Quantitative Methods 1

Miriam Niblack

DEPM 650

Section: 9040

April 22, 2015

Quantitative Method

DEPM 650 Assignment # 3 – Quantitative Methods

Report on Data Analysis

Quantitative Methods 2

Quantitative Research (QR) is about measuring numerical results (Woodley, 2004). In natural

and social sciences, QR is the investigation of observable phenomena via statistical, computable,

or mathematical techniques (Zawacki-Richter, Bäcker, & Vogt, 2009).

Task # 1 – Frequencies, bar chart

Answer Solutions Statistics: Research areas N Valid 695 Missing 0

Questions:

(a) Frequency Table for variable research areas

1. Frequency - how many times each score occurs (Field, 2013). Central tendency

(averages) is used to calculate “where the centre of frequency distribution lies” (Filed, 2013, p.

21). There are three kinds of averages and these measures are commonly used: mean, median,

and mode (Field, 2013).

Research areas

Frequency Percent Valid Percent Cumulative Percent

Valid Access, equity and ethics 31 4.5 4.5 4.5

Globalisation of education and cross-

cultural aspects 13 1.9 1.9 6.3

Distance teaching systems and

institutions 62 8.9 8.9 15.3

Theories and models 24 3.5 3.5 18.7

Research methods in distance

education and knowledge transfer 13 1.9 1.9 20.6

Management and organisation 18 2.6 2.6 23.2

Costs and benefits 12 1.7 1.7 24.9

Educational technology 48 6.9 6.9 31.8

Innovation and change 13 1.9 1.9 33.7

Professional development and faculty

support 41 5.9 5.9 39.6

Learner support services 23 3.3 3.3 42.9

Quality assurance 41 5.9 5.9 48.8

Instructional design 121 17.4 17.4 66.2

Interaction and communication in

learning communities 122 17.6 17.6 83.7

Learner characteristics 113 16.3 16.3 100.0

Total 695 100.0 100.0

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(b) Bar Chart for variable research areas

(c) Report research area with highest and lowest number of articles.

Highest: Interaction and communication in learning communities 122 articles

Lowest: Globalization of education and cross-cultural aspects 13 based on cumulative percent

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Task # 2 – Boxplots

Answer Solutions

Questions:

(a) Boxplot for research area and the ratings of importance 1-10 scale

Case Processing Summary

Cases

Valid Missing Total

N Percent N Percent N Percent

1. Access, equity and ethics 21 100.0% 0 0.0% 21 100.0%

2. Distance teaching

institutions 21 100.0% 0 0.0% 21 100.0%

3. Globalisation of education

and cross-cultural aspects 21 100.0% 0 0.0% 21 100.0%

4. Theories and models 21 100.0% 0 0.0% 21 100.0%

5. Research methods in

distance education and

knowledge transfer

21 100.0% 0 0.0% 21 100.0%

6. Management &

organisation 21 100.0% 0 0.0% 21 100.0%

7. Costs and benefits 21 100.0% 0 0.0% 21 100.0%

8. Educational technology 21 100.0% 0 0.0% 21 100.0%

9. Innovation and change 21 100.0% 0 0.0% 21 100.0%

10. Professional

development and faculty

support

21 100.0% 0 0.0% 21 100.0%

11. Learner support services 21 100.0% 0 0.0% 21 100.0%

12. Quality assurance 21 100.0% 0 0.0% 21 100.0%

13. Instructional design 21 100.0% 0 0.0% 21 100.0%

14. Interaction and

communication in learning

communities

21 100.0% 0 0.0% 21 100.0%

15. Learner characteristics 21 100.0% 0 0.0% 21 100.0%

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(b) Report median, interquartile range, and standard deviation for research area Globalization of

education and cross-cultural aspects

1. Median is the middle value or score and is used to quantify the centre of distribution by

looking at the middle score when scores are ranked (Field, 2013).

2. Quartiles are three values where the data are split into four equal parts (Field, 2013).

Interquartile range (IQR) center is median where the top 25% and bottom 25% are cut off and

only the middle 50% of scores are used (Field, 2013). Range is the “largest score subtracted by

the smallest” (Field, 2013, p. 24). Compute the range by “excluding 50% of scores and using

only the middle 50%” (Field, 2013, p. 22).

3. Standard Deviation is a measure of how spread out numbers are of how the mean

represents the data; where a large deviation reflects that data points are distant from the mean

(Zawacki-Richter, Bäcker, & Vogt, 2009). This measure is used to quantify the amount of

Quantitative Methods 6

variation or dispersion of a set of data values and is the square root of the variance; “variance is

the average error between the mean and the observations made” (Field, 2013, p.27).

Measures of Globalization of education and cross-cultural aspects:

Median = 7.00 is the middle score at least 50% of all responses; other half of all responses are on

either side meaning < or > than 7.

Standard deviation is 1.713 is the square root of the variance and shows how distant the mean is

from the data.

IQR= 7 where the middle 50% of scores are. Therefore, at least half of all responses were 7 on a

scale of 1 – 10.

Statistics

3. Globalisation of education and cross-

cultural aspects

N Valid 21

Missing 0

Median 7.00

Std. Deviation 1.713

Percentiles 25 6.00

50 7.00

75 9.00

3. Globalisation of education and cross-cultural aspects

Frequency Percent Valid Percent

Cumulative

Percent

Valid 4 1 4.8 4.8 4.8

5 1 4.8 4.8 9.5

6 7 33.3 33.3 42.9

7 2 9.5 9.5 52.4

8 3 14.3 14.3 66.7

9 5 23.8 23.8 90.5

very HIGH importance = 10 2 9.5 9.5 100.0

Total 21 100.0 100.0

(c) Describe how to interpret box plot of Globalization

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The boxplot provides an overview of the ratings on 10 point scale with 1 being least important

and 10 being highest importance Globalization.

They show:

the lowest and highest score

the middle score (interquartile range) in the tinted box

the top and bottom 25% of scores

the median

Task # 3 – Chi-square test

Answer Solutions

Questions:

(a) Create cross tab with variable Research area and Gender

1. Cross tabulation allows you to compare the relationship between two variables and see

how all jointly characterized (Zawacki-Richter, Bäcker, & Vogt, 2009).

Quantitative Methods 8

Totals: 384 Males 311 Females N = 695

(b) Run chi-square test and bar chart for above variables chi-square test formula:

Chi-square test is non-parametric and compares numbers actually in each cell that are observed

with what is expected to be there (Woodley, 2004). The bigger the chi-square result the more

likely results have not occurred by chance (Woodley, 2004).

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(c) Discuss results. Statistical significance between above variables? Which research area do

women publish more frequently than their male colleagues?

The association between gender and research areas is statistically not significant, x^2 = 51.76, df

= 14, p<.05. Women publish more than their male colleagues in the research topic of interaction

and communication learning communities.

Task #4 – Comparing two means: t-test

T-test is a form of the more powerful parametric test in which power refers to the “probability of

rejecting the null hypothesis when it is in fact false” (Woodley, 2004, p. 150). This tests relies on

assumptions; therefore, testing whether a distribution is normal is best (Woodley, 2004).

According to Field (2013), “degrees of freedom relate to the number of observations that are free

to vary” (p. 49) such as one less than the number of choices available.

Answer Solutions

Questions:

Female students are better in statistics…Is this true?

(a) Report mean of EXAMSCORE of male/female students

Statistics

GENDER Exam score

N Valid 427 386

Missing 0 41

Mean 56.05

M=56.05

GENDER

Frequency Percent Valid Percent

Cumulative

Percent

Valid female 188 44.0 44.0 44.0

male 239 56.0 56.0 100.0

Total 427 100.0 100.0

The average EXAMSCORE of females and males students:

Mean = 56.05

(b)Test hypothesis – H1: Female students achieve higher exam scores than males.

Quantitative Methods 10

Hypothesis is an explanation for events that needs to be tested. QR is used by “evaluating and

explanation, measuring concepts, and variables” (Cohen et al., 2007, p. 179). QR aims to

“observe what is invisible” (Cohen et al., 2007, p.180) and it begins with an abstract idea,

followed by measurement procedures, and ends with empirical data (Cohen et al., 2007).

Quantitative method is designed for testing hypotheses by collecting numerical data (Neumann,

2007). QR is used collaboratively to increase efficiency through division of labor as analyzing

data is more complex (Hunter & Leahey, 2008). Quantitative researchers “adopt a deductive

approach” (Neumann, 2007, p. 179) to test measures that can be expressed in numbers.

According to Cohen, Manion, & Morrison (2011), “People attempt to comprehend the world

around them by using three types of reasoning: deductive reasoning, inductive reasoning and the

combined inductive-deductive approach. Deductive reasoning is based on the syllogism,” (p. 6).

Group Statistics

GENDER N Mean Std. Deviation Std. Error Mean

Exam score female 166 58.57 13.278 1.031

male 220 54.15 14.281 .963

(b) Report Results.

The independent samples t-test is used to test two experimental groups that are assigned

to each condition (Field, 2013). Levene’s test the assumption is fulfilled.

The mean difference for EXAMSCORE for males and females is 4.422.

The t-statistic is calculated by diving the mean difference by the standard error (t =

3.104)

For the independent t-test, degrees of freedom are calculated by adding the two sample

sizes and then subtracting the number of samples: df = 166 + 220-2 = 384.

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The two-tailed significance value of t is .002 which is lower than .05 (the 95%

confidence interval value), so we can reject the null hypothesis and conclude that female

students did achieve higher scores than the male students.

Thus, we can report this result as:

On average, females achieved higher EXAMSCORES (M=58.57, SD=13.278), than males

(M=54.15, D=.963). This difference is significant, t (384) = 3.104, p<.01.

Task #5 – Bivariate correlation

Bivariate correlation “which is the correlation between two variables” (Field, 2013, p. 267).

Correlation expressed the strength between variables in a value between -1 and +1; where -1 is

negative correlation as if one increases the other variable decreases, +1 positive correlation as

one variable increases so does the other, and 0 means no relationship (Field, 2013).

Answer Solutions

Questions:

(a) Correlation test between number of authors and number of references.

Correlations

No. of authors No. of references

No. of authors Pearson Correlation 1 -.029

Sig. (2-tailed) .446

N 695 695

No. of references Pearson Correlation -.029 1

Sig. (2-tailed) .446

N 695 695

(b) Report Results. Correlation coefficient refers to how changes in one variable relate to changes in

another (Woodley, 2004). Correlation coefficient is interpreted through use of Pearson’s correlation

coefficients (Pearson’s r) since the levels of measurement of the number of authors and references are

both scale, which is used measure the relationship between the two variables (Field, 2013).

There is no significant association between no. of authors and references, r = -.029, p<.05.

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References

Cohen, L., Manion, K., Morrison, K. (2011). Research Methods in Education (7th ed.). Chapter

1 (The Nature of Inquiry – Setting the Field).

Field, A. (2013). Discovering statistics using SPSS (4th ed.). Thousand Oaks: Sage.

Hunter, L., & Leahey, E. (2008). Collaborative research in sociology: trends and contributing

factors. The American Sociologist, 39(4), 290-306.

Neumann, W. L. (2007). Social research methods: Qualitative and quantitative approaches.

Boston: Pearson. Chapter 7: Qualitative and Quantitative Measurement.

Woodley, A. (2004). Getting and analysing quantitative data. Vancouver: PREST,

Commonwealth of Learning (COL).

Zawacki-Richter, O., Bäcker, E. M., & Vogt, S. (2009). Review of distance education research

(2000 to 2008) – analysis of research areas, methods, and authorship patterns.

International Review of Research in Open and Distance Learning, 10(6), 21-50.