Download Quantitative Research - t-test, ANOVA, Multiple Regression

Quantitative Research - t-test, ANOVA, Multiple Regression Compared
Hypothesis
t-test
Research Question:
For A group there is a
statistically significant
difference between those
exposed to treatments as
measured by the DV
Hypothesis:
Ho: µ1=µ2
HA: µ1≠µ2
Model
N/A
Level of
Significance/
Risk
For this study the level of
risk will be set at 0.05
(α=0.05). This will
minimize the probability
of committing a type I
error
Independent sample ttest. This will allow us to
compare the means of a
single continuous DV for
two different groups.
Test Statistic
ANOVA
Research Question:
For a study of effectiveness of A vs. B
for C and the possible differential
effects of these 2 methods on D
1 – There is a stat sig diff between
those exposed to A compared to B as
measured by C
2 – There is a stat sig …(same as 1)
but according to D
3 – There is a stat sig diff for the
interaction of DV by AB and D
Hypothesis:
For A
Ho: µ1=µ2
HA: µ1≠µ2
For B
Ho: µ3=µ4
HA: µ3≠µ4
For interaction AxB
Ho: µ1x3=µ1x4=µ2x3=µ2x4
HA: µ1x3≠µ1x4≠µ2x3≠µ2x4
Xijk=µ+αi+βj+α*βij+εijk
Xijk=Popµ+(A)x1+(B)x2+(AxB)x3+
unique observation
For this study the level of risk will be
set at 0.05 (α=0.05). This will
minimize the probability of
committing a type I error.
Multiple Regression
Research Question:
For a study that includes A and B as 2
predictors of C:
For the groups are the attributes of A
and B predictive as an aggregate profile
of C?
The test statistic employed for this
study will be a nxn design factorial
ANOVA
This will allow us to compare the
means of a single continuous variable
(A) for n different categorical
variables (B and C)
DV(continuous) and
multiple IV’s(categorical – dummy
coded)
The test statistic that will be employed
for this study is multiple regression.
This will allow us to compare the
relationship between the continuous
dependent variable (A) and the n
different continuous variables (B, C,…)
Variables
N/A
Test
Assumptions
*Homogeneity of variance
*Normal distribution
*Independence of
observations
*Homogeneity of variance
*Normal distribution
*Independence of observations
Descriptive
Statistics
Measures of Center
Measures of Spread
Mean Differences
Measures of Center
Measures of Spread
Number of Observations
Mean Differences for each group
Hypothesis:
Treatment has no Impact
Treatment has an Impact
Yij=βo+β1X1+β2X2+εij
Yij= Int+(A)x1+(B)x2+Error
For this study the level of risk will be
set at 0.05 (α=0.05). This will minimize
the probability of committing a type I
error.
DV-criterion (continuous) and
multiple IV’s –predictors (continuous or
if categorical they have been dummy
coded)
*Homoscedasticity
*Normal distribution (for each variable,
the error variances, and the residuals)
*No Specification errors
*No Multicollinearity
*Linear relationship
Measures of Center
Measures of Spread
Number of Observations
Mean Differences for each group
Test Statistic
Computed
Observed t value
F-value
In summary table F-observed
reported for each IV as well as
interaction variables
Main Effects are determined
Simple Effects are determined (the
effect of each var at each level of
another var)
Critical Value
CV for t-statistic at
corresponding α level
from table
t-observed is compared to
t-critical and decide to
reject or fail to reject null
t-observed reported with
corresponding p-value for
the level of risk (p<.05)
Additional
Statistics
Effect size
.0-.2 small
.2-.5 medium
>.5 large
Confidence Intervals
=µ±1.96σ
CV for F-statistic for the
corresponding α level is obtained
from tables
F-obtained is compared to F-critical
and decide to reject the null or fail to
reject the null at the predetermined
level of risk
F-observed is reported with p-value
and whether or not outcome is sig
If F-obtained is significant Post-Hoc
tests should be conducted to
determine which individual factors
are truly sig
Eta-squared- coefficient of
determination (which explains
proportion of variance of DV
accounted for by the IV’s as a
percent)
Or omega-squared – is less biased
Confidence Intervals =µ±1.96σ
Results
Interpreted in light of
research problem
Decisions
Decision about
generalizability to larger
population
Limitations
Problems for
further study
Correlation matrix describes the
relationship of each variable to each
other variable in the model
R (Pearson) is reported for each var
Sig of each var
N’s for each var
Model Summary indicates R, adj R2
(coefficient of determination –
proportion of variance for the DV that
is described by IV’s (predictors) as a
percent)
ANOVA table
Coefficient Table – tells that if all other
vars were held constant, the predicted
Y value would be higher or lower by
the reported number of units
Standard MR was employed to
determine if IV’s stat sig predicted DV.
Tables x etc show the correlation
between vars, the unstandardized reg
coeff(B), intercept, standardized reg
coeff(β), semi part corr, R, R2, adj R2.
R for regression was stat sig diff from 0.
F( ) = __ p=__R2 of _ (__adj) indicates
that over _% of variability in the overall
variability in DV is predicted by IV’s