Chapter 14 - Quantitative data analysis

Question 1

How do you prepare for data analysis?

Answer 1

• Carefully consider how the data will be coded and analyzed before constructing instruments and collecting the dat
• Consider missing data
• Consider types of variables in the study (ratio, interval, ordinal, nominal)

Question 2

Explain a report structure

Answer 2

1. Method
   (describe the entire procedure)
2. Result section
   2.1 Descriptive statistics (describe the data, e.g. correlation)
   2.2 Inferential statistics (draw inferences from the sample on the population)

Question 3

What is type 1 error?

Answer 3

Rejecting a true null hypothesis

A “false alarm”

Example: You conclude that the population mean is not 368 g when it in fact is 368 g. This causes you to take corrective action although it is not needed (false alarm)

Probability of occuring: α
(called level of significance and is set in advance)

You control type I error by determining the risk level, α , that you are willing to have of rejecting the null hypothesis when it is true.

α = Probability of rejection when the null hypothesis is true.

Question 4

What is type 2 error?

Answer 4

Failing to reject a false null hypothesis

A “missed opportunity” to take corrective action

Example: You conclude that the population mean is 368 g when it in fact is not 368 g. Here you continue without corrective action, although it is needed (missed opportunity)

Probability of occurring: β (risk)
(Depends on statistical power, e.g. sample size)

Unlike the type I error (which you can control through the selection of ), the probability of making the type II error depends on the difference between the hypothesized and actual values of the population parameter.

This is because large differences are easier to identify than small ones

Question 5

What are the three basic methods for testing hypotheses?

Answer 5

1) Chi-square (nominal variables)
2) Correlation analysis
3) Regression analysis

Question 6

Explain chi-square

Answer 6

• use when you have categorical/nominal variable
• “does gender affect reasons for going to the gym?”

Chi-square is a statistical test used to determine whether there is a significant association between two categorical variables. It is a non-parametric test, which means that it does not rely on any assumptions about the underlying distribution of the data.

The p-value associated with the chi-square test statistic can be calculated using a chi-square distribution table or software. If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis and conclude that there is a significant association between the two variables.

Question 7

Explain linear correlation

Answer 7

Linear correlation is a statistical technique used to measure the strength and direction of the linear relationship between two quantitative variables. A linear correlation coefficient, denoted by “r”, ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no linear correlation.

To calculate the correlation coefficient “r”, we need to first calculate the covariance of the two variables, which measures the degree to which the two variables vary together. We then divide the covariance by the product of the standard deviations of the two variables.

• significance is affected by size of coefficient and the sample size
• “is there a relationship between number of filed patents/year and firm EBITA?”

Question 8

Explain linear regression analysis

Answer 8

• use when variables are at leads interval
• “how does number of filed patents/year affect firm EBITA?