Descriptive statistics

Analytic plan by study approach

1. Studies w/ no comparison group (case series + cross-sectional surveys): simple statistics like counts (frequencies), proportions and averages are sufficient

2. Studies comparing 2+ populations (case-control. cohort, experimental): description must be completed first THEN comparative statistics will be calculated

Variable definition

Not consistent or having fixed pattern, liable to change. Is a characteristic recorded for subjects in a study that can be assigned more than one value.

1. Independent: 1 thing you change in an experiment

2. Dependent: change that happens because of independent variable

3. Controlled: everything that remains constant/unchanged

Quantitative vs Qualitative

1. Qualitative: measures or observations of qualities, types or characteristics often not numbers but in text form.

2. Quantitative: values/counts expressed as numbers and can be compared on numeric scale.

Categorical data

Nominal and ordinal.

Variable that represents characteristics (e.g. gender, language, ethnicity). and can be represented in a dataset by numbers

1. categorical: variable is this if each observation belongs to 1 of a set of categories

2. Nominal: Unordered data representing discrete units + used to label a variable w/ no quantitative value, which also means that it has no natural value/rank (e.g., if you change order of data, meaning of data doesn’t change)

3. Ordinal: discrete units or categories w/ natural order/ranking to it (e.g. elementary > middle school > high school).

Numerical data

Numbers w/ real mathematical meaning

1. discrete: data separated such that this data can only take on certain value, being counted only in whole units (e.g. how many people did you text? cannot respond with 1.5 people)

2. Continuous: opposite of discrete and can be only measured and not counted through some kind of instrument (e.g., how heavy am I? requires scale to record data)

This kind of data can also be described in interval and ratio data:

1. Interval: no true zero (e.g., 0F does not mean that there is no temperature and scale stops), representing values ordered on scale w/ difference b/w any 2 values having meaning.

2. Ratio: holds all properties of interval variable, relating numbers that can be ordered on a scale. Has a TRUE ZERO (e.g., if variable is 0, means that there s none of that variable).

Quantitative vs Categorical

1. Key features of quantitative = center, aka. central tendency (mean, median, mode) + spread (variability), as descriptive statistics are often used to describe the average value of a variable in a population.

   1. Mean = sum of all values divided by number of values (least robust)

   2. Median = value in middle when all values are arranged in ascending order w/ taking both middle values if possible. In b/w mean and mode.

   3. Mode = value appearing most common (most robust)

2. Key features of categorical = % of observations in each category

Measures of spread

Data w/I set spread out/scattered about the mean (e.g., variability, dispersion, scatter). Further distance of data values from center = greater spread, opposite being “small spread”. Used to describe variability and distribution of kinds of data:

1. mini/maximum

2. range

3. quartiles

4. deciles

5. IQR

Can be shown in following graphs:

1. histogram

2. boxplot

3. bar chart

4. pie chart

Normal vs skewed curves, variance and standard deviation

Normal = Histogram showing normal distribution (aka Gaussian distribution) or approx normal distribution of responses/data will have bell shaped curve w/ 1 peak in middle.

Skewed = extend farther from peak on either left or right side of histogram

Three ways quantifying narrowness or wideness of distribution

1. variance

2. standard deviation

   1. Describes narrowness or wideness of range of responses with variables w/ relatively normal distribution. Z-scores indicate how many SD away from sample mean an individual’s response is (e.g., age exactly @ mean age = score of 0. Above mean = 1. Below mean = -2).

3. standard error

Reporting descriptive stats

1. For ratio + interval variables w/ normal distribution = both mean and SD are typically reported

2. ordinal variables = median and IQ range are often reported

3. categorical variables = proportions of participants w/ responses used to describe populations