Introduction to Statistics/ Statistical Procedures/ Examples

Level ofMeasurement
Average(CentralTendency)
Variation(Difference)
Relationship
Regression
Inferential Statistics/Hypothesis Testing

Nominal (type orkind)Example: Gender(male or female)
ModeThere are morefemales thanmales.
Index of Dispersion orIndex of QualitativeVariationThere is a strong variationin gender.
Chi Square, Cramer’s V orLambdaThere is a weakrelationship/associationbetween gender andmajor.*Chi Square value ranges0 to total N*Cramer’s V/Lambdavalue ranges 0 to 1
*Used for describing relationships and/or makingpredictions; Predicting the dependent variablebased upon the independent variable.A professor can predict how well students will doon an exam (dependent variable), based uponclass attendance (the independent variable).a (intercept): Persons will earn 40 points on theexam if we don’t know how many days theyattended class.b(slope): For every one day of attendancestudents will earn one-half point on the exam.r2(coefficient of determination): Ten percent ofthe variation in exam grades can be explained bydays of attendance.F sig. </= .05 (it is significant) model can be usedto make predictions; F sig. > .05 (it is notsignificant and can’t be used to make predictions)model can be used to describe relationshipsT sig. </= .05 (it is significant) the independentvariable can be used to predict the dependentvariable; T sig. > .05 (it is not significant and can’tbe used to make predictions) the independentvariable and dependent variable relationship canbe described can be used to describerelationships.
Inferential statistics allows the researcher to test forsignificance.7 Step Process#1 Describe the type of hypothesis to be used(difference, relationship, directional)#2 Confirm whether a parametric or non-parametrictest will be performed by running the KS Test fornormality KS sig. </= .05 is significant but NOTnormal; KS sig > .05 is not significant but IS normal#3 Run the parametric (one sample T test, TwoIndependent or Dependent Samples T Test, orANOVA test) or non-parametric (KS Test, MannWhitney U Test, or Wilcoxon Test) procedure#4 State the Null Hypothesis: There is no significantdifference in the test scores between male andfemale students.#5 State the Research Hypothesis Example: There is asignificant difference in the test scores betweenmale and female students.#6 Make a decision about the null hypothesis. Rejectthe null if the significance in item #3 is </= .05;Accept the null hypothesis if the significance in item#3 is > .05#7 Interpret:Example: There is a significant difference in the testscores between male and female students.

Ordinal (type,kind, or rank)Example:Student level(freshman,sophomore,junior, senior)
MedianThe averagestudent level issophomore.
RangeThere are three studentlevels around the medianstudent level of junior.
Spearman’s Rho orGammaThere is a strong positiverelationship betweenstudent level and studentplacement. As studentsgo from freshman tosenior year, theirplacement in the collegeranking also increases.*Value ranges -1 to +1

Interval/Ratio(type, kind, rank,or magnitude)Example: Age
MeanThe average ageis 23.
Standard DeviationStudent ages vary 5 yearsaround the mean of 23.
Pearson’s RThere is a weak negativerelationship betweenstudent age and salary.As student age increase,income decreases slightly.*Value ranges -1 to +1

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