 5% (0.05) level, (0.04) level, 3% (0.03) level, 2% (0.02) level, 1% (0.01) level etc. Infact the level Of significance is the direct measure of the chances of bychance (sampling error) e.g. 5% level indicate 5% chance of by chance & 95% chance of not by chance, 4% level indicate chance of by chance & 96% chance of not by chance and so on. Since p-value is the direct measure of the chances of by chance; so, the level of significance actually represent p-value at a definite level. If the calculated P•value of a result is more than that level; chance of by chance (sampling error) assumed to be high to accept Ho & to say result is not significant but if the calculated P.value of a result is equal to or less than that level; chance of by chance assumed to be low to reject Ho & to conclude that the result is significant. Message of 5% level of significance Here the P-value is 0.05. Since the P-value is equivalent to the chances of by chance (sampling error), so at this level the chances ofby chance is 5% and the chances of not by chance is 95%. For any result with P-value 0.05 will have probability to be due to by chance and 95% probability 199
abc method o 'og L Of research biostatist cs to chances be not of due by chance to by chance (sampling or 300 error) chance is assumed of Ho to to be be true low, so 95% researcher chance hypothesis. of will Ho ignore to Therefore be it false. to state thnt the result is not due to by chance (sampling error) under null hypothesis will be rejected alternative hypothesis will be accepted to conclude ignored), the result to null be significant. If the by chance (sampling error) is given importance (not decision be that. the result is due to by chance (sampling error) under Ho; so Ho accepted & result is stgmficant. not become non Simply significant stated: (Ho if accepted) researcher but side if researcher to by chance side to 95% chance not bychance of Ho to be (95% true), result Ho to be false), result become significant (Ho rejected). Therefore, at 5% level if decision chance of favour of not by chance will (not sampling error), Ho will be rejected the result side concluded of 5% chance goes to be in of significant- This conclusion be regarded wrong (false positive) from the by chance. Therefore, nt 306 level researcher is willing to take 5% risk of being wrong in his conclusion, since the 5% chance of by chance (that speak to risk accept of incorrect Ho & to rejection say result of not H significant) was ignored. That means at this level taking researcher will finally reject Ho & will say result is significant, there is effect / association. Risk of incorrect rejection of Ho is equivalent to the risk of false positivity (type-I error); that means "to say there is effect I association which is actually not". So, at level with p-value 0.05 if the result is stated significant; there is 5% risk of false positive conclusion (type I error) & confidence of correct conclusion (true positive conclusion) about the result to be true. Obese BP 140 5% chance of by chance for this result Ho accepted result not significant Obesity does not cause HTN Ignored So, final conclusion is false positive from the side of 5% by chance Non obese BP 130 Result (10 mmHg differene) 95% chance If its p-value = 0.05 of not by chance for this result 95% confidence for the result to be true Ho rejected result significant Obesity cause HTN Final conclusion BP : Blood pressure Obesity causes HTN I] TN : Hypertension Message of 1% level of signifi Here the P-value is 0.01. Since the P abc o' research error), so at this level the c For any result with P.value 0.01 andthe (sampling probability to be not due to by chance to be due to by chance and be low, so researcher will ignore it to state that the by chance (sampling error) is assumed to result is not due to by chance (sampling given importance (not ignored). decision (sampling error) me is to by chance (sampling result is due bychance, result become significant%fiqnt non si (Ho Significant. accepted) S • stated; if researcher side to favour of 99% not by chance (not sampling Therefore researcher side to 99% not be significant. This conclusionwillbe & the to wrong (false positive) from the side of chance conclusion, since the 1% c IS willing to take 1% risk ofbeing wrong in his significant) was ignored. That means at this level risk Of incorrect rejection of researcher will Risk "to say there is effect / association which result is stated significant; there is 1% risk actually of false not'. So, positivity at 1% level (type-I with error); p.value that 0.01 means if the confidence of correct conclusion (true about conclusion the (type to be I error) true. & 99% positive Same message is true for every level of significance. so. level of directly represent false positivity (type - 1 error) e.g. at 5% level is at level faLe positive is so, P.value at a definite level of significance indicate the probability to commit false positive mistake saying that; "there is effect or in Maximum P-value it does not exist". (chances of by chance) at below which we will ignore the chances of by chance will assume no by chance or no sampling emr to be operating is the 0.05 (5% level of significance); so it is called the critical level of that chances of one false significance. Statisticians have agreed positive cutoff P-value is taken at conclusion out of 20 is acceptable in the real world. So, the is ignorable to reject Ho & 0.05 to (5%), that means chances ofby chance (sampling error) up to 5% conclude the result significant with 5% risk of false positivity. If the P-value is >0.05, chances of by chance is more than 5% and chances of not by chance is less than 95%. Here, the amount of by chance is assumed to be high which can not be ignored. So researcher will side to chances ofbychance to say that the result he has got happened due to by chance (sampling error) under Ho, when Ho is true. Therefore null hypothesis (Ho) accepted the result is not significant. If more than 5% chances ofbychance is ignored & make conclusion infavour of the less than chance of not bychance saying that result is significant; there is more than 5% risk of false positivity that is unacceptable in real world. If P-value is 0.06, chances of by chance is 6% and chances of not by chance is 94%.6% by chance (sampling error) is regarded high and not ignorable. So decision will go in favour of 6% chances of by chance to accept Ho and to say result is not significant though at this level magnitude of not by chance (not sampling error) is still 94% (far greater than 6% by chance). Therefore P S 0.05 statistically significant result P>O.Oö —i statistically not significant result 201 200
abc Of research methodolo very low (S probability of Ho true sq Ho rejected in favor HA. Result is significant. abc of research' A acceptem Result is significant. 0.05 means: 6% 2. very high probability of the observed results to occur due to by chance or sampling error under I-cvel of significance IOo null hypothesis (Ho), when Ho is true. so null hypothesis is accepted. Test result is not significant & there is no obvious reason behind the test result. There P•valuc O is no effect/ no association. by chance Under null hypothesis (Ho) when Ho is true; sample result is a likely event to occur. So Ho is 6% not by chance & it is retained (fail to reject). Test result is not significant & there is no effect / no true 1% Fy chance association. 09%, not by chance by chance High probability of Ho to be true. So. Ho retained not (fail to reject). Test result is not significant. by chance weak or no evidence against Ho. So. Ho accepted (fail to reject). Test result is not significant. * p-value showg the amount of by chance (sampling (>0.05) pleads to conclude the error). Big amount of by chance result to be not z significant & gamll amount of by chance (g 0.05) pleads to conclude the Level of result to be significant. significance. false positivity and confidence False positive (to state (Type-I the error) result true or significant) : P-value 95% Level of significance 5% 0.05 0.04 2% 0.02 1% o 0.01 1% 0.1% 0.001 0.1% 1 96% Test statistic is a value calculated from sample data by doing an appropriate statistical test. 98% Test statistic is used to determine the P•value and to make statistical decision. 99% Test statistic reflects the amount of evidence against the null hypothesis (Ho). Usually larger the test statistic (irrespective of sign), greater the evidence against Ho. 99.9% Nature of test statistic depends on the interest of researcher & the statistical test done. Statistical test Test statistic Analogy to chances of by chance & statistical decision: Student's t-test decide to make a journey by air, you have to buy a ticket from any airline. Is it possible from the side of airlines to declare that, there is no chance of accident when you will make journey? Answer is Z-test simply no even if it is the best possible airline of the world. Knowing the fact that, there is a chance of ANOVA accident, you will take boarding pass. What is the basis of this courageous decision? Yes, although there is a chance of accident but that chance is very low say, 0.001%; where the chance of no accident Chi-square test is far greater (99.999%) than the chance of accident. so, here the chance (probability) of accident is low that. you will easily ignore it to assume that there is no chance of accident & you will fly. In contrast Correlation test to that if the self declared chance (probability) of accident by any airline is 20%; you will not ignore this Risk ratio test probability of accident and decide to avoid air journey though still chance of no accident (80%) is far greater than the chance of accident (20%); so, you will side to the 20% chance of accident Regression test and your decision will be not to fly by air. Similarly in research process also, always there is a chance ofby chance (sampling error) behind every result (event). Researcher will try to find out the amount of that by chance. If the amount of by chance is low researcher will ignore it to state that, the Test statistic is calculated t-value / t-statistic Z-value I Z-statistic F•value I F-statistic X2-value r-value (correlation coeffcient) Odds ratio (OR), relative risk (RR) Regression coemcient Intercept (a) value. Sample value varies from sample to sample. So, result is not due to by chance, so the result is significant. In contrast to that if the amount of by chance test stastic Under also the varies assumption from sample of null to hypothesis sample; therefore every test every statistic test has statistic already is been a random worked (sampling error) is high (>0.05). researcher will not ignore it rather he will say, my result has happened variable. to occur due to by chance (sampling error), so the result is not significant. out & presented in the name of statistical table e.g. t.table for t-statistics, Z-table for Z-statistics INTERPRETATION OF P-VALUE: Let us explain it in a multitude of ways etc. At a definite level of significance against a definite sample size, every test statistic has a definite value given in the relevant statistical table. This value is regarded as the maximum 1. P 0.05 means: value upto which that test statistic occur due to by chance or sampling error at that level of Very low probability of the observed result (event) to occur due to by chance or sampling error significance against that sample size. This value is called the critical value of that test under null hypothesis (Ho). when Ho is true. So null hypothesis is rejected & alternative statistic to occur under Ho due to by chance (sampling error) at that level of significance against hypothesis (HA) is accepted. Test result is significant & there is some obvious reason behind the that sample size. We relate the sample test statistic (calculated from sample data) with the test result. There is effect / association. critical value given in corresponding statistical table to obtain P•value. You can assume sample Under null and hypothesis it is rejected (Ho) in when Ho is true; sample result is an unlikely Test result event is to significant occur. So Ho & test statistic as calculated test statistic and the test statistic value worked out under Ho & is wrong favor of alternative hypothesis (HA). statistical table at a definite level of significance as critical value. given in there is effect / association. 203 202