MANAGEMENT RESEARCH METHODS 1 • EXAM REVISION
MANAGEMENT
RESEARCH METHODS 1
Printable exam study guide
Core concepts • formulas • test selection • interpreting results
THE COURSE IN ONE LINE Describe and check data → understand probability and distributions → choose a
suitable statistical test → interpret evidence against a null hypothesis.
1. Start with the data
Observational unit, variables and measurement levels
• Observational unit (case): the entity each row represents, e.g., one student. Each column is a variable.
Type Meaning Examples / exam clue
Binary categorical Exactly two categories Pass/fail; yes/no; left/right
ID number, gender category, dominant hand; ID is not
Nominal categorical Categories with no natural order
numerical just because it uses digits
Ordered categories, but gaps between
Ordinal categorical Poor / average / good; star ratings
levels are not known to be equal
Discrete numerical Countable separate values Number of defects or applicants
Continuous Measured on a continuum; decimal Height, age, time, mass; shoe size can be treated as
numerical values are meaningful continuous in these notes
• Independent variable (IV): predictor, grouping variable or proposed cause. Dependent variable (DV): outcome
being measured.
• Operational definition: specify exactly how a construct is measured, including unit, procedure, timeframe and
population/sample.
• Collect data at the highest practical level of measurement. Converting a numerical variable into categories loses
detail and flexibility.
Data quality: validity, reliability and error
Concept What it means Remember
Does the measure capture what it claims A delay percentage depends on how “delay” and the
Validity
to measure? timeframe are defined.
Clear instructions and consistent procedures reduce
Reliability Consistency/stability of measurement
avoidable variation.
A scale reading 80 kg when the true value is 83 kg has
Measurement error Observed value − true value
error −3 kg.
Systematic error /
Consistent directional deviation A device that is always +0.9 kg off may be calibrated.
bias
Random error / Unpredictable variation around the true Reduces precision; does not disappear through
spread value calibration.
EXAM TRAP Bias and spread are different. A biased but consistent device may be calibrated; a device with
wide random variation is imprecise.
2. Descriptive statistics
Measure Formula / definition Interpretation
Mean x̄ = Σxᵢ / n Average; sensitive to outliers.
Median Middle value after sorting More robust to outliers.
Mode Most frequent value Can describe categorical data.
Range Maximum − minimum Overall spread; sensitive to extremes.
IQR Q₃ − Q₁ Spread of middle 50%.
Average squared deviation from mean; use n−1 for sample
Sample variance s² = Σ(xᵢ − x̄ )² / (n − 1)
variance.
Sample SD s = √s² Typical spread in the original units.
Print-friendly study guide • Based on your MRM1 notes • Check exam instructions and lecture materials
, MANAGEMENT RESEARCH METHODS 1 • EXAM REVISION
Standard error of
SE = s / √n Uncertainty/variability of sample mean across samples.
mean
• Positive/right skew: long tail to the right; often mean > median.
• Negative/left skew: long tail to the left; often mean < median.
• Bimodal/multimodal: two or more peaks; may indicate different subgroups.
• A rough 95% confidence interval for a mean in your notes: x̄ ± 2(s/√n). Exact methods may use a t critical value.
Which graph?
Variables Useful graph Read it for
Counts/proportions by category; bars make
1 categorical Bar chart (pie chart also possible)
comparisons easier.
Distribution shape/skew; median, quartiles and
1 numerical Histogram or boxplot
possible outliers.
2 categorical Clustered/multiple bar chart; crosstab Compare category frequencies.
1 categorical + 1 Compare numerical distributions across groups;
Side-by-side boxplots
numerical category on X, numerical on Y.
Direction/strength of relationship; predictor X,
2 numerical Scatterplot
outcome Y when appropriate.
BOXPLOT Know Q₁ (25th percentile), median/Q₂ (50th), Q₃ (75th), IQR = Q₃−Q₁. Marked points are potential
outliers and need context.
3. Probability essentials
Probability is between 0 and 1 (or 0% and 100%). For a complete set of mutually exclusive outcomes,
probabilities sum to 1.
Notation / rule Meaning Use it when
P(A) Probability of event A A single event.
P(A ∩ B) A and B both occur Intersection / joint probability.
P(A ∪ B) A or B or both occur Union; avoid double-counting overlap.
P(A | B) = P(A ∩ B) / P(B) Probability of A given B has occurred Condition on B; P(B)>0.
P(A ∩ B) = P(A) × P(B | A) Joint probability rule Events may be dependent.
One event does not change the Independence must be justified, not
If independent: P(A ∩ B) = P(A)P(B)
probability of the other assumed.
• Complement: P(not A) = 1 − P(A). Example: if 80% conform, probability of not conforming = 20%.
• Conditional probability uses a reduced reference group. If 11 of 16 hard-court matches were won by player D,
P(D wins | hard court) = 11/16.
• Two fair dice: 36 equally likely ordered outcomes. Sum of 7 has 6 outcomes, so P(sum=7)=6/36=1/6. At least
one six has 11 outcomes, so P(at least one six)=11/36.
• In the dice example, P(sum=7 and at least one six)=2/36. Therefore P(sum=7 | at least one
six)=(2/36)/(11/36)=2/11≈0.182.
Numerical distributions and the CDF
• A probability mass function describes probabilities for a discrete numerical variable; a probability density
function describes a continuous variable.
• CDF(x) = P(X ≤ x): the probability of observing x or below.
• P(X > x) = 1 − CDF(x). For a continuous variable, P(a < X ≤ b) = CDF(b) − CDF(a).
• For a normal distribution, the CDF uses the mean μ and standard deviation σ. Example structure:
P(X>175)=1−CDF(175; μ, σ).
• A Q–Q plot checks whether observed quantiles fit a theoretical distribution. Points close to the 45° line suggest a
reasonable fit to that distribution; systematic curves suggest mismatch.
• For grouped analyses, assess distribution/normality separately for each group when that is the assumption
being checked.
NORMAL-DISTRIBUTION EXAM STEPS Identify μ and σ → identify whether the question asks ≤, >, or
between → use the CDF or complement/difference rule → state the probability in context.
4. Hypothesis testing: the logic
• H₀ (null hypothesis): usually no difference, no relationship or independence.
Print-friendly study guide • Based on your MRM1 notes • Check exam instructions and lecture materials
MANAGEMENT
RESEARCH METHODS 1
Printable exam study guide
Core concepts • formulas • test selection • interpreting results
THE COURSE IN ONE LINE Describe and check data → understand probability and distributions → choose a
suitable statistical test → interpret evidence against a null hypothesis.
1. Start with the data
Observational unit, variables and measurement levels
• Observational unit (case): the entity each row represents, e.g., one student. Each column is a variable.
Type Meaning Examples / exam clue
Binary categorical Exactly two categories Pass/fail; yes/no; left/right
ID number, gender category, dominant hand; ID is not
Nominal categorical Categories with no natural order
numerical just because it uses digits
Ordered categories, but gaps between
Ordinal categorical Poor / average / good; star ratings
levels are not known to be equal
Discrete numerical Countable separate values Number of defects or applicants
Continuous Measured on a continuum; decimal Height, age, time, mass; shoe size can be treated as
numerical values are meaningful continuous in these notes
• Independent variable (IV): predictor, grouping variable or proposed cause. Dependent variable (DV): outcome
being measured.
• Operational definition: specify exactly how a construct is measured, including unit, procedure, timeframe and
population/sample.
• Collect data at the highest practical level of measurement. Converting a numerical variable into categories loses
detail and flexibility.
Data quality: validity, reliability and error
Concept What it means Remember
Does the measure capture what it claims A delay percentage depends on how “delay” and the
Validity
to measure? timeframe are defined.
Clear instructions and consistent procedures reduce
Reliability Consistency/stability of measurement
avoidable variation.
A scale reading 80 kg when the true value is 83 kg has
Measurement error Observed value − true value
error −3 kg.
Systematic error /
Consistent directional deviation A device that is always +0.9 kg off may be calibrated.
bias
Random error / Unpredictable variation around the true Reduces precision; does not disappear through
spread value calibration.
EXAM TRAP Bias and spread are different. A biased but consistent device may be calibrated; a device with
wide random variation is imprecise.
2. Descriptive statistics
Measure Formula / definition Interpretation
Mean x̄ = Σxᵢ / n Average; sensitive to outliers.
Median Middle value after sorting More robust to outliers.
Mode Most frequent value Can describe categorical data.
Range Maximum − minimum Overall spread; sensitive to extremes.
IQR Q₃ − Q₁ Spread of middle 50%.
Average squared deviation from mean; use n−1 for sample
Sample variance s² = Σ(xᵢ − x̄ )² / (n − 1)
variance.
Sample SD s = √s² Typical spread in the original units.
Print-friendly study guide • Based on your MRM1 notes • Check exam instructions and lecture materials
, MANAGEMENT RESEARCH METHODS 1 • EXAM REVISION
Standard error of
SE = s / √n Uncertainty/variability of sample mean across samples.
mean
• Positive/right skew: long tail to the right; often mean > median.
• Negative/left skew: long tail to the left; often mean < median.
• Bimodal/multimodal: two or more peaks; may indicate different subgroups.
• A rough 95% confidence interval for a mean in your notes: x̄ ± 2(s/√n). Exact methods may use a t critical value.
Which graph?
Variables Useful graph Read it for
Counts/proportions by category; bars make
1 categorical Bar chart (pie chart also possible)
comparisons easier.
Distribution shape/skew; median, quartiles and
1 numerical Histogram or boxplot
possible outliers.
2 categorical Clustered/multiple bar chart; crosstab Compare category frequencies.
1 categorical + 1 Compare numerical distributions across groups;
Side-by-side boxplots
numerical category on X, numerical on Y.
Direction/strength of relationship; predictor X,
2 numerical Scatterplot
outcome Y when appropriate.
BOXPLOT Know Q₁ (25th percentile), median/Q₂ (50th), Q₃ (75th), IQR = Q₃−Q₁. Marked points are potential
outliers and need context.
3. Probability essentials
Probability is between 0 and 1 (or 0% and 100%). For a complete set of mutually exclusive outcomes,
probabilities sum to 1.
Notation / rule Meaning Use it when
P(A) Probability of event A A single event.
P(A ∩ B) A and B both occur Intersection / joint probability.
P(A ∪ B) A or B or both occur Union; avoid double-counting overlap.
P(A | B) = P(A ∩ B) / P(B) Probability of A given B has occurred Condition on B; P(B)>0.
P(A ∩ B) = P(A) × P(B | A) Joint probability rule Events may be dependent.
One event does not change the Independence must be justified, not
If independent: P(A ∩ B) = P(A)P(B)
probability of the other assumed.
• Complement: P(not A) = 1 − P(A). Example: if 80% conform, probability of not conforming = 20%.
• Conditional probability uses a reduced reference group. If 11 of 16 hard-court matches were won by player D,
P(D wins | hard court) = 11/16.
• Two fair dice: 36 equally likely ordered outcomes. Sum of 7 has 6 outcomes, so P(sum=7)=6/36=1/6. At least
one six has 11 outcomes, so P(at least one six)=11/36.
• In the dice example, P(sum=7 and at least one six)=2/36. Therefore P(sum=7 | at least one
six)=(2/36)/(11/36)=2/11≈0.182.
Numerical distributions and the CDF
• A probability mass function describes probabilities for a discrete numerical variable; a probability density
function describes a continuous variable.
• CDF(x) = P(X ≤ x): the probability of observing x or below.
• P(X > x) = 1 − CDF(x). For a continuous variable, P(a < X ≤ b) = CDF(b) − CDF(a).
• For a normal distribution, the CDF uses the mean μ and standard deviation σ. Example structure:
P(X>175)=1−CDF(175; μ, σ).
• A Q–Q plot checks whether observed quantiles fit a theoretical distribution. Points close to the 45° line suggest a
reasonable fit to that distribution; systematic curves suggest mismatch.
• For grouped analyses, assess distribution/normality separately for each group when that is the assumption
being checked.
NORMAL-DISTRIBUTION EXAM STEPS Identify μ and σ → identify whether the question asks ≤, >, or
between → use the CDF or complement/difference rule → state the probability in context.
4. Hypothesis testing: the logic
• H₀ (null hypothesis): usually no difference, no relationship or independence.
Print-friendly study guide • Based on your MRM1 notes • Check exam instructions and lecture materials
