statistical significance

Examples of statistical significance in the following topics:

• Tests of Significance

  • In relation to Fisher, statistical significance is a statistical assessment of whether observations reflect a pattern rather than just chance.
  • The statistical significance of the results depends on criteria set up by the researcher beforehand.
  • $P$-values smaller than, or equal to, the threshold are considered statistically significant and interpreted accordingly.
  • Assuming a conventional 5% level of significance ($\text{sig} \leq 0.05$), all tests are, thus, statistically significant.
  • Examine the idea of statistical significance and the fundamentals behind the corresponding tests.

• Was the Result Important?

  • Statistical significance is a statistical assessment of whether observations reflect a pattern rather than just chance.
  • When used in statistics, the word significant does not mean important or meaningful, as it does in everyday speech; with sufficient data, a statistically significant result may be very small in magnitude.
  • Such results are informally referred to as 'statistically significant (at the $p=0.05$ level, etc.)'.
  • The difference in this case is statistically significant at a certain level, but not important.
  • Distinguish the difference between the terms 'significance' and 'importance' in statistical assessments

• Statistical significance versus practical significance

  • While we still say that difference is statistically significant, it might not be practically significant.
  • Statistically significant differences are sometimes so minor that they are not practically relevant.

• Was the Result Significant?

  • Statistical significance is a statistical assessment of whether observations reflect a pattern rather than just chance.
  • When used in statistics, the word significant does not mean important or meaningful, as it does in everyday speech; with sufficient data, a statistically significant result may be very small in magnitude.
  • The result may therefore be considered statistically significant evidence that the coins are not fair.
  • The calculated statistical significance of a result is in principle only valid if the hypothesis was specified before any data were examined.
  • Such results are informally referred to as 'statistically significant (at the p = 0.05 level, etc.)'.

• Significance Testing

  • When the null hypothesis is rejected, the effect is said to be statistically significant.
  • Therefore, the effect of obesity is statistically significant and the null hypothesis that obesity makes no difference is rejected.
  • Do not confuse statistical significance with practical significance.
  • Why does the word "significant" in the phrase "statistically significant" mean something so different from other uses of the word?
  • Thus, finding that an effect is statistically significant signifies that the effect is real and not due to chance.

• Statistical Literacy

  • However, the evidence for the existence of the particle was not statistically significant.
  • One of the investigators stated, "We see some tantalizing evidence but not significant enough to make a stronger statement. " Therefore, they were encouraged by the result.
  • In a subsequent study, the evidence was significant.

• Creating a Hypothesis Test

  • Set up or assume a statistical null hypothesis ($H_0$).
  • $H_0$: It will not be possible to infer any statistically significant mean differences between the treatment and the control groups.
  • $p$-values are considered statistically significant if they are equal to or smaller than the chosen significance level.
  • If results are accepted as statistically significant, it can be inferred that the null hypothesis is not explanatory enough for the observed data.
  • All test statistics and associated exact $p$-values can be reported as descriptive statistics, independently of whether they are statistically significant or not.

• Significance Levels

  • A fixed number, most often 0.05, is referred to as a significance level or level of significance.
  • Such results are informally referred to as statistically significant (at the $p=0.05$ level, etc.).
  • For example, if someone argues that "there's only one chance in a thousand this could have happened by coincidence", a 0.001 level of statistical significance is being stated.
  • In some situations, it is convenient to express the complementary statistical significance (so 0.95 instead of 0.05), which corresponds to a quantile of the test statistic.
  • In general, when interpreting a stated significance, one must be careful to make precise note of what is being tested statistically.

• Elements of a Hypothesis Test

  • The lady correctly identified every cup, which would be considered a statistically significant result.
  • In statistics, a result is called statistically significant if it has been predicted as unlikely to have occurred by chance alone, according to a pre-determined threshold probability—the significance level.
  • Statistical hypothesis testing is a key technique of frequentist inference.
  • Select a significance level ($\alpha$), a probability threshold below which the null hypothesis will be rejected.
  • The decision rule is to reject the null hypothesis if and only if the $p$-value is less than the significance level (the selected probability) threshold.

• Inferential Statistics

  • In statistics, statistical inference is the process of drawing conclusions from data that is subject to random variation--for example, observational errors or sampling variation.
  • More substantially, the terms statistical inference, statistical induction, and inferential statistics are used to describe systems of procedures that can be used to draw conclusions from data sets arising from systems affected by random variation, such as observational errors, random sampling, or random experimentation.
  • Inferential statistics are based on the assumption that sampling is random.
  • Furthermore, when generalizing a trend found in a sample to the larger population, statisticians uses tests of significance (such as the Chi-Square test or the T-test).
  • Discuss how inferential statistics allows us to draw conclusions about a population from a random sample and corresponding tests of significance.