statistical significance

(noun)

A measure of how unlikely it is that a result has occurred by chance.

Related Terms

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.

  • Understanding Statistics

    • Statistics can be a powerful tool in public speaking if the speaker appropriately explains their use and significance.
    • Before a set of statistics can be used, however, it must be made understandable by people who are not familiar with statistics.
    • Use statistics that are easily understood.
    • Presenting findings from research, including determining which variables are statistically significant and meaningful to the results of the research.
    • This will likely use more complicated statistics.

  • APA: Reporting Statistics

    • Because papers using APA style often report experimental data, you must be able to discuss statistics in your paper.
    • To place the focus on the meaning of your statistical tests and their relevance to your overall argument, you should summarize each statistical relationship in clear, plain English.
    • Also, include the important values in parentheses, and the test information and significance at the end of the sentence.
    • This difference was significant; a t-test found a t-score of 2.34, and the p-value was 0.01.
    • This figure shows the proper way to report statistics in an APA-style paper.