Summary Management Research Methods 2
Week 1
Types of analytics:
Descriptive analytics: what happened?
Diagnostic analytics: why did it happen?
Predictive analytics: what will happen?
Prescriptive analytics: how can we make it happen?
Higher level -> more difficulty and more value (hindsight -> insight -> foresight).
Three levels:
Why -> concept.
What -> statistics.
How -> tools (SPSS).
Variables:
Predictor variable (PV): independent variable (IV) -> variable that explains.
Outcome variable (OV): dependent variable (DV) -> test variable (variable to be explained).
You have to estimate what variables explain and what variables are outcomes. After that check how
data look like -> make graph and remove outliers. Last step is finding relationships.
p-value: probability of obtaining a result (or test-statistic value) equal to or more extreme than what
was actually observed (the result you actually got), assuming that null hypothesis is true. Low p-value
-> null hypothesis is unlikely.
Conceptual models: visual representations of relations between theoretical constructs (and variables)
of interest. In research by model means a simplified description of reality. Variables can have different
measurement scales:
Categorical: subgroups are indicated by numbers:
o Binary variable: two outcomes (dead or alive).
o Nominal: values without difference or order (omnivore, vegetarian, or vegan).
o Ordinal: values with difference (sort of scale -> bad, intermediate, good).
Quantitative (numerical): use of numerical scales, with equal distances between values:
o Discrete data: data that counts (number of defects).
o Continuous: entities get a distinct score -> interval, ratio (age, body length,
temperature). In social sciences, ordinal scales are can be treated as interval scales
(Likert scales).
Applications conceptual models:
Boxes represent variables.
Arrows represent relationships between variables.
Arrows go from predictor variables to outcome variables.
Conceptual models:
Direct relationship (teachers that are more committed will increase the satisfaction level of
students in comparison to uncommitted teachers).
Moderation: one variable moderates the relationship between two other variables (other
variable affects relationship between two variables -> two predictor variables) -> proposed
effect is stronger in certain settings (teachers that are more committed will increase the
satisfaction level of students, when they have good communication skills -> communication
skills is moderating variable).
Mediation: one variable mediates the relationship between two other variables (variable A ->
variable B -> variable C) -> proposed relationship ‘goes via’ another variable (the positive
effect of teacher’s commitment on student satisfaction is mediated by quality of course
material -> lecture slides quality is mediating variable).
,Two measurements of variability (how much values differ in your data):
Variance: average of the squared differences from the mean.
Sum of squares: sum of squared differences from the mean.
Analysis of variance (ANOVA) helps to investigate with a certain level of confidence, what differences
there might be between different groups -> ANOVA compares the variability between the groups
against the variability within the groups (ANOVA helps to understand differences between groups).
Much of variability in outcome variable can be explained by predictor variable, but not all variability ->
creating groups.
Difference between groups should be as high as possible, and difference within groups should be as
low as possible. Groups are homogeneous within them, and different from each other -> difference
between groups.
ANOVA: test whether statistically significant differences exist in scores on a quantitative outcome
variable between different levels (groups) of a categorical predictor variable -> ANOVA statistically
examines how much of the variability in the outcome variable can be explained by the predictor
variable -> breaks down different measures of variability through calculating sum of squares. Via these
calculations, the ANOVA helps to test if the mean scores of the groups are statistically different. One
predictor variable -> one way ANOVE. One way ANOVA is used when:
Categorical predictor variable with more than 2 groups.
Quantitative outcome variable.
Variance is homogenous across groups (you need to test this)
Residuals are normally distributed (not necessary to test for exam).
Groups are roughly equally sized (they are always on exam).
Subjects can only be in one group (groups should be mutually exclusive).
Not adhering to assumptions can produce invalid outcomes. Calculations:
Total sum of squares: squared distance between observation and mean ->
n
SStotal =∑ ( y i ¿− ý .. )2 ¿, whereby y i = observation, and ý .. = mean.
i=1
Model sum of squares: difference between groups (comparison of group means with overall
3
mean) -> S S model =∑ n j ( ý . j ¿− ý ..)2 ¿, whereby ý . j = mean of specific group, and n j =
j=1
number of observations in group (group 1 consists of 3 observations -> n j = 3).
Residual sum of squares: difference within groups (explanation of variances that remain in
J nj
2
each group) -> S S residual =∑ ∑ ( yij ¿− ý . j ) ¿ , whereby y ij = observation, J = number of
j =1 i=1
groups (3 different groups -> J = 3).
SStotal =SS model + SSresidual
After this, you can calculate the proportion of total variance in the outcome variable that is explained
variability explained by model SSmodel
by the model -> R squared -> R 2= = .
total variability SStotal
F-test to investigate if the group means differ with an ANOVA. F-test: statistical test that checks the
ratio explained variability to unexplained variability ->
explained variability between group variability
F ( ratio )= = -> look at mean square between
unexplained variability wit h∈group variability
groups and mean square within groups.
, It’s not possible to just divide the model sum of squares by the residual sum of squares, because they
are not based on the same number of observations -> divide by degrees of freedom (different ways to
choose something):
d f model =k−1 , whereby k = number of groups.
d f residual=n−k .
S Smodel
( )
d f model M ean S quaremodel
Result is mean square (average sum of squares): F = = .
S Sresidual M ean S quareresidual
( )
d f residual
F-ratio tells if there is a difference -> F should be as high as possible. Compare F-ratio with
critical value to estimate if group means are significantly different (meaning of F depends on
df). Critical value can be found in F-table (d f model is column and d f residual is row) (df is
rounded up -> df 120 becomes df 200). F-ratio > critical value -> difference between group
means. F-ratio < critical value -> no difference between group means.
Hypotheses F-test:
H0: 𝜇1 = 𝜇2 = … = 𝜇I -> H0: there is no difference in means across the different categories.
H1: 𝜇i ≠ 𝜇j for some i and j -> H1: there is a difference in the means (at least one average is
different).
Null hypotheses can or cannot be rejected based on p-value.
Steps ANOVA:
1. Total sum of squares
2. Model sum of squares.
3. Residual sum of squares.
4. Sum of squares and R2.
5. F-test and mean squares.
Example ANOVA: is there a relation between shopping platform and customer satisfaction? Predictor
variable is shopping platform (categorical) -> brick-and-mortar store, web shop, reseller. Outcome
variable is customer satisfaction (quantitative) -> score from 1 to 50. 10 observations on customer
satisfaction scores with overall mean 32.3 (average of 10 customers). Calculations:
Total sum of squares ( SStotal ) = 1192.10.
After total sum of squares, introduction of model -> model sum of squares (between SS ->
SSmodel ) = 1140.68. Three group means are compared to grand overall mean.
Model doesn’t explain all variance in data -> residuals are the variances that remain in each
group -> residual sum of squares (within SS -> SSresidual ) = 51.42.
1192.10 = 1140.68 + 51.52.
R2 = 1140..10 x 100% = 95.7% -> 95.7% of the variance or difference in customer
satisfaction can be explained by which of the shopping platforms the respondents used ->
there is much variance.
df model = 3 – 1 = 2 and df residual = 10 – 3 = 7 -> F = (1140.) / (51.) = 77.60. For F(2, 7) the
critical value is 4.74 -> 77.60 > 4.74 -> differences between at least two of the groups are statistically
significant.
Week 1
Types of analytics:
Descriptive analytics: what happened?
Diagnostic analytics: why did it happen?
Predictive analytics: what will happen?
Prescriptive analytics: how can we make it happen?
Higher level -> more difficulty and more value (hindsight -> insight -> foresight).
Three levels:
Why -> concept.
What -> statistics.
How -> tools (SPSS).
Variables:
Predictor variable (PV): independent variable (IV) -> variable that explains.
Outcome variable (OV): dependent variable (DV) -> test variable (variable to be explained).
You have to estimate what variables explain and what variables are outcomes. After that check how
data look like -> make graph and remove outliers. Last step is finding relationships.
p-value: probability of obtaining a result (or test-statistic value) equal to or more extreme than what
was actually observed (the result you actually got), assuming that null hypothesis is true. Low p-value
-> null hypothesis is unlikely.
Conceptual models: visual representations of relations between theoretical constructs (and variables)
of interest. In research by model means a simplified description of reality. Variables can have different
measurement scales:
Categorical: subgroups are indicated by numbers:
o Binary variable: two outcomes (dead or alive).
o Nominal: values without difference or order (omnivore, vegetarian, or vegan).
o Ordinal: values with difference (sort of scale -> bad, intermediate, good).
Quantitative (numerical): use of numerical scales, with equal distances between values:
o Discrete data: data that counts (number of defects).
o Continuous: entities get a distinct score -> interval, ratio (age, body length,
temperature). In social sciences, ordinal scales are can be treated as interval scales
(Likert scales).
Applications conceptual models:
Boxes represent variables.
Arrows represent relationships between variables.
Arrows go from predictor variables to outcome variables.
Conceptual models:
Direct relationship (teachers that are more committed will increase the satisfaction level of
students in comparison to uncommitted teachers).
Moderation: one variable moderates the relationship between two other variables (other
variable affects relationship between two variables -> two predictor variables) -> proposed
effect is stronger in certain settings (teachers that are more committed will increase the
satisfaction level of students, when they have good communication skills -> communication
skills is moderating variable).
Mediation: one variable mediates the relationship between two other variables (variable A ->
variable B -> variable C) -> proposed relationship ‘goes via’ another variable (the positive
effect of teacher’s commitment on student satisfaction is mediated by quality of course
material -> lecture slides quality is mediating variable).
,Two measurements of variability (how much values differ in your data):
Variance: average of the squared differences from the mean.
Sum of squares: sum of squared differences from the mean.
Analysis of variance (ANOVA) helps to investigate with a certain level of confidence, what differences
there might be between different groups -> ANOVA compares the variability between the groups
against the variability within the groups (ANOVA helps to understand differences between groups).
Much of variability in outcome variable can be explained by predictor variable, but not all variability ->
creating groups.
Difference between groups should be as high as possible, and difference within groups should be as
low as possible. Groups are homogeneous within them, and different from each other -> difference
between groups.
ANOVA: test whether statistically significant differences exist in scores on a quantitative outcome
variable between different levels (groups) of a categorical predictor variable -> ANOVA statistically
examines how much of the variability in the outcome variable can be explained by the predictor
variable -> breaks down different measures of variability through calculating sum of squares. Via these
calculations, the ANOVA helps to test if the mean scores of the groups are statistically different. One
predictor variable -> one way ANOVE. One way ANOVA is used when:
Categorical predictor variable with more than 2 groups.
Quantitative outcome variable.
Variance is homogenous across groups (you need to test this)
Residuals are normally distributed (not necessary to test for exam).
Groups are roughly equally sized (they are always on exam).
Subjects can only be in one group (groups should be mutually exclusive).
Not adhering to assumptions can produce invalid outcomes. Calculations:
Total sum of squares: squared distance between observation and mean ->
n
SStotal =∑ ( y i ¿− ý .. )2 ¿, whereby y i = observation, and ý .. = mean.
i=1
Model sum of squares: difference between groups (comparison of group means with overall
3
mean) -> S S model =∑ n j ( ý . j ¿− ý ..)2 ¿, whereby ý . j = mean of specific group, and n j =
j=1
number of observations in group (group 1 consists of 3 observations -> n j = 3).
Residual sum of squares: difference within groups (explanation of variances that remain in
J nj
2
each group) -> S S residual =∑ ∑ ( yij ¿− ý . j ) ¿ , whereby y ij = observation, J = number of
j =1 i=1
groups (3 different groups -> J = 3).
SStotal =SS model + SSresidual
After this, you can calculate the proportion of total variance in the outcome variable that is explained
variability explained by model SSmodel
by the model -> R squared -> R 2= = .
total variability SStotal
F-test to investigate if the group means differ with an ANOVA. F-test: statistical test that checks the
ratio explained variability to unexplained variability ->
explained variability between group variability
F ( ratio )= = -> look at mean square between
unexplained variability wit h∈group variability
groups and mean square within groups.
, It’s not possible to just divide the model sum of squares by the residual sum of squares, because they
are not based on the same number of observations -> divide by degrees of freedom (different ways to
choose something):
d f model =k−1 , whereby k = number of groups.
d f residual=n−k .
S Smodel
( )
d f model M ean S quaremodel
Result is mean square (average sum of squares): F = = .
S Sresidual M ean S quareresidual
( )
d f residual
F-ratio tells if there is a difference -> F should be as high as possible. Compare F-ratio with
critical value to estimate if group means are significantly different (meaning of F depends on
df). Critical value can be found in F-table (d f model is column and d f residual is row) (df is
rounded up -> df 120 becomes df 200). F-ratio > critical value -> difference between group
means. F-ratio < critical value -> no difference between group means.
Hypotheses F-test:
H0: 𝜇1 = 𝜇2 = … = 𝜇I -> H0: there is no difference in means across the different categories.
H1: 𝜇i ≠ 𝜇j for some i and j -> H1: there is a difference in the means (at least one average is
different).
Null hypotheses can or cannot be rejected based on p-value.
Steps ANOVA:
1. Total sum of squares
2. Model sum of squares.
3. Residual sum of squares.
4. Sum of squares and R2.
5. F-test and mean squares.
Example ANOVA: is there a relation between shopping platform and customer satisfaction? Predictor
variable is shopping platform (categorical) -> brick-and-mortar store, web shop, reseller. Outcome
variable is customer satisfaction (quantitative) -> score from 1 to 50. 10 observations on customer
satisfaction scores with overall mean 32.3 (average of 10 customers). Calculations:
Total sum of squares ( SStotal ) = 1192.10.
After total sum of squares, introduction of model -> model sum of squares (between SS ->
SSmodel ) = 1140.68. Three group means are compared to grand overall mean.
Model doesn’t explain all variance in data -> residuals are the variances that remain in each
group -> residual sum of squares (within SS -> SSresidual ) = 51.42.
1192.10 = 1140.68 + 51.52.
R2 = 1140..10 x 100% = 95.7% -> 95.7% of the variance or difference in customer
satisfaction can be explained by which of the shopping platforms the respondents used ->
there is much variance.
df model = 3 – 1 = 2 and df residual = 10 – 3 = 7 -> F = (1140.) / (51.) = 77.60. For F(2, 7) the
critical value is 4.74 -> 77.60 > 4.74 -> differences between at least two of the groups are statistically
significant.
