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ANOVA / Regression

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  • #47495

    Kiran Varri
    Participant

    Hi Guys,
    Yesterday i was going through F-test used as part of ANOVA. Hre came a curious doubt. Though i could find a point or 2 how ANOVA differes from Regression; I was not 100% clear how/why/when i will need to use ANOVA and when i need to use Regression.
    Any Help will be appreciated
    Kiran Varri

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    #158370

    Szentannai
    Member

    Hi Kirani,
    a quick sort of explanation is that we have 3 models for our data  one more specific then the next. Model 1 is that there is no difference between the averages of the different groups, model 2 that there is at least one group that is different from the others and model 3 that all the groups differ in a very specific way, the group averages are on a straight line.
    We check model 2 against model 1 with ANOVA and model 3 against either model 1 or model 2 with regression.
    Hope this helps
     Sandor

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    #158371

    indresh
    Participant

    To further Sandor with example to give you more clarity
    Y=f(x)
    Use Anova when Y is dicrete and X is continuous data. If you wanna find if there is any difference that exist between time taken to deliver (continuous) between three different couriers (discrete)
    Use regression when both Y and X are continuous. Read Sandors model 3 and 1. Example : weight is dependent on age, time taken to deliver courier is dependent on distance etc
    Hope this helps
    Indresh

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    #158373

    Kiran Varri
    Participant

    Thanks for the insight.
    The details on this i found in Minitab is as follows:
    Anova differs from regression in 2 ways:
    1) The independent variables are Qualitative(categorial)
    2) No assumption is made about the nature of the relationship.
    Will appreciate if some one can elaborate on it….

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    #158375

    ANOVA/Regression
    Participant

    ANOVA and Regression are all part of the general linear model. ANOVA was “invented” in the 1920s as a computationally simpler formula for regression. An ANOVA can be run as a regression with dummy variables.

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    #158391

    annon
    Participant

    The basic functioning element of the anova is simply to compare within and between variances to determine if a significant difference exists between 2 or more means. 
    It  tells you if something is statistically different from something else.  This difference may still be practically insignificant.
    Regression will indicate the direction and magnitude of the of relationship between the predictor variables (ie inputs or Xs) and the response variable (ie output or Y).  The ANOVA table in this case tells you only if the input was significant statistically.  If not (see pvalue) then you remove it and rerun the model without it.
    Note that regression can be used for any combination of  data formats (variable X or Y, discrete X or Y)
    It will not illuninate interactive effects in your experiment or  curvlinearity (i think), although check the latter…You need DOE for this.
    Good luck.

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    #158394

    ANOVA/Regression
    Participant

    A few annotations to annon’s comparison of ANOVA and Regression:

    The Eta squared in an ANOVA table is the same as the R-squared in a regression analysis. The Eta/R-squared gives you the “practical significance” as a proportion of explained variance (Factor sum of squared/Total sum of squared).
    The F-test in ANOVA tells you the statistical significance.
    “Directionality” is implied in both regression and ANOVA. ANOVA was originally used in experimental data only. That is why the term “factor” is used in Minitab for example. Regression analysis was originally used for observational data and in survey research. That is why the term “predictor” is used in books talking about regression. In many cases you establish “concurrent predction”, i.e. the prediciton is not projected in the future but Variable Y is “predicted” from Variable X). So, “directionality” is not a function of the statistical formula (ANOVA vs. Regression) but of the assumptions that you make about the underlying relationship of the variables.
    There is a difference between research design (experimental vs. survey) and statistical analysis (ANOVA/Regression). Interaction effects can be analyzed in Regression using survey data by multiplying two independent variables and adding them as an additional variable in the equation. If this term is significant, you can establish an interaction effect.   
    In general, the confusion about ANOVA and Regression has come about because the two formulas for the statistically equivalent methodologies were developed by two competing schools of thought in biometric statistics. Originally, regression was applied to observational data, ANOVA to experimental data. Since the 1970s and with the development of the general linear model, it can be shown that they are part of the same family of statistics that make the assumption that variables can be viewed as a linear combination of each other.

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