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Steps in Writing an Academic Article

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Steps in Writing an Academic Article. Introduction (tell cute story) Literature Review ... NOTE: We rarely have data for the population. ... – PowerPoint PPT presentation

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Title: Steps in Writing an Academic Article


1
Steps in Writing an Academic Article
  • Introduction (tell cute story)
  • Literature Review
  • Describe Data
  • Create model
  • Identify dependent variable
  • Identify independent variables
  • State hypothesis
  • Estimate model

2
Data Summary and Description
  • Population Parameters Summary and descriptive
    measures for the population.
  • Sample Statistics Summary and descriptive
    measures for a sample.
  • NOTE We rarely have data for the population.
    Hence we need to be able to draw inferences from
    a sample.

3
Measures of Central Tendency
  • Mean The average
  • Issue You must note the distribution of the
    sample. If it is unbalanced the mean may be
    misleading.
  • Median Middle observation

4
Symmetrical vs. Skewness
  • Symmetrical A balanced distribution. Median
    Mean
  • Skewness A lack of balance.
  • Skewed to the left Median Mean
  • Skewed to the right Median
  • Again, if the data is skewed, the average will be
    misleading.

5
Measures of Dispersion
  • Range Difference between the largest (maximum)
    and smallest (minimum) sample observations.
  • Only considers the extremes of the sample
  • Variance and Standard Deviation
  • Sample Variance Average squared deviation from
    the sample mean.
  • Sample Standard Deviation Squared root of the
    sample variance.
  • NOTE These are used when we discuss competitive
    balance in sports.

6
Hypothesis Testing
  • Hypothesis Testing Statistical experiment used
    to measure the reasonableness of a given theory
    or premise
  • NOTE WE DO NOT PROVE A THEORY
  • Type I Error Incorrect rejection of a true
    hypothesis.
  • Type II Error Failure to reject a false
    hypothesis.

7
Regression AnalysisDefinitions
  • Regression analysis statistical method for
    describing the relationship between a dependent
    variable Y and independent variable(s) X.
  • Deterministic Relation An identity
  • A relationship that is known with certainty.
  • Statistical Relation An inexact relation
  • We use regression analysis for statistical
    relations, not deterministic.

8
Regression AnalysisTypes of Data
  • Time series A daily, weekly, monthly, or annual
    sequence of data. i.e. Attendance data for the
    49ers from 1970 to 2007.
  • Cross-section Data from a common point in time.
    i.e. Attendance data for each team in the NFL for
    the 2007 season.
  • Panel data Data that combines both
    cross-section and time-series data. i.e.
    Attendance data for each team in the NFL from
    1970 to 2006.

9
The Least Squares Model
  • Ordinary Least Squares a statistical method that
    chooses the regression line by minimizing the
    squared distance between the data points and the
    regression line.
  • Why not sum the errors? Generally equals zero.

10
The Error Term
  • Error term (e) random, included because we do
    not expect a perfect relationship.
  • Sources of error
  • Omitted variables
  • Measurement error
  • Incorrect functional form

11
Univariate Analysis
  • Y a bX Where
  • Y The Dependent Variable, or what you are
    trying to explain (or predict).
  • X The Independent Variable, or what you believe
    explains Y.
  • a the y-intercept or constant term.
  • b the slope or coefficient

12
The t-statistic
  • To evaluate the quality of our slope coefficient
    we refer to the
  • t-statistic.
  • T-statistic slope coefficient / standard error
  • Standard error - estimated standard deviation of
    the coefficient
  • Rule of thumb T-stat 2
  • This is in absolute terms.
  • In other words, the coefficient should be more
    than double the standard error.
  • Why is this important? We want to know whether or
    not the coefficient is statistically different
    from zero.

13
Statistical vs. Economic Significance
  • Just because we find a statistically significant
    relationship, that does not mean we have found
    something important.
  • You should understand the difference between
    statistical significance and economic
    significance.

14
The slope coefficient
  • How do we interpret the slope coefficient?
  • Example
  • WINS -82.5 1.3(Points per game)
  • Each additional one point per game results in a
    1.3 more wins.
  • Is this the truth? We never know the truth, we
    are simply attempting to derive estimates.
  • Is this a good estimate? Clearly points alone
    do not explain wins (and consequently, this is a
    bad estimate).

15
The constant term
  • How do we interpret the constant term?
  • The constant term must be included in the
    regression, or else we are forcing the regression
    line through zero.
  • The constant term is used captures all the
    factors not explicitly utilized in the equation.
  • The constant term is theoretically the value of Y
    when X is zero. Frequently this is outside the
    range of possibility, and therefore the constant
    term should not be interpreted.

16
Multivariate Analysis
  • Introducing the idea of ceteris paribus.
  • Ceteris paribus holding all else constant
  • One cannot impose ceteris paribus unless all
    relevant variables are included in the model.

17
Wins and ORB
18
Wins and Missed Shots
19
Offensive Rebounds and Missed Shots
20
Wins, ORB, and Missed Shots
  • Wins -57.8 - 1.3ORB
  • As illustrated earlier, the estimated impact of
    offensive rebounds (ORB) on wins is negative.
  • Wins 149.4 - 2.4(Missed Shots)
  • ORB -5.1 0.4(Missed Shots)
  • In words, missed shots and offensive rebounds are
    positively related. So when we estimate wins as
    a function of offensive rebounds, we are simply
    picking up the relationship between wins and
    missed shots.

21
R-squared
  • How do we know how accurate our equation is?
  • R-squared How much variation your model
    explained divided by how much variation there was
    to explain.
  • Or, how much variation did our model explain.
  • In more technical terms.
  • R-squared Explained Sum of Squares / Total Sum
    of Squares

22
TSS, ESS, RSS in words
  • Total Sum of Squares TSS How much variation
    there is to explain.
  • Explained Sum of Squares ESS How much
    variation you explained.
  • Residual Sum of Squares RSS How much
    variation you did not explain.

23
TSS, ESS, RSS in math
  • TSS ESS RSS
  • Total sum of squares Sum of the squared
    difference between the actual Y and the mean of
    Y, or,
  • TSS ?(Yi - mean of Y)2
  • Explained sum of squares Sum of the squared
    differences between the predicted Y and the mean
    of Y, or,
  • ESS ?(Y - mean of Y)2
  • Residual sum of squares Sum of the squared
    differences between the actual Y and the
    predicted Y, or,
  • RSS TSS - ESS
  • RSS ? e2

24
Adjusted R-Squared
  • Adding any independent variable will increase R2.
  • To combat this problem, we often report the
    adjusted R2.

25
Model Evaluation
  • It is important to note that R-squared tells us
    something, but it is not everything.
  • Low R-squared does not necessarily mean the model
    is bad, high R-squared does not necessarily mean
    the model is good.
  • Models must be theoretically sound. In other
    words, we do not play with data until we get a
    model with the highest r-squared. You have to
    have a reason why your model is constructed as
    you suggest.

26
Multicollinearity
  • Multicollinearity - more than two independent
    variables exhibit a linear correlation.
  • Example Including total rebounds and defensive
    rebounds in the same model.
  • Consequences
  • Standard errors will rise, t-stats will fall
  • What does that mean? You will think variables are
    insignificant when they are not.

27
Other Issues
  • Omitted Variable Bias You cannot impose ceteris
    paribus if relevant independent variables are not
    included in the model.
  • Small Sample Bias You cannot adequately assess a
    relationship with an inadequate sample.
    Remember, we are trying to learn about the
    underlying population.
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