9.5: Pause and Process Check, Pulling P Values and Effect Sizes Together
- Page ID
- 50684
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Let us pause and do a process check on our inventory of questions and possible responses when making decisions about statistical test results. You should consider your effect size as a complementary piece of information with the p value. Here is a suggested order of questions and a list of simple answers when interpreting statistical test results. Remember, the KISS method – “keep it simple, silly.”
- Does the statistical test result indicate significance? Your response choices are yes or no
- If the answer is no, then there is no need to complete the remaining steps.
- If the answer to the question is yes, then you ask what the pattern is.
- There are only two patterns.
- Pattern one is - finding differences among groups.
- The statistical test for this pattern is usually a t-test or an F-test.
- The possible pattern is that Group A is higher / lower than Group B
- Pattern two is - finding associations among variables.
- The statistical tests are correlations or regressions.
- As Variable X increases, Variable Y increases / decreases
- If significant, are these findings or these patterns expected or unexpected, given the context of the research question? Your response choices are yes or no.
- If significant, what is the effect size? Your response choices are low, medium, and high.
- If not significant, there is no pattern
- If there is no pattern, Group A is like Group B, or
- If there is no pattern, we say there is no relationship between Variables X and Y.
- And there is no effect size. Is there no finding of a pattern that is expected or unexpected, given the context of the research question?
After you go through those decisions, the complementary question is, are these statistical results valid? That question entails examining statistical information and research design.
For the statistical information, you could consider these factors.
- Sample size. Is the sample size too low or too high? A sample size that is too low might be unstable in its estimates of statistical significance. A sample size that is too high, coupled with a significant effect, might yield a Type I error. Both scenarios cast doubt on the stability of the statistically significant finding.
- Sampling error. Are the means too high or too low? Sampling errors always occur, resulting in a sample mean that is too high or too low compared to the population mean. There is no way to gauge this issue because there is no population answer key about what the population mean should be. When you interpret the means, do they seem too high or too low compared to your theoretical understanding of what the means should be?
- The quality of the distribution of the variables. Normal distribution increases confidence in the results. Skewed distributions do not. However, some variables are meant to have skewed distributions. The question is whether the skewness is severe enough to warrant a different statistical analysis, such as a non-parametric analysis. More on that later.