Statistical tests

Question 1

Define type 1 errors?

Answer 1

• Type 1 errors occur when a statistical test wrongly rejects the null hypothesis. If you have set your p value at 0.05, there is only a 5% chance that your results are due to a type 1 error and 95% chance that they are truly significant

Question 2

Define type 2 errors?

Answer 2

• Type 2 errors occur when a statistical test fails to reject the null hypothesis despite there being a significant difference, type 2 errors are related to the statistical power of a test and they can be reduced by using tests with higher power (e.g. parametric tests over non-parametric tests) and by increasing sample size

Question 3

Explain what standard deviation is?

Answer 3

• Measure of how data varies from the mean
  68% of data will fall within 1 standard deviation from the mean
• Around 95% of data will fall within 2 standard deviations of the mean

Question 4

Explain what standard error is?

Answer 4

• The standard error tells you how accurate the mean of any given sample from that population is likely to be compared to the true population mean. When the standard error increases, i.e. the means are more spread out, it becomes more likely that any given mean is an inaccurate representation of the true population mean

Question 5

Describe parametric vs non parametric tests and examples?

Answer 5

• Use parametric tests for data with a normal distribution (normal distribution is just is it a nice bell curve shape)
• Use non parametric tests for data that is not normally distributed or data where you cant make assumptions about distribution
• Parametric tests have greater statistical power (statistical power of a test = probability that it will lead to correct rejection of the null hypothesis) however if you use a parametric test on non parametric data your result is meaningless/ incorrect
• You can do calculations e.g. Shapiro wilk to see if your data is normally distributed or not if you don’t know
• Parametric tests usually involve using actual numerical values, whereas non-parametric tests tend to rank the data (this is why they have less power as the true connections between data is lost in order to rank it but this has to be done due to lack of normal distribution)
• Examples of parametric tests = t-test, ANOVA
• ANOVA is used when there are more than 2 sets of data e.g. t test for comparing men vs women heart rates, ANOVA for comparing men, women and children heart rates
• Non parametric: chi squared, mann whitney U, Wilcoxin rank, Kruskall Wallis rank sum test

Question 6

Paired vs unpaired t test?

Answer 6

• Paired vs unpaired t test: A paired t-test is designed to compare the means of the same group or item under two separate scenarios. An unpaired t-test compares the means of two independent or unrelated groups. In an unpaired t-test, the variance between groups is assumed to be equal. In a paired t-test, the variance is not assumed to be equal

e.g. paired t test would be for a group of students results before a study course compared to the same group of students results after the study course

whereas unpaired would involve 2 separates groups of students, 1 who get a study course, and one who dont and then comparing their results