What is the role of p-values in hypothesis testing and how do you interpret them?

In hypothesis testing, p-values help determine if your results are due to chance. A low p-value means there's strong evidence against the null hypothesis. However, it's important to know that p-values are influenced by sample size and don't tell you the effect's importance. Also, if you run many tests, you might get significant p-values just by chance.

p-values help you decide whether the results of your study are statistically significant. Assuming the null hypothesis is true, the p-value represents the probability of observing what you have already observed or something even more extreme. A low p-value is considered an evidence against the null hypothesis. p-values are compared with the level of significance (1%, 5%, 10% are common levels of significance). Example: If you are working with a significance level of 5% and the p-value comes out to be 2%, then this is considered as an evidence against the null hypothesis.

In hypothesis testing, the p-value measures the probability of obtaining results at least as extreme as those observed, assuming the null hypothesis (H?) is true. The null hypothesis often suggests no effect or difference, while the alternative hypothesis (H?) suggests an effect. For example, in banking, if a new credit risk model is tested to see if it improves default prediction compared to an existing model, a p-value of 0.03 indicates a 3% chance of observing the results due to random variation alone. If this p-value is ≤ 0.05, it suggests the new model significantly improves prediction accuracy, guiding strategic decisions.

This article is tactical rather than strategic in nature. It narrowly provides P-Value basics in the context of hypothesis testing. While this is useful, it ignores strategic issues. Does the data have bias? Is a focused subset of the data more likely to provide a better test? Was the most appropriate hypothesis test and test statistic used? Does the test fully utilize available data substructure or has a too simplistic a test statistic has been used? Do you fully understand the project's context? Failure to address strategic issues can lead to under interpretation, misinterpretation or overinterpretation of a P-Value's meaning.

A p-value less than 5% (thresh hold value) is considered to be significant result for testing the desired hypotheses. Always a p-value less than 5% is favoring the alternative hypothesis. Some times we set a thresh hold value at 1% to have strongly significant value and seek a p-value less than 1%.

when we wish to test our hunch feeling/statistical assumption, we develop hypotheses first. Null and the alternative hypothesis. Null Hypothesis actually nullifies the claim while alternative is our claim. P values helps us in understanding (to a certain extent) the significance of our claim. Lower the p value stronger is the evidence of our claim - alternative hypothesis.

Let's say a soft drink company claims an average soda content of 250 ml per bottle, and you, as an officer, are asked to verify this claim. You randomly pick a sample of 30 bottles from their production line and note down the amount of soda in these bottles. You find that the average amount of soda in these 30 bottles is 240 ml. Will you reject the company's claim? Not necessarily. Just because your 'sample of 30 bottles' has an average of 240 ml, it doesn't mean that the entire population of bottles also has an average of 240 ml. It could be the case that, by chance, you ended up selecting bottles where the mean came out to be lower. And this is where hypothesis testing comes into the picture.

Take an example of music. The null hypothesis says - the new music does not increase energy and excitement levels compared to regular music. Conversely, the alternative hypothesis says - the new music boosts energy levels. To test these hypotheses, the scientist conducts an experiment with two groups: one listens to the new music, the other to regular music and rate their energy levels. The scientist calculates a test statistic and determines out the p-value and significance level, then scientist decides whether to reject the null hypothesis. A small p-value indicates the difference is unlikely due to chance. However, other factors like effect size, sample size, and confounding variables should also be considered.

NA MINHA EXPERIêNCIA UTILIZO MUITO OS TESTES DE SIGNIFIC?NCIA EM ESPECIAL O TESTE-t, POIS ESTOU SEMPRE COMPARANDO MéDIAS RELACIONADAS A COMPARATIVOS DE EQUIPAMENTOS, COMPARA??ES INTERLABORATORIAIS, ANáLISE DE SéRIES HISTóRICAS E ETC. ASSIM SE TIVERMOS UM PROCESSO ROBUSTO E PADRONIZADO O TESTE DE HIPóTESE é EXCELENTE E SENSíVEL PARA DAR-NOS RESULTADOS TANTO DE QUE O PROCESSO ESTá ESTáVEL, MAS PRINCIPALMENTE QUANDO OS TESTES MOSTRAM-SE SIGNIFICANTES PARA EVIDENCIAR QUE ALGUMA COISA SAIU DE CONTROLE. ASSIM é O PRIMEIRO PASSO PARA RASTREAR PROBLEMAS.

O valor de p é um parametro onde julgamos aceitar ou rejeitar a hipótese nula para aquele distribui??o, no entanto, a veracidade da hipóteses n?o é prova de que é verdadeira.

Para lembrar como o resultado de P afeta o teste de hipóteses, eu uso a frase "If p is low, null has to go" (se p é baixo, descarte a nula"). é um jeito fácil de memorizar, muita gente se confunde.

Um valor de p baixo significa que, se a hipótese nula fosse verdadeira, seria raro obter um resultado t?o extremo quanto o observado. Isso sugere que há evidências significativas contra a hipótese nula, permitindo-nos rejeitá-la em favor da hipótese alternativa. Por outro lado, um valor de p alto sugere que seus dados s?o bastante típicos sob a hipótese nula, o que significa que n?o temos evidências suficientes para rejeitar a hipótese nula com base nos dados coletados. No entanto, é importante lembrar que um valor de p alto n?o prova que a hipótese nula seja verdadeira; apenas indica que n?o há evidências suficientes nos dados para rejeitá-la.

NA MINHA EXPERIêNCIA SEMPRE QUE OBTIVE VALORES DE p N?O COMPATíVEIS COM O ESPERADO FOI MUITO úTIL PARA DEMONSTRAR PROBLEMAS COM PROCESSOS OU AMOSTRAGEM.

Interpreting p-values correctly is crucial as they are often misunderstood. A p-value indicates how compatible your data is with the null hypothesis, not the probability that the null hypothesis itself is true. A low p-value signifies that if the null hypothesis were true, it would be unlikely to observe a result as extreme as what was found in the data. Conversely, a high p-value suggests that the observed data is likely to occur under the null hypothesis, indicating weaker evidence against it. Understanding this distinction helps in accurately assessing the significance of findings in hypothesis testing, ensuring informed decision-making based on empirical evidence.

Il faut garder en tête que, en général, valeurs p sont très dépendantes de la taille de l'échantillon testé. Un constat général est que les tests d'hypothèses échouent en général sur les grands échantillons. Donc, en termes d'interprétation, les valeurs p sont fiables pour de petits échantillons (quelques dizaines, voire quelques centaines d'observations). Par contre, pour les grands échantillons, il vaut mieux se fier à des indications qualitatives.

Type 1 Error occurs when we reject the null hypothesis even when it is true. The probability of Type 1 Error is called level of significance. The level of significance is determined by the researcher (common values are 1%, 5% and 10%). The choice depends on how sure the researcher wants to be before rejecting the null hypothesis.

Even though your data is in the same field, the p value used can be different. This depends on the size of the data population and the level of data confidence intervals. To get an idea of the sample size with different p values, you can use an easy formula such as the Slovin formula. In sample calculations, population size and p value are very important because they affect the sample size required to obtain representative results. Adjusting the p value and population size appropriately can help determine the sample size needed for research or data analysis.

O TEXTO AO LADO EXPRIME MUITO BEM O SIGNIFICADO PRáTICO DO p. O SEU PROCESSO PODE ESTAR EM FASE DE PADRONIZA??O E UM p MUITO PEQUENO PODE MOSTRAR QUE SEUS RESULTADOS N?O FORAM BONS, MAS ISSO N?O SIGNIFICA QUE TUDO ESTá RUIM OU DEVE SER REFEITO. TALVEZ MELHORIAS PONTUAIS POSSAM SER MOSTRADAS, CORRIGIDAS E SE ESTIVER EM ESTABILIDADE Aí SIM PODEMOS FAZER UM TESTE COM UM p MAIS EXIGENTE.

O limiar depende do risco que estamos dispostos a assumir. Por exemplo, um nível de confian?a de 68% é aceitável para medir o pH da água, pois o risco é pequeno. No entanto, para substancias perigosas como o arsênio, é melhor usar um nível de confian?a alto (95% ou 99%) e um nível de significancia baixo ( ??=0,01 ou 1%). Isso minimiza o risco de liberar uma amostra prejudicial. Portanto, há mais risco com um nível de confian?a de 68% do que com um de 99%.

Parfois, il est plus intéressant de regarder un seuil en termes d'ordre de grandeur?: Est-ce que ma valeur p est de l'ordre du centième?? du millième?? ... Les valeurs exactes du type 0.05 sont rassurantes mais cachent souvent des questions importantes. Il faut garder en tête que les tests d'hypothèses sont des aides à la décision, pas des décisions en soi !

O EFEITO, NA MINHA OPINI?O, NO CASO DE UM TESTE t SERIA A DIMENS?O DAS MéDIAS ENTRE SI, SUAS DIFEREN?AS PRáTICAS ASSOCIADAS AOS SEUS DESVIOS. NA MINHA PRáTICA ASSOCIO N?O Só O VALOR DO TESTE, MAS TAMBéM A VARIA??O QUE NESSE CASO O VALOR DE p PODE N?O INFLUENCIAR MUITO NA MINHA DECIS?O.

I would like to add that increasing the sample size increases the test power and decreases the type-II error. Type-ll error determines the likelihood of failing to reject a null hypothesis, while in fact should have been rejected with more observations. The lower the error the more certain you are on the inability to reject the null hypothesis. Keep in mind that the null should never be accepted but rather failed to be rejected in statistics.

En plus des valeurs de p, il est souvent utile d'analyser les intervalles de confiance des paramètres d'intérêts. Si possible (dans un contexte bayesien par exemple), la distribution à posteriori des paramètres donne des informations bien plus nuancée qu'une simple valeur de p (probabilité que la valeur du paramètre soit comprise entre deux valeurs, asymétrie de la distribution, extrémités de la distribution, etc.).

ENTENDO QUE A LIMITA??O DE p RESIDE NO FATO DE QUE SER MAIS EXIGENTE OU MENOS, N?O SIGNIFICA QUE ESTá MELHOR OU PIOR. A EXPERIêNCIA NO PROCESSO, SEU CONHECIMENTO TOTAL E SUAS VARIA??ES, NA MINHA OPINI?O, S?O ATé MAIS úTEIS DO QUE ESCOLHER UM VALOR DE p MAIS OU MENOS EXIGENTE.

1- a p value doesn’t indicate if the comparison is justified 2- p value doesn’t talk about whether the statistical test used is appropriate 3- p value threshold being still kept at .05 is always an intresting topic for discussion. It was in fact decided by sir Fisher then basically for agriculture experiments. How relevant it is for other experiments is debatable. 4- p value is dependent on sample size. Larger the sample size, smaller is the value leading us to believe that there could be large departure from Null hypothesis. 5- p value always refers to summary statistics of specific study samples only.

O p-value, apesar de útil, n?o conta toda a história. Gráficos como histograma, boxplot, de quantidades, para a análise, revelando: Distribui??o dos dados (histograma, boxplot) Rela??o entre variáveis (gráfico de quantidades) Validade do modelo (gráfico de resíduos) Compara??o de estudos (forest plot)

As an example of interpreting p values in hypothesis testing, let’s look at clinical RCTs analyzing the treatment arm vs placebo or a standard treatment. Statistical significance does not necessarily translate to clinical significance. Look at the RCTs of antidepressants in children and adolescents, and you will see these issues between statistical and clinical significance often come up, and if not clinically significant, then other considerations of the treatment (ie side effects) take more prominence in clinical decision making, whether or not to proceed with such treatment.

In hypothesis testing, the null hypothesis is assumed to be true to start with. This means that we do not reject the null hypothesis if we fail to find sufficient evidence for the alternative hypothesis. So, we place the burden of proof on those who support the alternative hypothesis. Note that we never 'accept' the null hypothesis, we either 'reject' or 'do not reject' the null hypothesis. This is because lack of evidence to support alternative hypothesis doesn't imply that the null hypothesis is true; it implies that we do not have enough evidence to reject the null hypothesis.