Module 2: Stats and Research

Measurement

the act of assigning numbers to observations

• we could assign the number 20 to represent someone’s age and the number 1 to represent that they are male.

a Constant

a uniform set of observations

a variable

a non-uniform set of observations

2 categories of variables

quantitative and qualitative

quantitative variable

their values reflect having more or less of some attribute (eg age)

Qualitative variable

their values reflect different categories (different qualities). (eg gender)

Population 

the complete set of observations

Parameter 

describes aspects of the population (eg average)

Sample 

subset of the population → estimates a parameter in the population

statistic

escribes aspects of the sample (eg average); denoated by different roman letters

inference

when sample statistics are used to estimate the population statistic

symbol for the mean of a sample

x¯ (x bar)

symbol for the mean of the populations

μ (mu)

Sampling Error

the discrepancy between a population parameter and its corresponding sample statistic

Sampling Error calculation: mean

sampling error = |mean of the sample - mean of the population|

• = |x¯-μ|

rules of sampling error

• always positive (abs value)

• always present (greater than 0)

• different samples of the same population have different amounts of sample error

central tendency

tells us what a typical score is in a set of scores.

types of central tendency

mean, median, mode

how does mode understand the typical score of a set

most commonly occurring score. commonly used for qualitative variables

how does mean understand the typical score of a set

mathematical average of all the scores; used for quantitative variables that are normally distributed (bell curve shaped)

normal ditrubution/normal curve

• has a belled shape → lots of intermediate values, few extremely high or extremely low values

• mean has less sample error than median

parameter mean calculation

μ=(∑X)/N​

• sum of all scores divided by the number of scores

how does Median understand the typical score of a set

middle score or the midpoint between the two middle scores

what is median used for

quantitative variables with skewed distribution. mean is bad because it is influenced by the outliers more

Skewed meaning

distribution contains either extremely high scores (positively skewed) or extremely low scores (negatively skewed).

the left is ___ the right is ___

positively skewed, negatively skewed

which measure of central tendency: skewed quantitative distribution uses __ while normal distribution uses ___

median, mean

which measure of central tendency: typical score of qualitative data

mode

what is standard deviation

how much scores tend to deviate from a typical (or standard) score

standard deviation as a parameter

represented by sigma σ

standard deviation as a statistic

represented by s

variance

mean of squared deviation (mean of (x-average)² in a set of x values)

what does variance tell us

how typical the scores in a set tend to be; higher variance = more atypical scores present

standard deviation calculation

σ=root(∑(X−μ)² / N) → square root of variance

• x is each number in a set

• μ is the mean of the set

• N is the number of values in a set

what is the sum of the deviation scores of any set of numbers

0

Correlation Coefficient

statistic that describes the strength and direction of the relationship between two variables

• same set of individuals measured for 2 variables

common way of illustrating a correlation between variables

scatter plots

correlation: positive relationship

High values on one variable are associated with high values on the other variable, positive slope on a scatter plot

correlation: negative relationship

high values on one variable are associated with low values on the other; negative slope on a scatter plot

values of the correlation coefficient can range from

-1 to 0 to 1

• negative → negative relationship, positive → +ve relationship

• close to 0 → weak/absent correlation

• the straighter the line of the scatter plot, the stronger the correlation; completely straight means magnitude 1

inferential test

compares the two samples, determines if their difference is from sampling error, or from real difference between the two groups.

inferential test: t test

• when p is less than 0.05, then test is statistically significant (the difference between 2 samples is real and not due to sampling error)

• when p is equal or greater than 0.05, then test is not statistically significant (the difference between 2 samples is probably due to sampling error)

• tests differences between only 2 groups

inferential test: F test

• tests for differences between 3 or more groups

• when p is less than 0.05, then test is statistically significant (the difference between 2 samples is real and not due to sampling error)

• when p is equal or greater than 0.05, then test is not statistically significant (the difference between 2 samples is probably due to sampling error)