Krzywinski, Martin; Altman, Naomi (30 October 2013). "Points of significance: Significance, P values and t-tests". Nature Methods. 10 (11): 1041–1042. doi: 10.1038/nmeth.2698. PMID 24344377. That’s why APA guidelines advise reporting not only p values but also effect sizes and confidence intervals wherever possible to show the real world implications of a research outcome. Other types of significance in research

Poletiek, Fenna H. (2001). "Formal theories of testing". Hypothesis-testing Behaviour. Essays in Cognitive Psychology (1sted.). East Sussex, United Kingdom: Psychology Press. pp.29–48. ISBN 978-1-841-69159-6. García-Pérez, Miguel A. (2016-10-05). "Thou Shalt Not Bear False Witness Against Null Hypothesis Significance Testing". Educational and Psychological Measurement. 77 (4): 631–662. doi: 10.1177/0013164416668232. ISSN 0013-1644. PMC 5991793. PMID 30034024. Brian, Éric; Jaisson, Marie (2007). "Physico-Theology and Mathematics (1710–1794)". The Descent of Human Sex Ratio at Birth. Springer Science & Business Media. pp.1–25. ISBN 978-1-4020-6036-6. Fisher, Ronald A. (1925). Statistical Methods for Research Workers. Edinburgh, UK: Oliver and Boyd. pp. 43. ISBN 978-0-050-02170-5. Neyman, J.; Pearson, E.S. (1933). "The testing of statistical hypotheses in relation to probabilities a priori". Mathematical Proceedings of the Cambridge Philosophical Society. 29 (4): 492–510. Bibcode: 1933PCPS...29..492N. doi: 10.1017/S030500410001152X. S2CID 119855116.Usually, the significance level is set to 0.05 or 5%. That means your results must have a 5% or lower chance of occurring under the null hypothesis to be considered statistically significant. Clarke, GM; Anderson, CA; Pettersson, FH; Cardon, LR; Morris, AP; Zondervan, KT (February 6, 2011). "Basic statistical analysis in genetic case-control studies". Nature Protocols. 6 (2): 121–33. doi: 10.1038/nprot.2010.182. PMC 3154648. PMID 21293453.

Babbie, Earl R. (2013). "The logic of sampling". The Practice of Social Research (13thed.). Belmont, CA: Cengage Learning. pp.185–226. ISBN 978-1-133-04979-1. a t value (the test statistic) that tells you how much the sample data differs from the null hypothesis, Main articles: Statistical hypothesis testing, Null hypothesis, Alternative hypothesis, p-value, and Type I and type II errors In a two-tailed test, the rejection region for a significance level of α = 0.05 is partitioned to both ends of the sampling distribution and makes up 5% of the area under the curve (white areas). Sprent, P. (1989), Applied Nonparametric Statistical Methods (Seconded.), Chapman & Hall, ISBN 978-0-412-44980-2

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To begin, research predictions are rephrased into two main hypotheses: the null and alternative hypothesis. a b c Sirkin, R. Mark (2005). "Two-sample t tests". Statistics for the Social Sciences (3rded.). Thousand Oaks, CA: SAGE Publications, Inc. pp.271–316. ISBN 978-1-412-90546-6.

Next, you perform a t test to see whether actively smiling leads to more happiness. Using the difference in average happiness between the two groups, you calculate: In statistical hypothesis testing, [1] [2] a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. [3] More precisely, a study's defined significance level, denoted by α {\displaystyle \alpha } , is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; [4] and the p-value of a result, p {\displaystyle p} , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. [5] The result is statistically significant, by the standards of the study, when p ≤ α {\displaystyle p\leq \alpha } . [6] [7] [8] [9] [10] [11] [12] The significance level for a study is chosen before data collection, and is typically set to 5% [13] or much lower—depending on the field of study. [14]a b c Wasserstein, Ronald L.; Lazar, Nicole A. (2016-04-02). "The ASA's Statement on p-Values: Context, Process, and Purpose". The American Statistician. 70 (2): 129–133. doi: 10.1080/00031305.2016.1154108.