,1 Introduction
1.1 What & Why?
BRM is about analyzing data
Data selection and cleaning = not included in this course.
1.1.1 Transformation
For the needs of the analysis, it may be necessary to recode some of the raw data. (Examples: scale into
binary, continuous into scales…)
1.1.2 Analysis
Use input (raw data) + software (SPSS, STATA, R…) + data analysis techniques to obtain outputs
(regression tables, test-statistics, indicators, etc.). Many data analysis techniques exist. Their choice
depends on the question that needs to be answered and type of data available.
1.1.3 Interpretation
Make sense of the output, i.e. be able to read the tables/indicators/statistics and explain their meaning;
use them for decision making/answering your research question.
2 Brushing up: Hypothesis testing and linear Regression + SPSS
2.1 Hypothesis testing
2.1.1 Different types of data
2.1.1.1 Qualitative data
• Nominal data: subdivide in non-overlapping groups without a logical order (you cannot rank the
group)
o Ex. Type of car, gender, city you live in…
• Ordinal data: subdivide in non-overlapping groups, but there is a logical order between the
groups
o Ex. Attitude against something, level of education…
Sometimes you define numbers to qualitative data, but the numbers don’t mean anything (ex. Female =
1, Male = 0)
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, 2.1.1.2 Quantitative data
Ex. Price, exam score, number of customers… ® you can do real calculations.
2.1.2 Obtaining data
- Experiments
- Observation
- Survey
Sometimes we can obtain data on all individuals concerned (=population data), but usually you can only
obtain data on some individuals concerned (=sample data).
2.1.3 Symbols
Population Sample
Mean µ 𝑥̅
Variance 𝜎! s2
Proportion 𝜋 p
2.1.4 Hypothesis testing
When we want to test a statement about a population, using sample data, we perform hypothesis
testing. (When we have data on the whole population, hypothesis testing is not necessary)
A hypothesis = a statement (about a population parameter) ® We want to check whether this statement
hold on the whole population.
Hypothesis testing is a formal procedure used by statisticians to accept or reject a hypothesis.
® The formal procedure (assuming you already have the data):
1) State the hypothesis (H0 and H1)
2) Formulate analysis plan (specify formula or test statistic and the significance level)
3) Analyze data (compute value of test statistic from data)
4) Interpret result (decide if you can reject H0 in favor of H1, or not)
2.1.4.1 Null hypothesis versus alternative hypothesis
The alternative hypothesis = research hypothesis (something new, something controversial)
The proportion of students that pass the statistics exam:
H0 : 𝜋 = 0,5
H1 : 𝜋 > 0,5
The null hypothesis is always an equality.
2.1.4.2 One-sided tests versus two-sided tests
One-sided test ® H1 > x or H1 < x
Two-sided test ® H1 ≠ x
2.1.4.3 Specify the test statistic and significance level
We need a formula based on which to decide whether to reject H0 in favor of H1 (= test statistic). There
are different formulas for test statistics, depending on type of data and on hypothesis H0 and H1 (ANOVA-
test, T-test, Z-test…).
The formal testing procedure can lead to errors:
- Type 1 error: The null hypothesis is true, but we reject is (= significance level)
- Type 2 error: The null hypothesis is false, but we fail to reject is
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