Exploring research - Descriptive Statistics and distributions

Population vs sample - what are they?

Population = the group we would like to draw conclusions about

Sample = a smaller number of people we can recruit into a study

What are descriptive statistics?

Summarise and describe a sample

What are inferential statistics?

they allow us to ‘infer’ - draw conclusions and/or make predictions about a larger populations

Descriptives can be broken down into two broad types…

1. Measures of central tendency

2. Measures of dispersion or variability

What are the four types of data?

1. Nominal

2. Ordinal

3. Interval

4. Ratio

(Last two are often referred to jointly as scale data)

Three types of central tendency -

1. Mean - average

2. Median - middle score

3. Mode - most frequent observation

4 types of measures of dispersion/variability

1. Range = range from highest to lowest value in data

2. Interquartile range = 50% of the distribution between the first and fourth quartile

3. Standard deviation = average deviation from her mean

4. Variance = average squared deviation from the mean

Tables vs charts

Tables best for - reporting exact precise data values.

Charts best for. - visual representation, showing trends patterns, relationships

Distributions tell us how often a value occurs in a data set

What does a frequency distribution tell us eg?

Allows us to see how frequently a value or set of values occur

(visualised mostly by histogram)

Normal distribution often assumed by what kind of statistics

Inferential

Area under the curve represents…

Proportions within specific ranges

What is the Z score?

Tells us how many standard deviations a single score is form the Mean

Bimodal vs skewed

Bimodal - two peaks

Skewed - floor to ceiling

What do the distribution shapes tell us?

How well our summary statistics represent data captured

Measures that describe normal distribution?

Mean us a food valid measure of central tendency

Standard deviation is good measure of spread

For skewed data?

• mean is pulled in one direction by extreme values

• Median is often better

• Range can give better indication of spread than SD

For Bimodal data?

oSingle means or medians are slightly misleading because there isn't one center.

oIn these instances, it's important to report and show the distribution shape.