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Probability and Significance

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Probability and Significance

What are probability and significance in psychology? What role do they play in research? We dig into both theory and methodology, as well as examples of significance tests and probability, in the hopes of bringing these seemingly abstract concepts to life.

Significance tests are commonly used in psychological research to determine whether differences between groups could be due to chance. The results of the tests (inferential statistical data) determine whether to reject the null hypothesis.

Significance tests and probability

Significance tests give researchers a statistical value to measure how likely the research results are due to chance. Another word for this is the alpha level. In psychology, this is written as.

Significance and probability explained

Researchers have a consensus about what alpha level is acceptable, which is 0.05. If the significance value is too high, the alternative hypothesis cannot be accepted. The significance value is a quantitative value that tells the researcher and readers how likely the results are due to chance.

Chance refers to the data being due to the relationship between the independent and dependent variables and not due to extraneous or confounding variables.

A significance value of 0.05 means a 95% probability that the results are not due to chance.

Researchers cannot determine 100% that their results are due to the variables they are studying. This is because researchers cannot control for every factor (that is not the independent variable) that might affect the dependent variable and, therefore, the experiment results.

The significance values that are commonly used in research are:

  • 0.05 - 5% chance results are due to chance.
  • 0.01 - 1% chance: results are due to chance.
  • 0.001 - 0.01% chance results are due to chance.

Researchers must also decide whether to use a one-tailed or two-tailed test when conducting a statistical test. It depends on the research hypothesis.

  • One-tailed: you have determined the independent variable's specific effect on the dependent variable. (The hypothesis is only in one direction).
  • Two-tailed: You believe that the independent variable affects the dependent variable, but you are not sure how significant that effect is.

How are significance tests used in psychology research?

Whenever researchers use inferential statistics, they do significance testing. As a result, the researcher can determine if the results can be generalised to the target population. Researchers can also determine if their research needs to be revised, such as the procedure used.

Significance test and hypotheses

Hypotheses:

  • Alternative The observed results are due to the independent and dependent variables' interaction. If this is the case, we should find a significant p-value.

  • Null The results are not due to the independent variable but to chance. If this is the case, we should find a non-significant p-value.

Acceptance of:

  • The alternative hypothesis is accepted if a value is found at or below the significance level.

  • The null hypothesis is accepted if a value above the significance level is found.

Rejection of:

  • The alternative hypothesis is rejected if a value above the significance level is found.

  • The null hypothesis is rejected if a value at or below the significance level is found.

Type 1 and Type 2 errors

A Type 1 error is when we incorrectly reject the null hypothesis when it is in fact true. If the significance level is at 0.05, this means there is a 5% chance of a Type 1 error. A Type 2 error is when we incorrectly reject the alternative hypothesis when it is true.

Significance tests and methodology

Occasionally, non-significant results are due to problems with the methodology used. Significant results can be found once these have been corrected and the experiment retested.

Suppose a research design does not use a standardised protocol. In that case, the results may reflect the conditions under which the participants were experimented on and, therefore, are likely due to chance. The researcher must repeat the experiment but use a standardised procedure to counteract this.

Reporting of significance tests

  • p = significance value.

  • < = the significance value is less than the number reported (e.g. < 0.05 = significance is less than 0.05).

  • > = the significance value is greater than the number reported (e.g. > 0.05 = significance is greater than 0.05).

Significance tests and inferential statistics

The inferential statistic is a quantitative statistical value that measures the data collected. It can be used to make generalisations about the target population.

If a significant value is found, the inferential statistic can be used to make inferences about the target population supported by evidence. However, if this is not the case, the study should not make inferences about the target population.

If a non-significant value is not found, it does not mean that there is no relationship/interaction between the independent and dependent variables. Instead, it means that other variables are also influencing the dependent variable. Therefore the study cannot provide an accurate (reliable or valid) measure of the interaction between the independent and dependent variables.

An example of a significance level for a correlation analysis that would be accepted is:

r (56) = .63, p = <.05

This example shows:

  • A correlational analysis was performed (r).

  • A positive correlation was found (.63).

  • There were 56 participants (56).

  • The significance value was accepted because the significance value is below the accepted alpha value of 0.05.

  • The alternative hypothesis should be accepted.

r (56) = .63, p = < .08

This example shows:

  • The significance value is non-significant as it is above .05.

  • The null hypothesis should be accepted.

Probability and Significance - Key takeaways

  • Significance tests are commonly used in psychological research to determine whether differences between groups could be due to chance. The results of the tests (inferential statistical data) determine whether to reject the null hypothesis.
  • Significance tests give researchers a statistical value to measure how likely the research results are due to chance.
  • There is a consensus among researchers as to what level of significance is acceptable, 0.05.
    • This value can be converted to a percentage of 5%, which means that there is a 5% chance that the results are due to chance.
  • If a significant inferential statistic is found, the researcher can use their data to make inferences about the target population.

Frequently Asked Questions about Probability and Significance

If less than a 5% probability (0.05 significant value) is found, the probability is significant.

No, the significance value is a number used in psychology to measure probability. The significance value used in psychology is 0.05, so if we get that value in our results, there is a 5% probability that the results occurred by chance, and we can reject the null hypothesis. 

The significance value is an element of probability. It tells us the probability of how confidently the researchers can accept or reject the research hypothesis. 

If a significance value of 0.05 is found, there is a 95% chance the results are not due to chance.

Significance tests are used in psychology research to determine if the differences between groups could be due to chance. The results of the tests (inferential statistical data) determine whether to reject the null hypothesis. If a significance value of 0.05 is found then it can be assumed that the data is statistically significant.

Final Probability and Significance Quiz

Question

What does a .05 significance value indicate?

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Answer

If a significance value of 0.05 is found then this means that there is a 95% chance the results are not due to chance or a Type 1 error.

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Question

Which of the following is a Type 1 error?

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Answer

Reject the null hypothesis when it is true.

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Question

What is a significance test?

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Answer

Significance tests are frequently used in psychology research to determine the probability of the results (inferential statistical data) rejecting the null hypothesis when it is true (Type 1 error).

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Question

How is the significance value reported in research?

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Answer

p

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Question

What is another name for the significance value?

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Answer

Alpha value.

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Question

What should the researcher do if the significance value is measured as, < .08?

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Answer

Accept the alternative hypothesis.

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Question

What should the researcher do if the significance value is measured as, < .03?

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Answer

Accept the alternative hypothesis.

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Question

If a non-significant result is found, does no relationship between the independent and dependent variables exist? 

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Answer

No.

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Question

Correlational research on 56 people found a .63 positive relationship between time spent studying and exam results. The significance value was .05. How would this be reported? 

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Answer

r (56) = .63, p <.05

Show question

Question

Correlational research carried out on 56 people found a .63 positive relationship between time spent studying and exam results, the significance value was found to be .08. How would this be reported?

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Answer

r (56) = .63, p < .08 (n.s)

Show question

Question

What can researchers infer about their data when a significant value is found?

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Answer

If a significant value is found, the inferential statistic can be used to make inferences the evidence supports concerning the target population.

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Question

What can researchers infer about their data when an insignificant value is found? 

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Answer

The research should not make inferences about the target population.

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Question

What is a factor that can contribute to insignificant findings?

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Answer

Occasionally, non-significant results are due to issues with the methodology used.

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Question

How are statistical significance and probability related?

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Answer

The significance value tells us the probability of how confidently the researchers can accept or reject the research hypothesis. For psychology, the significance value is 0.05.

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Question

What is the consensus of the acceptable statistical value in research?

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Answer

Researchers have a consensus about what alpha level is acceptable, which is 0.05.

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