This summary entails the necessary study materials for the end-term for QDA2. It is subdivided by week of study materials and includes information from the book, lectures and seminars.
This summary has as content all the material needed for the end term. It is organized by week and contains informa...
qda qda2 quantitative data analysis quantitative data analysis 2 field spss business administration uva discovering statistics using ibm spss statistics
Connected book
Book Title:
Author(s):
Edition:
ISBN:
Edition:
More summaries for
Exam Guide for Applied Multivariate Data Analysis – Get yourself a Wonderful Grade!
Summary of Statistics (IBC), Radboud University
Answers assignment 3 business research methods
All for this textbook (117)
Written for
Universiteit van Amsterdam (UvA)
Business Administration
Quantitative Data Analysis 2 (6012B0423Y)
All documents for this subject (8)
Seller
Follow
lacoste
Content preview
QDA2
The p-value stands for the 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 the null hypothesis is true. A low p-value
indicates that the null hypothesis is unlikely.
OV = Outcome Variable
- Or DV = Dependent Variable
- Test variable, variable to be explained
PV = Predictor Variable
- Or IV = Independent Variable
- Variable that explains
ANOVA: analysis of variance, is a statistical procedure that uses the F-statistic to
test the overall fit of a linear model. In experimental research this linear model
tends to be defined in terms of group means, and the resulting ANOVA is
therefore an overall test of whether group means differ.
We use the ANOVA and the independent sample T-test when:
- The Outcome Variable = quantitative
- The Predictor Variable(s) = categorical
o Number of categories = 2 or more
o Participants = Different
So independent, mutually exclusive samples
A.k.a. Between subjects design
o You want to compare the means of two independent groups. Then
we have a quantitative outcome variable, two independent groups in
the PV so categorical.
- Further assumptions
o Variance is homogeneous across groups: Levene’s test value >
0.05 assume equal variances.
o Residuals are normally distributed
o Groups are roughly equally sized
Distinguish between
- Number of categories within one (categorical) predictor variable
o E.g. PV = gender 2 categories
- Number of (predictor) variables
o E.g. PV gender, PV nationality, PV education level etc.
One-way ANOVA
- 1 OV = quantitative
- 1 PV = categorical, 2 or more categories
o Participants = independent One Way Independent/Between
Subjects ANOVA
ANOVA decomposes total variability observed in OV.
1
, - How much is caused by differences between groups (explained)?
- How much is caused by differences within groups (unexplained)?
Test-statistic: F-test
- F-values are looking to explain variability:
o Variance = The average of the squared differences from the Mean
o Sum of Squares = The sum of the squared differences from the
Mean
Total SS is the total variability to be explained.
Model SS is between SS. Squared deviations group means
from grand overall mean. How much variability can be
explained by differences between groups?
Residual SS is within SS. Squared deviations observations
from group means. How much variance is there within the
groups? Thus, not explained by the groups we
compare/PV/model.
R2 is the proportion of the total variance that is explained by the model.
F-statistic is the ratio of the explained to the unexplained variation.
We want the F-value to be big since we want to explain as much as possible
between the groups. What is big?
2
,F-ratio = How much the model fits the data relative to how much error there is. Is
the ratio of the experimental effect to the background ‘error’. Signal to noise
ratio. It is the ratio of how good the model is compared to how bad it is (its error).
Are the group means significantly different? We first use an F to test whether we
significantly predict the outcome variable by using group means (which tells us
whether, overall, the group means are significantly different) and then use the
specific model parameters (the bs) to tell us which means differ from which.
If the p-value < 0.05 it is a significant effect. Predicting our outcome based
on group means is significantly better than not doing that. So, in other words: our
group means are significantly different.
The p-value stands for the 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 the null hypothesis is true. A low p-value indicates
that the null hypothesis is unlikely.
E.g. p<0.001 tells us that there is less than a 0.1% change that an F-statistic at
least this large would happen if the null hypothesis were true. Therefore, we
conclude that our model results in significantly better prediction of album sales
than if we used the mean value of album sales.
Conclusion: given the sample and a significance level of 5% there is (not)
sufficient statistical evidence that the mean weight of the tablets differs from
12mg.
P-value of 1% is the chance of finding it assuming that she hid it (H 0 = she hid the
marker)
- H0 is not rejected and H1 is not supported, if p-value > α
- H0 is rejected and H1 is supported, if p-value < or equal to α
HOWEVER, this is a preliminary conclusion. So, there is a statically significant
difference (p < 0.05) between at least two of the groups in the PV. But this is not
very informative, how do we know what exactly is going on and between which
groups? Mean plots can give an indication but is not a statistical test. Therefore,
we need to do a follow-up analysis:
- When there were specific hypotheses beforehand, planned contrasts can
be used.
Planned contrasts should only be run if you had a priori expectations about
differences between groups.
o H1 = partner attractiveness is lower in the alcohol conditions than in
the non-alcohol conditions.
o H2 = partner attractiveness is lower in the 4-beer condition than in
the 2-beer condition.
Each group gets assigned a contrast weight (can also be 0). Negative
weights are assigned to the groups with lower expected values.
o Coefficient Total should be zero “proper” contrastproper” contrast
o Contrasts should be orthogonal (independent):
Sum of multiplied weights should be zero: 1*0 + -0.5*1 + -
0.5*-1 = 0
3
, Orthogonal (independent) contrasts: can be run simultaneously without
problems of INFLATION OF TYPE I ERROR (α). Which is the reason we
wanted to know in the first place.
Assume equal variances when Levene’s > 0.05. The Value of the Contrast
shows whether the direction of the hypotheses is correct. Sig. needs to be
divided by 2 when there is a direction in the hypotheses.
- If not, post-hoc tests can be used.
Post hoc tests can be used to explore the data even if you had no a priori
expectations about differences. Each group is compared to every other
group (pairwise comparisons).
BUT: Multiple comparisons cause artificial inflation of α (family wise error
rate). So, we “proper” contrastadjust” for that. All post hoc tests are adjustments for this.
Bonferroni, the most common method, lacks statistical power. More power
when number of comparisons is small. “proper” contrastBonferroni” divides the alpha over
all comparisons.
o We look at significance of mean differences.
o We look at the direction of the mean differences.
So, what is your final story? I.e. how has statistics helped you to answer a
research question thoroughly and convincingly?
What if...
- We have a within-subjects design. Repeated-measures ANOVA
OV: time to retch
PV: what did you have to eat?
Set up data set. Every person in the sample needs to do every step.
Repeated measures since more than 2 steps.
- Variances are not homogenous (unequal variances) Welch’s ANOVA
o Also, an analysis of variance, also has a test statistic, null
hypothesis, alternative hypothesis, and p value
4
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller lacoste. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.03. You're not tied to anything after your purchase.
