Inferential statistics

Define inferential statistics

Inferential statistics = a process of inferring features of a population by looking at a small sample (an educated guess) 

• Is it due to chance, or is it representative of the population? 

• Is the data a result of chance? Yes or no 

• NOT DESCRIBING DATA 

What is probability and how is it used in inferential stats. (in research)

Probability = the chance or likelihood that an event is going to happen, given all the possible outcomes 

• The study of random events  

• Expressed as a decimal (or %) and ranges from low (0 = no chance) to high (1 = certainty) 

• A means of prediction 

EX: chance of rain, coin flip 

• What will happen in the long run 

• After event happened, it can no longer be “probable” because it happened or didn’t as predicted 

In research = to determine if observed treatment differences are likely to be representative of population differences or if they could have occurred by chance 

• Try to predict what would happen to other populations based on our small sample 

Define sampling

Choosing of samples as representatives of the entire population 

• Randomization is important (however, it may not be representative because the sample is smaller than the population) 

• Used to estimate the real value 

Define sampling distribution

Shows how a statistic varies from a sample to sample 

• Can be affected by location, demographics 

• Data will not be the same between samples (variable) 

• Is theoretical (because would have to do it multiple times) 

  Get the mean from a population multiple times (different samples of same population) 

• Therefore, the BIGGER THE SAMPLE, THE BETTER 

How do you calculate the standard error of the mean? What is it

Standard deviation of a theoretical sampling distribution

What is the confidence interval?

a range of scores with specific boundaries (confidence limits), that should contain the population mean 

• Based on the sample mean and standard error 

• The wider the interval = the more confident you are the population mean will fall in it 

• Reduce the risk of being wrong by sacrificing precision 

• Therefore 95% is a balance between precision and confidence 

Ex: we are 95% confident that the population mean will fall between 37.3 and 42.7 

How do you calculate confidence interval

What is the population mean and sample mean?

Sample mean = X-bar = mean of the sample gathered 

Population mean = µ = a parameter 

What is type 1 error and an example

(alpha) = False positive 

• Saying results are significant, when they aren’t really 

Providing treatments that are not effective 

What is type 2 error and an example

(beta) = false negative 

• Saying results are not significant, when they really are

Stop researching areas that have potential 

What is “significance” in inferential statistics

Results of an analysis are unlikely to be due to chance at a specified probability level 

• If results are statistically significant, then null hypothesis is rejected 

P-value – level of significance 

• The selected alpha level defines the maximal acceptable risk of making a type 1 error (reject null) 

• Alpha value should be equal to or less than 5% (0.05) 

• p-value = 0.03 therefore, you reject the null (because 0.03 < 0.05)

List and describe the 4 types of data

Nominal = Categorical  

• Consists of arbitrary labels with no implied order, unranked 

• Can be numbered, but they have no significance 

• Male = 1 & female = 2 

• Counted as frequencies 

• Non-parametric tests 

Ordinal = Ranking  

• Consists of numerical ranked data that is ranked according to some criterion (each rank is different from the others but the differences may not be equal) 

• Do not represent quantity, only positions within a distribution 

• EX: 5-star rating, pain rating scale 

• Non-parametric tests 

Interval = 0 has no real value 

• Consists of ranked data with intervals between each order being equal but with no meaningful zero point 

• Actual value of one interval scale is NOT the same as another 

• Ex: 100 C is not the same as 100 F 

• Ex: IQ, calendar dates, temps,  

• Parametric tests (but can be non-parametric) 

Ratio = 0 has a meaning  

• Like interval data, but zero point is meaningful (highest level of measurement) 

• Therefore can’t go below 0 

• Ex: thyroid hormone levels, height, weight, age 

• Parametric tests & continuous values 

Identify the data type on the table