8.2: Statistical Decision - Is a Result Significant or Not Significant?
- Page ID
- 50672
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The following is a framework for what significance means.
- A result is not significant if:
- It occurs frequently and has a high probability of occurring,
- It is common
- It is not interesting
- It is boring
- It is random; this result likely occurred by random chance. Nothing happened.
- A result is significant if:
- It does not frequently occur and has a low probability of occurring
- It is not common
- It is interesting
- It is not boring
- It is not random; this result likely did not occur by chance. Something happened.
Yes, it is safe to say that we want significant results. We would like to think that if we have an interesting result, that something is going on that is responsible for the result that we observe. Usually, something is a treatment effect – for example, our treatment led to this positive clinical outcome. Or that something is an important variable that is associated with a clinical concern – for example, increases in the number of racist experiences are associated with severe depression symptoms.
There are plenty of times when we do not want significant results. Sometimes, we do not want significant results as part of a research design to establish equivalency. For example, when comparing a new treatment to an established treatment, we want the client demographics in both treatment groups to be the same. We want the number of males and females to be equal in both groups, equal in average age, income, and education levels. The reason is so one group is not imbalanced or favors one demographic that might have a role in the treatment outcome. We want everything to be the same in both groups, meaning we want to see non-significant results, or equivalency, between the two groups.
We do not want significant results when we want things to be similar. This scenario depends on the research question. Sometimes, you want conditions to be equivalent. For example, the idea that talk therapy is just as effective as medication. In this scenario, it would be good to establish that talk therapy produces outcomes similar to those of medication. In a climate where we medicate all mental health issues, it is worthwhile to demonstrate that talk therapy is an alternative to medication.
Sometimes, you want to have no relationship between variables. For example, an increase in self-esteem is not associated with a decrease in alcohol use. That might be a helpful finding because feeling better about yourself does not mean you are engaging in behaviors to decrease your alcohol use. Another example is finding no relationship between parenting styles and ADHD. That might be a helpful finding because it will relieve the blame parents experience if they think their parenting style resulted in their child having ADHD. The point is always about conceptualizing the issue. Always think conceptually to determine if non-significant results are helpful.