Experimental Biology: Differences Between Two Groups

These flashcards cover the fundamental concepts of experimental biology statistics, focusing on paired vs. unpaired data, parametric vs. non-parametric tests, and specific statistical analyses like T-tests, Mann-Whitney U, Wilcoxon, and Chi-square tests.

Unpaired Data

Also known as independent data, it refers to separate populations or things measured in parallel.

Paired Data

Also known as dependent data, it occurs when the same populations or things are measured repeatedly, such as an individual or test tube tested before and after chemical exposure.

Parametric Data

Data that is "normally" distributed, characterized by a symmetrical distribution around the mean.

Non-parametric Data

Data that is not symmetrically distributed around the mean (skewed) or data for which there is not enough information to assume a normal distribution.

T-test

A commonly used parametric test used to compare two means by evaluating whether the difference between groups is larger than what would be expected from sampling variation alone.

Direct requirements for T-test

The dependent variable must be continuous and approximately normally distributed, and the variances must be homogeneously distributed.

Independent Two-Sample T-test

An unpaired test version that compares the means of two entirely separate groups, such as a treatment group versus a control group.

Paired T-test

A test version that compares means from the same group at two different times, such as "Before" versus "After" an intervention.

T-value

The ratio between the difference of means versus the variation in the groups used to determine if a difference is substantial compared to natural variation.

Standard Error calculation (Transcript)

The variation used in t-test calculations, represented in the notes as $SE = \frac{SD}{n}$.

Rejecting the Null Hypothesis

Occurs when the derived $p$-value is $< 0.05$, indicating there is likely a real difference between groups.

Mann-Whitney U test

A non-parametric test equivalent to the unpaired t-test that compares "rank sums" and medians rather than means.

U-values

Values calculated from rank sums $T1$ and $T2$ during a Mann-Whitney U test.

Z-value

A calculated value using standard deviation and number of samples; a value close to zero indicates consistency with the null hypothesis, while a value far from zero suggests a significant difference.

Wilcoxon signed ranks test

The non-parametric version of a paired t-test based on the ranks of the paired differences.

Wilcoxon Rank Statistic ($W$)

A value obtained from the minimum of the positive or negative rank sums in a Wilcoxon signed ranks test.

Chi-square test ($\text{X}^2$)

A non-parametric test used to determine if there is a relationship between two categorical variables by comparing actual frequencies to expected frequencies.

Contingency table

A table used in a Chi-square test to display categorical variable data before converting it to an expected frequency table.

Degrees of freedom ($Df$)

For a Chi-square test, it is calculated as $(no.\text{ of rows} - 1) \times (no.\text{ of columns} - 1)$.

Standard Deviation

The square root of the variance; a measure of dispersion showing how far apart values in a dataset are from the mean.

Standard Error of the Mean

A measure of sampling error that describes how accurately the mean of a sample distribution represents the mean of the population.