KIN6005 Statistical Analysis Studio

Credits & citation

Created by Jacob Goodin, PhD, Goodin Performance, for KIN6005 statistical analysis education.

Software implementation was assisted by OpenAI Codex. Visualizations use D3; the interface uses React. Example datasets are synthetic unless you upload your own data.

Cite this studio

Goodin, J. (2026). KIN6005 statistical analysis studio [Computer software]. Goodin Performance. https://stats.plnusportscience.com/

Suggested in-text citation: (Goodin, 2026). Add your access date when your assignment requires it. Describe the specific analysis and its assumptions in your methods section.

Methods and reporting

The question-mark buttons, assumptions sections, and APA reporting guides explain the methods and limits of each analysis.

APA reporting guide

Use the results as parts of a report. Explain the study design, variables, units, missing data, and assumptions. Include effect estimates and confidence intervals where available. Do not invent an interval that this tool does not estimate.

Regression and ANCOVA. Report model terms, reference categories, centering, N, b, SE, confidence intervals, t(df), p, and R². Explain which covariates are held fixed in plots.

Repeated-measures ANOVA. Report participant count and occasions. Give F with both df, Greenhouse–Geisser ε, corrected df and p, and the named effect size.

Mixed models. Describe fixed and random effects, REML estimation, participant and observation counts, b/SE/CI, Wald z and p, variance components, and convergence. These intervals use a normal approximation.

Report exact p values to three decimals, or p < .001. Omit leading zeros for probabilities and correlations. Use italics for Latin statistical symbols; keep Greek symbols upright. Precision should suit the measurement scale.

APA numbers and statistics guide · APA reporting standards

Model data

Source: Simulated teaching data (draw 941). This analysis uses 48 of 48 rows; Excluded rows: 0 (unselected groups or missing/invalid selected values).

Inspect input rows

First 12 rows (before exclusions)

First 12 rows (before exclusions)
outcomex1x2
43.79728092917411423.21237612115822224.545706142795233
38.00206845908165616.62504194989376716.564575046310342
38.06723474773746618.08212139874618518.484461372351447
43.7544316695013722.53575000029930626.39471256481898
42.879475742619915.57103947814657417.991751409513277
43.6377286734008718.9452565868429317.735632317160984
37.6790961420793626.3559766342314625.319323883138708
41.1805261912144621.81760855396140623.53111551801241
37.5643747230760215.80417951588849618.428615889438618
43.5648853404881718.33741822073820822.906370239469652
51.7856559849087927.094426540477724.90295208123971
52.47147240787716524.12261258160650728.513659605796175

Numeric predictors are centered at their observed means. The first selected variable is the primary predictor: x1. Adjustment does not establish causation.

Adjusted estimates

Overall linear model: F(2, 45) = 14.42, p < .001; R² = .39; N = 48. Coefficient intervals use 95% confidence.

Coefficient tests use residual df = 45. N = 48. Numeric predictors are centered; coefficients and intervals are in original outcome units per predictor unit.

95% coefficient intervals

95% coefficient intervals
TermEstimateSEtpLowerUpper
Intercept42.370.6565.04< .00141.0643.68
x1 (centered)0.610.232.64.0110.141.07
x2 (centered)0.410.211.93.060-0.020.83
R²
.39
Adjusted R²
.36
Residual SD
4.51
Unadjusted primary slope
0.89

Try this: Add another predictor or group term. Compare the primary slope before and after adjustment.

Explain what happens

The adjusted slope describes an association at fixed values of other included predictors. A change does not, by itself, identify the reason or prove that confounding has been removed.

Assumptions and method

Independent errors, appropriate functional form, constant error variance, and normally distributed errors for exact small-sample t/F inference. Numeric predictors are centered. ANCOVA additionally needs meaningful overlap between groups; a group-by-covariate interaction relaxes a common-slope model.

Read the method reference

Prediction and uncertainty

Predict at x1
Predict at x2
Conditional fitted curve; dashed inner lines are mean intervals and outer lines are prediction intervals304050152025Conditional meanMean CI lowerMean CI upperPrediction lowerPrediction upperObserved 23.212376121158222, 43.797280929174114Observed 16.625041949893767, 38.002068459081656Observed 18.082121398746185, 38.067234747737466Observed 22.535750000299306, 43.75443166950137Observed 15.571039478146574, 42.8794757426199Observed 18.94525658684293, 43.63772867340087Observed 26.35597663423146, 37.67909614207936Observed 21.817608553961406, 41.18052619121446Observed 15.804179515888496, 37.56437472307602Observed 18.337418220738208, 43.56488534048817Observed 27.0944265404777, 51.78565598490879Observed 24.122612581606507, 52.471472407877165Observed 23.652491200589147, 35.45629083767725Observed 15.99499638833488, 38.29740589260025Observed 25.840266509298523, 39.84336542433921Observed 17.50526176636708, 39.06084013487773Observed 16.81738038130621, 38.64771164160845Observed 19.729200957716102, 46.49867229551402Observed 14.730283790347002, 33.37733567752365Observed 19.882134780286833, 47.48031377449445Observed 20.520638365494097, 40.02960155693196Observed 22.304360333728685, 46.518254689741916Observed 15.653530388209575, 32.96462919110313Observed 21.30708059430355, 38.917924010119684Observed 22.873221948201444, 46.06203139033985Observed 16.222697848325353, 42.206817123152376Observed 26.591353987715358, 55.88389360340615Observed 20.273469030294308, 39.49531327566164Observed 21.60813473099372, 47.5250434366397Observed 21.660304621784565, 44.70651763953483Observed 21.064392266298853, 51.74701577342654Observed 21.74970380590032, 41.56466536228824Observed 12.507824249453527, 38.67947083877422Observed 11.860958672041138, 34.16335314026739Observed 17.6783211666871, 46.1519099137246Observed 11.67063293600115, 35.078394394518405Observed 23.9608564003394, 51.51135552213994Observed 21.697092619412082, 48.88107613575055Observed 18.885279266907276, 32.48787354861837Observed 21.982748174101076, 46.157000708168916Observed 19.33079737513183, 47.023034111440346Observed 20.271247740702336, 51.91905609852795Observed 17.311453122922856, 39.157903629134715Observed 22.23063609809188, 41.94111600742514Observed 15.658691708408256, 36.72896930185786Observed 19.35638862045902, 38.87133445586468Observed 20.149163037951464, 41.73923277829905Observed 21.613869008517092, 42.494994299371456x1outcome

Horizontal: x1. Vertical: outcome.

Conditional fitted curve; dashed inner lines are mean intervals and outer lines are prediction intervals
  • Conditional mean
  • Mean CI lower (dashed)
  • Mean CI upper (dashed)
  • Prediction lower (dashed)
  • Prediction upper (dashed)
Export APA PNG

The export uses your selected graph colors and Arial, with 10-point graph labels and an 11-point caption at 6.5 inches wide (300 dpi). Check variable units, title case, and the note before downloading. Custom captions persist until you reset them.

Transparent exports keep dark text and are intended for light backgrounds. Grayscale removes color from the entire figure, including the legend. Check group labels and line styles.

Turn this off if you will add the caption in your manuscript. Match your manuscript’s figure numbering and caption font. A figure does not replace a complete statistical report.

Points show raw observed outcomes with varying covariates. The curve holds other covariates fixed at the values above.

Selected prediction

Selected prediction
EstimateMean lowerMean upperPrediction lowerPrediction upper
42.3741.0643.6833.1851.55

Model diagnostics

Residuals versus fitted values−10−505103540455045.97, -2.1738.73, -0.7340.39, -2.3346.31, -2.5638.67, 4.2140.61, 3.0348.19, -10.5144.71, -3.5338.99, -1.4242.34, 1.2248.47, 3.3148.13, 4.3444.66, -9.2039.89, -1.5949.74, -9.8938.84, 0.2239.94, -1.2943.68, 2.8136.92, -3.5443.68, 3.8040.49, -0.4644.30, 2.2239.38, -6.4144.89, -5.9744.75, 1.3140.79, 1.4247.39, 8.4942.72, -3.2345.26, 2.2743.84, 0.8743.74, 8.0040.81, 0.7637.81, 0.8733.93, 0.2442.71, 3.4435.21, -0.1347.22, 4.2942.63, 6.2541.18, -8.6943.84, 2.3142.02, 5.0043.72, 8.2041.41, -2.2543.39, -1.4536.22, 0.5141.03, -2.1641.26, 0.4842.88, -0.38Fitted outcomeResidual

Horizontal: Fitted outcome. Vertical: Residual.

Residuals versus fitted values
Export APA PNG

The export uses your selected graph colors and Arial, with 10-point graph labels and an 11-point caption at 6.5 inches wide (300 dpi). Check variable units, title case, and the note before downloading. Custom captions persist until you reset them.

Transparent exports keep dark text and are intended for light backgrounds. Grayscale removes color from the entire figure, including the legend. Check group labels and line styles.

Turn this off if you will add the caption in your manuscript. Match your manuscript’s figure numbering and caption font. A figure does not replace a complete statistical report.

Normal Q–Q plot of internally standardized residuals−202−3−2−10123Normal reference-2.31, -2.44-1.86, -2.35-1.62, -2.10-1.45, -1.95-1.32, -1.46-1.20, -1.35-1.10, -0.82-1.01, -0.79-0.93, -0.72-0.85, -0.58-0.78, -0.52-0.71, -0.51-0.64, -0.49-0.58, -0.49-0.52, -0.36-0.46, -0.33-0.40, -0.32-0.35, -0.29-0.29, -0.16-0.24, -0.11-0.18, -0.09-0.13, -0.03-0.08, 0.05-0.03, 0.060.03, 0.110.08, 0.120.13, 0.180.18, 0.200.24, 0.210.29, 0.280.35, 0.300.40, 0.330.46, 0.500.52, 0.510.58, 0.520.64, 0.640.71, 0.680.78, 0.780.85, 0.800.93, 0.861.01, 0.961.10, 0.981.20, 1.011.32, 1.121.45, 1.421.62, 1.801.86, 1.852.31, 1.99Theoretical normal quantileStandardized residual

Horizontal: Theoretical normal quantile. Vertical: Standardized residual.

Normal Q–Q plot of internally standardized residuals
Export APA PNG

The export uses your selected graph colors and Arial, with 10-point graph labels and an 11-point caption at 6.5 inches wide (300 dpi). Check variable units, title case, and the note before downloading. Custom captions persist until you reset them.

Transparent exports keep dark text and are intended for light backgrounds. Grayscale removes color from the entire figure, including the legend. Check group labels and line styles.

Turn this off if you will add the caption in your manuscript. Match your manuscript’s figure numbering and caption font. A figure does not replace a complete statistical report.

Cook’s distance by complete-case row; reference is 4/n0.00.10.20.3010203040501.00, 0.002.00, 0.003.00, 0.004.00, 0.015.00, 0.026.00, 0.017.00, 0.198.00, 0.019.00, 0.0010.00, 0.0011.00, 0.0212.00, 0.0413.00, 0.1014.00, 0.0015.00, 0.2716.00, 0.0017.00, 0.0018.00, 0.0119.00, 0.0220.00, 0.0121.00, 0.0022.00, 0.0023.00, 0.0424.00, 0.0325.00, 0.0026.00, 0.0027.00, 0.1628.00, 0.0029.00, 0.0030.00, 0.0031.00, 0.0332.00, 0.0033.00, 0.0034.00, 0.0035.00, 0.0236.00, 0.0037.00, 0.0238.00, 0.0439.00, 0.0340.00, 0.0041.00, 0.0142.00, 0.0443.00, 0.0044.00, 0.0045.00, 0.0046.00, 0.0047.00, 0.0048.00, 0.00Complete-case rowCook’s distance

Horizontal: Complete-case row. Vertical: Cook’s distance.

Cook’s distance by complete-case row; reference is 4/n
Export APA PNG

The export uses your selected graph colors and Arial, with 10-point graph labels and an 11-point caption at 6.5 inches wide (300 dpi). Check variable units, title case, and the note before downloading. Custom captions persist until you reset them.

Transparent exports keep dark text and are intended for light backgrounds. Grayscale removes color from the entire figure, including the legend. Check group labels and line styles.

Turn this off if you will add the caption in your manuscript. Match your manuscript’s figure numbering and caption font. A figure does not replace a complete statistical report.

Variance inflation factors (design columns)

Variance inflation factors (design columns)
TermVIF
x1 (centered)1.68
x2 (centered)1.68

Five most influential observations

Five most influential observations
Complete-case rowLeverageCook’s DStandardized residual
150.130.27-2.35
70.090.19-2.44
270.110.161.99
130.060.10-2.10
230.050.04-1.46

Try this: Look for curvature or increasing spread in the residual plot, tail departures in Q–Q, and unusually influential rows.

Explain what happens

These patterns can suggest misspecification, unequal variance, unusual observations, or dependence. Check the study and data before changing the model or removing observations. High VIF describes imprecision from predictor overlap, not bias by itself.

Assumptions and method

Residual plots cannot prove independence or establish a correct causal model. Cook's D and VIF thresholds are screening aids. Confidence intervals above use ordinary homoscedastic covariance; robust alternatives are not silently substituted.

Read the method reference