2017/06/17

Basic Statistical Concepts

data 
nominal - male vs. female/  frequencies , percentages (non-parametric)
ordinal - e.g. Likert scale / first,second, third (non-parametric)
interval - discrete, parametric , continuous (eg temperature)
Ratio level - usually interval data, zero point reflects absence of characteristic

Discrete - adult/ non adult 

Continuous - angry to super angry 

Test Statistic = Systematic Variance / Unsystematic variance

We are comparing the amount of variance created by an experimental effect against the amount of variance due to random factors (such as differences in motivation, or intelligence)

t-value 

what is the probability that our samples are from the same population . You basically compare the means of two or more samples
it is a measure of unsystematic variance or variance not caused by the experiment

r-value (Effect Size)

is simply an objective and standardized measure of the magnitude of the observed effect. 
Pearson Correlation Coefficient
r = .1 (weak effect) 1% of variance between variables is explained
r = .3 (medium effect). 9% of variance between variables is explained
r = .5 (strong effect) 25% of variance is explained

p-value 

Significance - Chance of Error (being wrong), in other words the chance of a finding being due ot error
The chance of the null hypothesis to be rejected where it is actually true.
in Business this is accepted

p < .05


z-value 

are standard scores. it states the position of a raw score in relation to the mean of the distribution, using the standard deviation as the unit of measurement
z = raw score - mean / standard deviation

Standard Error 

the  standard deviation (or variability) of sample means. The higher the SE, the more the sample means differ from each other
The lower it is the more it accurately reflects the entire population


Mean: Sum / n

Median: right in the middle of samples
Mode: the most occuring

Standard Deviation 

Average distance of the values from the mean

Variance Extracted 

Summary measure of convergence among a set of items representing a latent construct.
It is the average % of variation explained among items



Type 1 Error (False Positive) 

Accepting effects that are in reality untrue

Type 2 Error (False Negative) 

Rejecting effc├ęcts that are in reality true



Construct Validity (relationship betweeb measurement instrument and the construct)

Discriminant, Convergent, nomological validity

Discriminant Validity

Eg how good do the items of the construct of innovation differentiate from frome the construct of strategic validity

Convergent Validity

How good are the items for the innovation construct converging ?
If they do not converge the are likely not measuring the same phenomenon
- Cronbach Alpha, cut-off value > .70
- Composite reliability, cut-off value > .60
- AVE Average variance extracted, cut-off value AVE > .50
(AVE = average squared factor loading)

Indicator reliability / validity

- significant factor loadings of items >.70, t-values > 1.645

Multicollinearity

phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, meaning that one can be linearly predicted from the others with a substantial degree of accuracy

Solution:

Variance inflation factors (VIF) measure how much the variance of the estimated regression coefficients are inflated as compared to when the predictor variables are not linearly related.
Use to describe how much multicollinearity (correlation between predictors) exists in a regression analysis. Multicollinearity is problematic because it can increase the variance of the regression coefficients, making them unstable and difficult to interpret.


Parametric Tests 
Kolmogorov Smirnov Test 
if p > .05 distribution is probably normal 

Levene Test 

tests hypothesis that variances of two samples are equal
if p > .05 variances are more or less equal 

Anova 

Main Effect 
A “main effect” is the effect of one of your independent variables on the dependent variable, ignoring the effects of all other independent variables

Interaction Effect

A statistical interaction occurs when the effect of one independent variable on the dependent variable changes depending on the level of another independent variable



Independent T-Test of two samples 


Taken from https://statistics.laerd.com/statistical-guides/independent-t-test-statistical-guide.php

Independent t-test for two samples

Introduction

The independent t-test, also called the two sample t-test, independent-samples t-test or student's t-test, is an inferential statistical test that determines whether there is a statistically significant difference (variance in means for instance) between the means in two unrelated groups.

Null and alternative hypotheses for the independent t-test

The null hypothesis for the independent t-test is that the population means from the two unrelated groups are equal:
H0: u1 = u2
In most cases, we are looking to see if we can show that we can reject the null hypothesis and accept the alternative hypothesis, which is that the population means are not equal:
HA: u1 ≠ u2
To do this, we need to set a significance level (also called alpha) that allows us to either reject or accept the alternative hypothesis. Most commonly, this value is set at 0.05.

The concept of falsification is based on Popper's falsification theory. You cannot know scientific laws with absolute certainty. you can only falsify them --> Null hypothesis