Week 2 - data wrangling

characteristics that differ among individuals or other sampling units.

Categorical variables: qualitative characteristics of individuals that do not have magnitude on a numerical scale. Nominal - no order Ordinal - can be ordered (letter grades)

Numerical data: quantitative measurements that have magnitude on a numerical scale. Continuous Discrete

Explanatory variable: independent variable Response variable: dependent variable

the number of times each variable occurs in a sample.

distribution of a variable in the whole population.

bell-shaped curve.

Sample mean: the sum of all observations in a sample divided by n, the number of observations.

Standard deviation: a common measure of the spread of a distribution. It indicates how far the different measurements typically are from the mean. Calculated from variance ⅔ of data within 1 sd 95% within 2 sd Can be calculated from a frequency table

Coefficient of variation: the standard deviation expressed as a percentage of the mean. Higher CV means more variability and lower means more consistency relative to the mean

the middle measurement of a set of observations

the difference between the third and first quartiles of data. It is the middle 50% of the data.

Displays median, interquartile range, first and third quartiles, median, smallest and largest non-extreme values (not more than 1.5x IQR from box edge

Mean is more sensitive to extremes than median (middle) Standard deviation is more sensitive to extremes than mean. IQR is not and is a better measurement when there are extremes

when processed

Location (central tendency) Width (spread)

If median, mean and mode values are similar, their values will be close to normal distribution If median, mean and mode values are not similar, data will be skewed

Corrects bias which occurs during the estimation process (aside from this we don’t need to know all the details about why this happens). Lose a degree of freedom

Gets rid of negatives Weights larger deviations more heavily

Estimation: is the process of inferring a population parameter from sample data. The value of an estimate calculated from the data is almost never the exact same as the true value (the parameter). Use standard error formula to see what variability we should expect and if we can trust our estimates By repeatedly sampling tables we eventually end up with the probability distribution of all the values of an estimate we might have obtained if we sampled the population this way

an estimate of the standard deviation of the sampling distribution. Predicts the sampling error of the estimate. It can indicate uncertainty and precision In most cases we do not have the real sampling distribution so use standard error of the mean

Sampling distribution: theoretical distribution of an estimate. The larger the sample size the more narrow and precise the sampling distribution

Standard error of the mean: gives us understanding of the likely difference between our sample mean and the true population mean.

Variance is larger than standard deviation Standard deviation has same units as data values whereas variance does not