Spss dr arsay wm

UNIVERSITI UTARA MALAYSIA

SPSS WORKSHOP 16 JUNE 2013 ARSAYTHAMBY VELOO arsay@uum.edu.my

1. Define Variable

2. Enter Data

OUR AGENDA‌ 4. Data screening

3. Recode and Compute

Stages of the Research Process

L I T E R A T U R E

Problem Discovery and Definition

Research Design

L I T E R A T U R E

Discovery and Definition

and so on Conclusions and Report

Sampling Data Processing and Analysis Data Gathering

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Statistics There are two types of statistics: ď Ž Descriptive statistics. ď Ž Inferential statistics.

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Descriptive statistics Central Tendency.

Mean, Median, Mode  Variability Range, Variance, Standard Deviation Standard Score Z score / T score 

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Inferential Statistics Parametric.

T-test, ANOVA, Correlation, etc.  Non-Parametric.

Chie-square, Man-whitney, Wilcoxon Sign Rank Test, Spearman, Friedman Two Way ANOVA 

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Levels of Measurement

Nominal Low

Ordinal

Interval

Ratio

High More Information

Variable and Values Variable

Gender Male

Values Female

Variable and Values Variable

Age

Values

0, 1, 2, …. 20, 21, 22, …, 40, 41, 42, ….60, 61, 62, ….

Example: Income Did your annual income exceed US $5K last year?

What was the amount of your income last year?

What was the amount of your income last year?

1. Less than $3K 1.Yes

2. $3.1K - $5K

2.No

3. $5.1K - $10K 4. More than $10K

Nominal

Ordinal

US $ __________

Ratio

Percentile Rank 22 43 53 58 68 28 44 54 59 72

Raw Score

Tally

Freq

Cum. Freq.

Cum.Freq.( %) Percentile Rank

 80

{ <90 }

//

2

50

100

31 45 54 61 73

70 –79

{ <80 }

///// //

7

48

96

33 45 55 62 74

60 – 69 { <70 }

///// ////

9

41

82

35 46 55 64 75

50 – 59 { <60 }

///// ///// ////

14

32

64

40 – 49 { <50 }

///// /////

10

18

36

30 – 39 { <40 }

///// /

6

8

16

< 30

//

2

2

4

35 47 55 64 75 37 48 56 65 76 39 49 56 65 77 40 50 57 66 84 42 52 58 68 88

SPSS Data Editor Data View Variable View Name, Type, Width, Decimals, Label, Values, Missing, Columns, Align, Measure

Different Types of Scores in a Normal Distribution

Working With Data Compute -To sum or average

Recode ( - & + worded items) i. ii.

I enjoying my course I hate my course

1. Hypotheses testing

2. Assumption

OUR AGENDAâ&#x20AC;Ś 4. Analysing and Interpretation

3. Type of t-test 29

Degree of Problem Definition Exploratory Research (Unaware of Problem) “Our sales are declining and we don’t know why.”

“Would people be interested in our new product idea?”

Descriptive Research (Aware of Problem)

Causal Research (Problem Clearly Defined)

“What kind of people are buying “Will buyers purchase more of our product? Who buys our our products in a new package? competitor’s product?”

“Which of two advertising “What features do buyers prefer campaigns is more effective?” in our product?”

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Inferential Statistics â&#x20AC;˘ Inferential statistics are used to draw conclusions and make generalizations about a population based upon data gathered from a sample drawn from that population.

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Statistical Analyses The type of statistical analysis used depends on:

• Scale of measurement: the type of data collected.

• Random sampling: randomly sampled from the population of interest.

• Normality: the scores should be normally distributed in the population.

• the research question being addressed 32

Types of Data • Nominal Data (Unordered Categories).

• Ordinal Data (Ordered Categories).

• Interval Data (Measured Variables).

• Ratio Data (Counts).

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Normal Distributions • Normal distribution is also called a probability distribution.

• Normal distribution is a special type of frequency distribution which is generated from a variable that is “normally distributed.”

• If enough data are collected and if the intervals used are small enough, the result is a smooth curve called a “bell-shaped curve” or a normal distribution.

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Distribution Shapes: Normal

Mean =15.036

Median = 15.035

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Box-and-Whisker Plots max point 1.5 IQ units from box

mean

75th percentile 50th percentile median 25th percentile min point 1.5 IQ units from box more than 1.5 IQ units from box

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ď Ź

A hypothesis is a proposition that is empirically testable. It is an empirical statement concerned with the relationship among variables.

ď Ź

A variable is anything that may assume different numerical values.

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Statistical Significance â&#x20AC;˘ Determines the extent to which the differences or relationships found may have occurred due to chance. â&#x20AC;˘ Determines whether the null hypothesis can be rejected and the research hypothesis can be accepted.

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Level of Statistical Significance • The level of statistical significance used to decide whether to reject or not reject the null hypothesis (or to accept or not accept the research hypothesis) is called either: the alpha, decision value, criterion level, confidence level, or significance level.

• The level of statistical significance obtained in a study is called the probability value (p).

• The most commonly used alpha in research is p < .05.

• A p equal to .05 means there is a ninety-five percent level of confidence that the results were not due to chance 40

Errors â&#x20AC;˘ Type I Error: A Type I Error entails the rejection of a null hypothesis that should not have been rejected.

(Accepting a research hypothesis that should not have been accepted.) â&#x20AC;˘ Type II Error: A Type II Error entails not rejecting a null hypothesis that should be rejected. (Not accepting a research hypothesis that should have been accepted.)

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T-test Testing Hypotheses Comparing Two Means

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Parametric Tests â&#x20AC;˘ Parametric tests are used to compare means if: 1. The data are interval or ratio data.

2. Random sampling: randomly sampled from the population of interest.

3. The data are normally distributed.

4. There is homogeneity of variance. *1 & 2 are a matter of Research design and not statistical analysis.

â&#x20AC;˘ Most common parametric test is the t-test.

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t-Tests â&#x20AC;˘ One sample t-test â&#x20AC;˘ Dependent or correlated samples (paired samples) use a t-test for paired samples. â&#x20AC;˘ Independent or uncorrelated samples (unpaired samples) use a t-test for unpaired samples.

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Summary of the statistical tests most commonly used to compare means: Samples Paired Samples Unpaired Samples

Parametric Test t-test for paired samples t-test for unpaired samples

Compare 2 or > means Interaction

One Way ANOVA

Correlation

Non-Parametric Test Wilcoxon signed ranks test Mann-Whitney U test

Kruskal-Wallis One Way ANOVA Two Way ANOVA Friedman Two Way ANOVA Pearson Correlation Spearmanâ&#x20AC;&#x2122;s Rho and Kendallâ&#x20AC;&#x2122;s Tau-B 45

A major oil company developed a petrol additive that was supposed to increase engine efficiency. Twenty-two cars were test driven both with and without the additive and the number of kilometers per litre was recorded. Whether the car was automatic or manual was also recorded. During an earlier trial, 22 cars were test driven using additive. The mean number of km per litre was 10.5.

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• • •

Are the cars in the present trial running more efficiently than those in the earlier trial?

Does engine efficiency improve when the additive is used?

Does engine efficiency with and without the additive differ between manual and automatic cars?

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t-Test for Difference of Means

1   2 t S X1  X 2 X1 = mean for Group 1 X2 = mean for Group 2 SX1-X2 = the pooled or combined standard error of difference between means.

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Degrees of Freedom 49

One Sample t-test Purpose-to test whether a sample mean is significantly difference to a predetermined/constant value (Test) Test Value often a population mean, it does not have to be.

Any value specified by a reasearchers (Q2 and Q3) 50

RESEARCH QUESTIONS 1. Do inner-city homeowners have higher mortgages than the national average?

2. On average, do university lecturers spend more or less time at work than the 37.5 hours per week stipulated in their enterprise agreements? (condition of the lecturersâ&#x20AC;&#x2122; employment) 3. Is there a difference between perceived quality of life today, and perceived quality of life in the 1960s? â&#x20AC;&#x201C; (historical research) 51

One Sample t-test Checklist • Scale of measurement • Normality • Interpreted : t-value, degrees of freedom, significance, mean difference and confidence interval for your write up • Effect size (Cohen’s d ) • Reported your results in the APA style?

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Effect Size

M  d s



74.9282 5.693

 1.244 53

Effect Size • An Effect size of d = -1.244 indicates that the sample mean is arround 1.23 standard deviations lower than the population mean.

• Cohen’s (1988) conventions, a difference of this magnitude is “large” • Jacob Cohen (1988): d = .20 (small) , .50 (medium) and .80 (large) 54

Results A one sample t-test was used to compare the National Standardised Literacy Test performance of a class of 28 year-seven students (M=74.92, SD=5.69) against the national average of 82. The year-seven students scored 7.08 points (95% CI=-4.73 to -9.43points) below the national average. This difference was found to be statistically significant, t (27)=-6.23, p<.05, and large, d= -1.24.

The Shapiro-Wilk statistic and a visual inspection confirmed that the studentsâ&#x20AC;&#x2122; test scores were normally distributed.

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Keputusan

Ujian-t satu sampel digunakan untuk membandingkan pencapaian pelajar Tahun 6 yang terdiri dari 25 orang pelajar (M=74.92, SD= 5.69) berbanding purata pencapaian kebangsaan iaitu 82.0. Pelajar tahun 6 mencapai 7.08 poin (95% CI = 4.73 hingga 9.43 poin) kurang dari pencapaian kebangsaan. Perbezaan pencapaian pelajar didapati signifakan secara statistik, t(25)= -6.218, p < .05, dan d=1.24.

Statistik Shapiro-Wilk dan pemerhatian dari Stem-dan-Leaf mengesahkan skor ujian pelajar ditabur secara normal.

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Interpretasi Ujian-t Satu Sampel adalah signifikan (t(661) = - 1.61, p < .05 ) secara statistik. Keputusan ini berjaya menolak Ho dan menerima HA. Keputusan ini menunjukkan terdapat perbezaan antara min sekolah dengan min JPN Kedah dalam pencapaian Matematik.

Min (40%) JPN Kedah adalah lebih tinggi berbanding Min (18.42%) sampel dalam pencapaian Matematik di sekolah menengah.

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Paired Samples t-test â&#x20AC;˘ Purpose-to test for a statistically significant difference between two related sample means â&#x20AC;˘ Two samples are considered related when: i. Whoâ&#x20AC;&#x2122;ve provided data on two separate occasions (eg. Before and after a treatment) ii. Each individual in one sample is connected or linked with a specific individual in the other (eg husband and wife) 58

Research Questions 1. Do people report a higher sense of subjective wellbeing after 15 minutes of aerobic exercise? â&#x20AC;&#x201C; to measure the subject wellbeing of each participant twice 1. Is studentsâ&#x20AC;&#x2122; short-term memory more accurate when tested in quite or noisy surroundings?

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Paired Sample t-test Checlist • Scale of measurement • Normality • Interpreted : t-value, degrees of freedom, significance, mean difference and confidence interval for your write up • Effect size (Cohen’s d - ) • Reported your results in the APA style?

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Effect Size

M 1 M 2 20.60  18.40   0.9556 d 2.30217 Sp

S1  S 2 Sp  2

2.30217  2.30217   2.30217 2 63

Effect Size • An Effect size of d = 0.96 • Cohen’s (1988) conventions, a difference of this magnitude is “large” but finding is not significance (p > .05) • Jacob Cohen (1988): d = .20 (small) , .50 (medium) and .80 (large) 64

Results A paired sample t-test was used to compare mean reaction times (in milliseconds) to virtual cyclists wearing either fluorescent (M=320.80, SD=32.37) or non-flourescent (M=422.60, SD=53.84) vest in an evening driving simualtion. On average, the participants reacted 101.80 msec (95% CI=75.78 to 127.82) faster during the flourescent trials than they did during the nonfluorenscent trials. This difference was statistically significant, t(14)=8.39, p<.05, and large, d=2.36.

The Shapiro-Wilk statistic and a visual inspection confirmed that the studentsâ&#x20AC;&#x2122; test scores were normally distributed.

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Keputusan Ujian-t berpasangan adalah signifikan (t(41)=38.94, p<.05). Keputusan ini berjaya menolak HO dan menerima HA. Ini menunjukkan terdapat keberkesanan penggunaan kalkulator dalam pembelajaran Matematik. Skor (85.10) selepas menggunakan kalkulator adalah lebih tinggi berbanding skor (66.10) sebelum menggunakan kalkulator.

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Independent Samples t-test Purpose-to test for a statistically significant difference between two independent sample means.

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Research Questions 1. Is there a difference between male and female students on maths achievement?

2. Do students who listen to classical music while studying achieve higher grades than those who listen to rock music?

3. Are nursing home residents withh pets happier than those without?

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Independent Sample t-test Checlist • Scale of measurement • Each group of data is approximately normally distributed.

• Homogeneity of variance • Interpreted the appropriate t-test (equal variances assumed vs equal variances not assumed) • Interpreted : t-value, degrees of freedom, significance, mean difference and confidence interval for your write up • Effect size (Cohen’s d - ) • Reported your results in the APA style?

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Example Directional Research Hypothesis: The mathematics achievement of male senior high school students is statistically significantly higher than the mathematics achievement of female senior high school students.

Male Students

Female Students

N

Mean

SD

N

Mean

SD

t

637

83.95

7.43

645

79.58

7.51

2.36

p <.05

70

71

M1= 37.13, M2= 43.33

M1  M 2 37.13  43.33  d = -1.54 2 2 (15  1)2.825  (15  1)4.938 sp sp  15  15  2

n1 = 15, n2 = 15

s21 = 2.8252 , s22 = 4.9382

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M1= 37.13, M2= 43.33

M1  M 2 37.13  43.33  d = -1.54 2 2 (15  1)2.825  (15  1)4.938 sp sp  15  15  2

n1 = 15, n2 = 15

s21 = 2.8252 , s22 = 4.9382

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Results An independent sample t-test was used to compare mean of male and female on maths achievement. The mean (M=76.30, SD=12.20) score for male students is higher than mean (M=70.00, SD= 11.20) for female students in math achievement. On average, the participants (95% CI=75.78 to 127.82). This difference was statistically significant, t(14)=8.39, p<.05, and large, d=2.36.

The Shapiro-Wilk statistic and a visual inspection confirmed that the studentsâ&#x20AC;&#x2122; test scores were normally distributed.

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â&#x20AC;˘ Ujian Levene adalah tidak signifikan (p>.05). Keputusan ini telah memenuhi andaian kehomogenan varians antara pelajar lelaki dan perempuan dalam sikap pembelajaran Matematik. â&#x20AC;˘ Ujian-t Sampel Bebas adalah signifikan (t(668) = -3.49, p < .05) secara statistik. Keputusan ini berjaya menolak Ho dan menerima HA.. Keputusan ini menunjukkan terdapat perbezaan sikap pembelajaran Matematik berdasarkan jantina. Min sikap (3.01) pelajar perempuan lebih tinggi berbanding min sikap (2.91) pelajar lelaki dalam pembelajaran matematik.

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Pearson Product Moment Correlation Technique • An r with a plus sign (+) indicates a positive relationship exists between the variables--as one variable increases, the other variable also increases.

• An r of 0 indicates there is no relationship between the variables.

• An r with a minus sign (-) indicates that a negative relationship exists between the variables--as one variable increases, the other decreases.

SGDP5053: Statistics in Education

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Overview

Continuous Variable

Correlation

Continuous Variable SGDP5053: Statistics in Education

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• When testing the statistical significance of the relationship between two variables, take into account the nature of the data.

• Pearson product moment correlation technique is used if:

 both variables are interval or ratio data.  the data are normally distributed.  the cases are paired.

• Spearman rank order correlation technique is computed if either of the variables is ordinal data and the cases are paired.

SGDP5053: Statistics in Education

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Example Directional research hypothesis: The intelligence of elementary school students as measured by the Wechsler Intelligence Scale for Children is statistically significantly positively related to the creativity of elementary school students as measured by the Torrance Tests of Creativity.

Intelligence

Creativity

N

Mean

SD

Mean

SD

r

p

630

103.74

15.27

63.72

6.43

+.87

.005

SGDP5053: Statistics in Education

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Association ď Ź

ď Ź

An association exists between two variables if the distribution of one variable changes when the level (or values) of the other variable change.

If there is no association, the distribution of the first variable is the same regardless of the level of the other variable.

SGDP5053: Statistics in Education

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Chi-Square Test • Chi-Square is used to determine whether the difference between two proportions is statistically significantly different.

 Used when the data are nominal data.  Used when the data are in the form of categories or dichotomies.

• Chi-Square is a non-parametric test.

• Chi-Square compares the distribution of a sample (observed values) to the distribution of a known population (expected values).

SGDP5053: Statistics in Education

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Univariate Hypothesis Test Chi-square Example

 O1  E1  

2

X

2

E1

 O2  E 2  

SGDP5053: Statistics in Education

2

E2

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Example Directional Research Hypothesis: The graduation rate of seniors who participated in a tutoring program is statistically significantly higher than the graduation rate of seniors who did not participate in a tutoring program.

Table 1. Results Obtained from Pearson Chi-Square Test Number of Seniors Who Graduated

Number of Seniors Who Did Not Graduate

Total

Number of Seniors Who Participated in Tutoring Program

75

30

105

Number of Seniors Who Did Not Participate in Tutoring Program

23

80

103

Total

98

110

208

Results. ď Ł2 = 50.31, p < .001 SGDP5053: Statistics in Education

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arsay@uum.edu.my