Exploring One–Variable Data

Chi-squared test statistic

Pearson's correlation coefficient

Scatterplot slope

Spearman's rank correlation coefficient

Left-skewed distribution

Uniform-distribution

Right-skewed distribution

Bimodal-distribution

Increased cognitive load or complexity associated with specific stimuli enhances response diversity amongst participants therewith inflating variance.

Variance discrepancies merely result from flawed measurement tools leading inconsistent readings rather than true group disparities.

Presence of external factors affecting participant concentration during particular trials causes sporadic outcome variations hence greater variances.

Response variation remains constant across all stimuli so observed difference should be attributed solely sampling error.

Larger samples always yield more accurate standard deviations hence any similarity indicates underestimation in small samples' variability measure.

Sample size does not inherently affect standard deviation calculation; similarity suggests comparable population variability despite different sample sizes.

Similarity insinuates that both populations might not actually be distinct given parallel dispersion around each respective mean value point estimator-wise.

The smaller sample must have less intrinsic variability which compensates for estimation errors due to lower N count.

Median

Interquartile range

Standard deviation

Mean

The data points are closely clustered around the mean.

The sample size must be small.

There is no relationship between standard deviation and mean.

The data points are widely scattered from the mean.

The dataset with the larger range has greater variability.

Variability cannot be inferred from range differences alone without standard deviation information.

The dataset with the smaller range has greater variability.

Both datasets have equal variabilities since their means are similar.

Pie chart

Histogram

Scatterplot

Bar chart

The probability that either event A occurs or event B occurs or both occur.

The combined probabilities that events A and B will both occur simultaneously.

The ratio between the probabilities that neither event A nor event B will occur over their joint occurrence.

The difference in probabilities between event A's occurrence and event B's non-occurrence.

Differences varaince cannot interpreted from shape histogram alone

Both look identical due having same center measure

The one higher variance must also have greater right skewness

One will appear more spread out than other due differences variability