REVIEWCOMPREHENSIVE-EXAM. BY bjohn MBpptx

COMPREHENSIVE EXAM
REVIEW
MSCJFC 2- STATISTICS FOR CRIMINAL JUSTICE EDUCATION

Review on Basic Concepts in Statistics
2
Statistics
Involves collection, organization,
summarization, presentation and
interpretation of data
Descriptive
Collect, organize,
summarize and present
data
Inferential
Interprets and draw
conclusion

3
VARIABLE/DATA
This refers to some specific characteristic
of a subject that assumes one or more
different values. (EX. Age)
Quantitative
numerical in nature
and can be ordered
or ranked
Qualitative
variables that can be placed
into distinct categories,
according to some
characteristic or attribute. (sex,
religion,blood type)

4
VARIABLE/DATA
Discrete
assume values that
can be counted
Continuous
can assume all values
between any two specific
values. They are obtained
by measuring

LEVEL OF DATA

VARIABLE OF INTEREST
 a changing quantity that is
measured
 factors of the study
 the thing being influenced
 Dependent variable

SAMPLING TECHNIQUES
Sampling is a technique of selecting individual members or a
subset of the population to make statistical inferences from them and
estimate characteristics of the whole population.

REVIEWCOMPREHENSIVE-EXAM. BY bjohn MBpptx

SLOVIN’S FORMULA
 FORMULA TO DETERMINE THE SAMPLE SIZE
N- Population Size
n- sample size
E-margin of error (e≤0.05)

Example: Determine the Sample Size
Region N n
1 500 0.2052*500 = 103
2 350 0.2052*350 = 72
CAR 700 0.2052*700= 143
Total 1550 318
N = 1550
n = 1550
1+ (1550 * (0.05)(0.05))
n = 1550
1+3.875
= 317.94 ~ 318
P = n/N =
318/1550=20.52%
0r 0.2052

Descriptive Statistics
Descriptive statistics can be used to summarize and
describe a single variable (aka, UNIvariate)
 Frequencies (counts) & Percentages
 Use with categorical (nominal) data
 Levels, types, groupings, yes/no, Drug A vs. Drug B
 Means & Standard Deviations
 Use with continuous (interval/ratio) data
 Height, weight, cholesterol, scores on a test

Interval & Ratio Data
Measures of central tendency and measures of dispersion are often computed with
interval/ratio data
 Measures of Central Tendency (aka, the “Middle Point”)
 Mean, Median, Mode
 If your frequency distribution shows outliers, you might want to use the median instead
of the mean
• Measures of Dispersion (aka, How “spread out” the data are)
― Variance, standard deviation, standard error of the mean
― Describe how “spread out” a distribution of scores is
― High numbers for variance and standard deviation may mean that scores are “all
over the place” and do not necessarily fall close to the mean
In research, means are usually presented along with standard deviations or standard errors.

Properties of Normal Distribution
 The curve is symmetric about the mean.
 Mean=Median=Mode
 The tail or ends are asymptotic relative
to the horizontal axis
 Each half represents 50% of
the total area.
 The total area under the normal
curve is 1 or 100%
Areas can be thought of as
probabilities. Areas could be written as percents. Areas can
not be negative.
 The normal curve area may be subdivided into standard
deviations, at least 3 units to the left and 3 units to the
right of the vertical line
17

18
Empirical Rule
-20 -10 0 10 20
0.00
0.02
0.04
0.06
0.08
Normal Density Plot
x
f(x)
The 68-95-99.7 Rule
In the normal distribution with
mean µ and standard deviation σ:
68% of the observations fall
within σ of the mean µ.
95% of the observations fall
within 2σ of the mean µ.
99.7% of the observations fall
within 3σ of the mean µ.
3σ 2σ
σ
σ
2σ3σ

Hypothesis
in statistics, is a claim or statement
about a property of a population
Hypothesis Testing
is to test the claim or statement

Two types of Hypothesis
 Null Hypothesis (denoted H0):
is the statement being tested in a test of
hypothesis.
 Alternative Hypothesis (H1):
is what is believe to be true if the null
hypothesis is false.

STATING THE HYPOTHESIS
 A researcher wants to determine if there is a significant
difference between the level of acceptance of the male and
female workers on the implementation of work from home
scheme.
Answer:
 a. Variable: ____________________________________
 b. Ho:__________________________________________
 c. Ha:___________________________________________

Type of Error in Hypothesis
Testing
Type 1 Error
 The mistake of rejecting the null hypothesis when it is true.
 Example: rejecting a perfectly good parachute and
refusing to jump
Type II Error
 the mistake of failing to reject the null hypothesis when it is false.
 denoted by ß (beta)
 Example: failing to reject a defective parachute and
jumping out of a plane with it.

Correlation
 When to use it?
 When you want to know about the association or relationship between two
continuous variables
 Ex) food intake and weight; drug dosage and blood pressure; air temperature and
metabolic rate, salary and savings
 What does it tell you?
 If a linear relationship exists between two variables, and how strong that relationship
is
 What do the results look like?
 The correlation coefficient = Pearson’s r
 Ranges from -1 to +1
 See next slide for examples of correlation results

Correlation
Guide for interpreting strength
of correlations:
 0 – 0.25 = Little or no
relationship
 0.25 – 0.50 = Fair degree of
relationship
 0.50 - 0.75 = Moderate
degree of relationship
 0.75 – 1.0 = Strong relationship
 1.0 = perfect correlation

T-tests
 When to use them?
 Paired t-tests: When comparing the MEANS of a continuous variable in two non-
independent samples (i.e., measurements on the same people before and after a treatment)
 Ex) Is diet X effective in lowering serum cholesterol levels in a sample of 12 people?
 Ex) Do patients who receive drug X have lower blood pressure after treatment then they did
before treatment?
 Independent samples t-tests: To compare the MEANS of a continuous variable in
TWO independent samples (i.e., two different groups of people)
 Ex) Do people with diabetes have the same Systolic Blood Pressure as people without diabetes?
 Ex) Do patients who receive a new drug treatment have lower blood pressure than those
who receive a placebo?
Tip: if you have > 2 different groups, you use ANOVA, which compares the means of 3 or more groups

LINEAR/MULTIPLE REGRESSION
• What is it?
 A statistical analysis that tests the relationship
between multiple predictor variables and one
continuous outcome variable
o Predictors: Any numbers of continuos or
dichotomous variable
o Outcome: continuous variable
• Commonly Associated Terms
Multivariate, statistical regression

REVIEWCOMPREHENSIVE-EXAM. BY bjohn MBpptx

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