business proposal

1. RESEARCH AND
STATISTICS
1
MASTER IN MANAGEMENT MAJOR IN EDUCATIONAL MANAGEMENT

2. PRESENTORS
(Riyadh Group)
TR. ROBERT DAYLE R. GUANZON
TR. LAUREN ANGELIE L. NGARANGAD
TR. RONILLO H. MAPULA
TR. EMIL JOHN R. LATOSA II
TR. LOVELY MAE I. PANGANIBAN

4. TYPES OF ORGANIZATIONAL TOOLS
▰ FREQUENCY DISTRIBUTION
▰ GRAPHS
▰ HISTOGRAM
▰ FREQUENCY DISTRIBUTION
4

5. FREQUENCY DISTRIBUTION
A table in which all of the scores are listed along with
the frequency with which each occurs.
5
FREQUENCY AND RELATIVE FREQUENCY
DISTRIBUTIONS OF EXAM DATA

6. CLASS INTERVAL
FREQUENCY DISTRIBUTION
A table in which the scores are grouped into intervals
and listed along with the frequency of scores in each interval.
6
CLASS INTERVAL FREQUENCY
DISTRIBUTIONS OF EXAM DATA

7. BAR GRAPHS
A bar graph is a graphical representation of a
frequency distribution in which vertical bars are centered
above each category along the x-axis and are separated from
each other by a space, indicating that the levels of the variable
represent distinct, unrelated categories.
7
BAR GRAPH REPRESENTING
POLITICAL AFFILIATION
FOR A DISTRIBUTION OF
30 INDIVIDUALS

8. HISTOGRAMS
A graphical representation of a frequency distribution
in which vertical bars centered above scores on the x-axis
touch each other to indicate that the scores on the variable
represent related, increasing values.
8
HISTOGRAM
REPRESENTING IQ SCORE DATA
FOR 30 INDIVIDUALS

9. FREQUENCY POLYGONS
A line graph of the frequencies of individual scores.
9
FREQUENCY POLYGON
OF IQ SCORE DATA FOR
30 INDIVIDUALS

10. DESCRIPTIVE STATISTICS
Descriptive statistics are numerical measures that
describe a distribution by providing information on the central
tendency of the distribution, the width of the distribution, and
the distribution’s shape.
10

11. MEASURE OF CENTRAL TENDENCY
A measure of central tendency is a representative
number that characterizes the “middleness” of an entire set of
data. The three measures of central tendency are the mean,
the median, and the mode.
11

12. TYPES OF CENTRAL
TENDENCY MEASURES
▰ MEAN
▰ MEDIAN
▰ MODE
12

13. Mean
The mean is the arithmetic
average of a group of scores. Not for use
with distributions with a few extreme
scores.
13
FREQUENCY DISTRIBUTION OF EXAM
SCORES, INCLUDING fX COLUMN

14. Median
The median is the middle score
in a distribution after the scores have
been arranged from highest to lowest or
lowest to highest.
14
YEARLY SALARIES FOR
25 EMPLOYEES

15. Mode
A measure of central tendency; the score in a distribution
that occurs with the greatest frequency.
15
Name John Alex Mark Paul Anthony Caleb
Marks
Obtained
(out of 100)
73 80 73 70 73 65

16. MEASURE OF VARIATION
A measure of variation indicates the degree to which
scores are either clustered or spread out in a distribution.
16
TWO
DISTRIBUTIONS OF
EXAM SCORES

17. THREE MEASURES OF VARIATION
▰ RANGE
▰ AVERAGE DEVIATION
▰ STANDARD DEVIATION
17

18. Range
A measure of variation; the difference between the lowest and
the highest scores in a distribution.
18
Standard Deviation
A measure of variation; the average difference between the scores in the
distribution and the mean or central point of the distribution, or more precisely, the
square root of the average squared deviation from the mean.
Average Deviation
An alternative measure of variation that, like the standard deviation,
indicates the average difference between the scores in a distribution and the mean
of the distribution.

19. TYPES OF DISTRIBUTIONS
▰ NORMAL DISTRIBUTIONS
▰ POSITIVELY SKEWED DISTRIBUTIONS
▰ NEGATIVELY SKEWED DISTRIBUTIONS
19

20. NORMAL DISTRIBUTION
A theoretical frequency distribution that has certain special
characteristics. It is a symmetrical bell-shaped unimodal curve.
20
A NORMAL
DISTRIBUTION

21. POSITIVELY SKEWED DISTRIBUTIONS
A distribution in which the peak is to the left of the center point, and the
tail extends toward the right, or in the positive direction. It is a lopsided curve with
a tail extending toward the positive or right side.
NEGATIVELY SKEWED DISTRIBUTIONS
A distribution in which the peak is to the right of the center point, and the
tail extends toward the left, or in the negative direction. It is a lopsided curve with a
tail extending toward the negative or left side.
POSITIVELY SKEWED
DISTRIBUTIONS
NEGATIVELY SKEWED
DISTRIBUTIONS
21

22. CORRELATIONAL
METHODS AND
STATISTICS

23. CONDUCTING CORRELATIONAL
RESEARCH
The correlational method is a type of
nonexperimental method that describes the
relationship between two measured variables.
Correlations allow us to make predictions from one
variable to another. If two variables are correlated,
we can predict from one variable to the other with a
certain degree of accuracy.
CORRELATIONAL METHODS
AND STATISTICS 23

24. TYPES OF RELATIONSHIPS
▰ POSITIVE
▰ NEGATIVE
▰ NONE
▰ CURVILINEAR
CORRELATIONAL METHODS
AND STATISTICS 24

25. POSITIVE RELATIONSHIPS
The variables increase and decrease together.
CORRELATIONAL METHODS
AND STATISTICS 25
Positive Relationship

26. NEGATIVE RELATIONSHIPS
As one variable increases, the other decreases—an
inverse relationship.
CORRELATIONAL METHODS
AND STATISTICS 26
Negative Relationships

27. NO RELATIONSHIPS
Variables are unrelated and do not move together in
any way.
CORRELATIONAL METHODS
AND STATISTICS 27
No Relationships

28. CURVILINEAR RELATIONSHIPS
Variables increase together up to a point and then as
one continues to increase, the other decreases.
CORRELATIONAL METHODS
AND STATISTICS 28
Curvilinear Relationships

29. MISINTERPRETING CORRELATIONS
CORRELATIONAL METHODS
AND STATISTICS 29
Types of Misinterpretations:
▰ CAUSALITY AND DIRECTIONALITY
▰ THIRD VARIABLE
▰ RESTRICTIVE RANGE
▰ CURVILINEAR RELATIONSHIP

30. CAUSALITY AND DIRECTIONALITY
Causality refers to the assumption that the correlation
indicates a causal relationship between two variables,
whereas directionality refers to the inference made with
respect to the direction of a causal relationship between two
variables.
CORRELATIONAL METHODS
AND STATISTICS 30
Misinterpretation: We assume the correlation is causal and
that one variable causes changes in the other.

31. THE THIRD-VARIABLE PROBLEM
The third-variable problem results when a correlation
between two variables is dependent on another (third)
variable.
CORRELATIONAL METHODS
AND STATISTICS 31
Misinterpretation: Other variables are responsible for the
observed correlation.

32. RESTRICTIVE RANGE
A variable that is truncated and has limited variability.
CORRELATIONAL METHODS
AND STATISTICS 32
Misinterpretation: One or more of the variables is truncated or
restricted and the opportunity to observe a relationship is
minimized.

33. CURVILINEAR RELATIONSHIP
Variables increase together up to a point and then as
one continues to increase, the other decreases.
CORRELATIONAL METHODS
AND STATISTICS 33
Misinterpretation: The curved nature of the relationship
decreases the observed correlation coefficient.

34. PREDICTION AND CORRELATION
Correlation coefficients not only describe the
relationship between variables; they also allow you to make
predictions from one variable to another.
Correlations between variables indicate that when one
variable is present at a certain level, the other also tends to be
present at a certain level.
CORRELATIONAL METHODS
AND STATISTICS 34

35. STATISTICAL ANALYSIS:
CORRELATION COEFFICIENT
CORRELATIONAL METHODS
AND STATISTICS 35
TYPES OF COEFFICIENTS:
▰ Pearson
▰ Spearman
▰ Point-Biserial
▰ Phi

36. PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT
(Pearson’s r )
The most commonly used correlation coefficient is the
Pearson product-moment correlation coefficient, usually
referred to as Pearson’s r (r is the statistical notation we use
to report this correlation coefficient).
It is the most commonly used correlation coefficient
when both variables are measured on an interval or ratio
scale.
CORRELATIONAL METHODS
AND STATISTICS 36

37. SPEARMAN’S RANK-ORDER
CORRELATION COEFFICIENT
The correlation coefficient used when one (or more) of
the variables is measured on an ordinal (ranking) scale.
CORRELATIONAL METHODS
AND STATISTICS 37
POINT-BISERIAL
CORRELATION COEFFICIENT
The correlation coefficient used when one of the
variables is measured on a dichotomous nominal scale, and
the other is measured on an interval or ratio scale.

38. PHI COEFFICIENT
The phi correlation coefficient (phi) is one of a number
of correlation statistics developed to measure the strength of
association between two variables. The phi is a nonparametric
statistic used in cross-tabulated table data where both
variables are dichotomous.
CORRELATIONAL METHODS
AND STATISTICS 38

39. ADVANCED CORRELATIONAL
TECHNIQUES: REGRESSION ANALYSIS
CORRELATIONAL METHODS
AND STATISTICS 39
Regression Analysis
A procedure that allows us to predict
an individual’s score on one variable based on
knowing one or more other variables.
Regression Line
The best-fitting straight line drawn through
the center of a scatterplot that indicates the
relationship between the variables.
THE RELATIONSHIP BETWEEN
HEIGHT AND WEIGHT WITH THE
REGRESSION LINE INDICATED

40. HYPOTHESIS TESTING
AND INFERENTIAL
STATISTICS

41. What is hypothesis testing?
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 41
It is the process of determining
whether a hypothesis is supported by
the results of a research project.

42. NULL HYPOTHESIS
The hypothesis stating that the independent
variable has no effect and that there will beno
difference between the two groups.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 42

43. ALTERNATIVE HYPOTHESIS OR
RESEARCH HYPOTHESIS
The hypothesis stating that the independent
variable has an effect and that there will be a
difference between the two groups.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 43

44. TWO-TAILED OR
NONDIRECTIONAL TEST
An alternative hypothesis stating that a
difference is expected between the groups, but there
is no prediction as to which group will perform better
or worse.
The mean of the sample will be different from
or unequal to the mean of the general population.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 44

45. ONE-TAILED OR
DIRECTIONAL TEST
An alternative hypothesis stating that a
difference is expected between the groups, and it is
expected to occur in a specific direction.
The mean of the sample will be greater than
the mean of the population, or the mean of the
sample will be less than the mean of the population.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 45

46. TYPE I ERROR
The error of rejecting H0 when we should have
failed to reject it.
This error in hypothesis testing is equivalent to
a “false alarm,” saying that there is a difference when
in reality there is no difference between the groups.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 46

47. TYPE II ERROR
The error of failing to reject H0 when we should
have rejected it.
This error in hypothesis testing is equivalent to
a “miss,” saying that there is not a difference
between the groups when in reality there is.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 47

48. STATISTICAL SIGNIFICANCE
When the probability of a Type I error is low
(.05 or less).
The difference between the groups is so large
that we conclude it is due to something other than
chance.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 48

49. INFERENTIAL STATISTICS
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 49
Inferential statistical procedures that require certain assumptions about
the parameters of the population represented by the sample data, such as knowing
and and that the distribution is normal. Most often used with interval or ratio data
PARAMETRIC INFERENTIAL STATISTICS
Inferential procedures that do not require assumptions about the
parameters of the population represented by the sample data; and are not needed,
and the underlying distribution does not have to be normal Most often used with
ordinal or nominal data.
NONPARAMETRIC INFERENTIAL STATISTICS

50. THE Z TEST:
What it is and What it does
The z test is a parametric statistical test that allows us
to test the null hypothesis for a single sample when the
population variance is known.
This procedure allows us to compare a sample with a
population to assess whether the sample differs significantly
from the population.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 50

51. SAMPLING DISTRIBUTION
A sampling distribution is a distribution of sample
means based on random samples of a fixed size from a
population.
Used for comparative purposes for z tests—a sample
mean is compared with the sampling distribution to assess
the likelihood that the sample is part of the sampling
distribution.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 51

52. THE STANDARD ERROR OF THE MEAN
The standard deviation of the sampling distribution.
Used in the calculation of z.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 52

53. THE t TEST:
What It Is and What It Does
The t test for a single sample is similar to the z test in
that it is also a parametric. The t test for a single sample is
similar to the z test in that it is also a parametric statistical
test of the null hypothesis for a single sample. statistical test
of the null hypothesis for a single sample.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 53

54. The Chi-Square (X
2) Goodness-of-Fit Test:
What It Is and What It Does
The chi-square (
X
2) goodness-of-fit test is a
nonparametric statistical test used for comparing categorical
information against what we would expect based on previous
knowledge.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 54

55. CORRELATION COEFFICIENTS AND
STATISTICAL SIGNIFICANCE
Correlation Coefficients are used to describe the
strength and direction of a relationship between two variables.
Statistical significance is a measure of how unusual
your experiment results would be if there were actually no
difference in performance between your variation and
baseline and the discrepancy in lift was due to random chance
alone.
HYPOTHESIS TESTING AND
INFERENTIAL STATISTICS 55

56. FOR LISTENING!
-RIYADH GROUP
56
THANK
YOU