SPSS problems solved

8/11/2019 SPSS problems solved

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1. FACTOR ANALYSIS

Factor analysis is a statistical method used to describe variability among observed,

correlated variables in terms of a potentially lower number of unobserved variables called

factors.

1. People have rated their opinion on why they prefer kallada travels upon other bus service to

Kerala on the basis of seven ratings given to them by the manager.1 is completely agree,7 is

completely disagree.

On time Service

Comfortable Seats

Easy Bookings

New Multiaxle Bus

Economic Pricing of Ticket

Shortest Travel time when compared to other Service

Carry out factor Analysis

Ans.

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INTERPRETATION

COMFORT

Ontime Bus

New Volvo Multiaxle

CONVINIENCE

Shortest travelling Time

Easy Booking

ECONOMIC

Pricing

Comfortable Seat

ONTIME BUS FACTOR 1 (.976)

COMFORTABLE SEATS FACTOR 3 (.780)

SHORTEST TRAVEL TIME FACTOR 2 (.861)

EASY BOOKING FACTOR 2 (.775)

ECONOMIC TICKET PRICING FACTOR 3 ( .813)

NEW MULTIAXLE VOLVO FACTOR 1 (.949)

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2. TWO WAY ANOVA

In statistics, the two-way analysis of variance (ANOVA) test is an extension of the one-way ANOVA

testthat examines the influence of different categorical independent variableson one dependent

variable.

The two-way ANOVA can not only determine the main effect of contributions of each independent

variable but also identifies if there is a significant interaction effect between the independent

variables.

A professor in physical education conducts an experiment to compare the effects on sleep of different

amounts of exercise and the time of day when the exercise is done. The experiment uses a fixed

effects, 3 2 factorial design with independent groups. There are three levels of exercise (light,

moderate, and heavy) and two times of day (morning and evening).Thirty-six college students in good

physical condition are randomly assigned to the six cells such that there are six subjects per cell. The

subjects who do heavy exercise jog for 3 miles; the subjects who do moderate exercise jog for 1 mile;

and the subjects in the light exercise condition jog for only mile. Morning exercise is done at 7:30

A.M., whereas evening exercise is done at 7:00 P.M. Each subject exercises once, and the number of

hours slept that night is recorded.

TIME OF THE

DAY

EXERCISE

LIGHT

(1)

MODERATE

(2)

HEAVY

(3)

MORNING

(1)

6.5

7.4

7.3

7.2

6.6

6.8

7.4

7.3

6.8

7.6

6.7

7.4

8.0

7.6

7.7

6.6

7.1

7.2

EVENING

(2)

7.1

7.7

7.9

7.5

8.2

7.6

7.4

8.0

8.1

7.6

8.2

8.0

7.4

8.0

8.1

7.6

8.2

8.0

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Row, 1 = Morning and 2 = Evening

Column, 1 = Light, 2 = Moderate, and 3 = Heavy

Using SPSS, what do you conclude regarding the main effect for the column variable Exercise, the main

effect for the row variable Time of Day, and the interaction effect between the row and column

variables Exercise and Time of Day? Use = 0.05.

Ans.

Thus, for each sleep score, we need to enter two grouping values, the row and column numbers

associated with that sleep score. In all, there are three variables, the row variable, the column variable,

and the sleep score variable. Lets name these variables, Row, Column, and Sleep.

SPSS outputs three tables, the Between-Subjects Factors table, the Descriptive Statisticstable, and

the Tests of Between-Subjects Effectstable.

The Between-Subjects Factorstells us that there were two independent variables, the row variablewith two levels and the column variable with three levels. It also tells us the number of scores at each

of the levels of the two variables.

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The Descriptive Statisticstable gives us the cell and marginal mean values and standard deviations.

The Tests of Between-Subjects Effects table gives us information about the main and interaction

effects.

This table shows that for the Row main effect, Fobt = 48.416 and has an obtained probability

of .000. Since .000< .05, Hence reject H0.

There is a significant row main effect. Since the row independent variable is Time of Day, this means

that there is a significant Time of Day main effect. This table also shows that for the Columnmain

effect, Fobt = 12.787, with an obtained probability of .000. Since .000 < .05, reject H0. There is a

significant column main effect. Since the column independent variable is Exercise, this means that

there is a significant Exercise main effect.

Finally, the table shows that for the Row X Column interaction, Fobt = 4.604, with an obtained

probability of .018. Since .0180 < .05, we reject H0.There is a significant Time of Day X Exerciseinteraction.

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3. T-TEST

T-test (or Z-test) tests whether theres a significant difference in dependent variable between two

groups (categorized by independent variable).

To see whether the average sales of Garment Retailer A are different between weekends and

weekdays. Data: Given sales of Retailer A during Weekends (During =1) and Weekdays(during = 2).

Weekends Sales Weekdays Sales

1 75 2 51

1 87 2 70

1 83 2 37

1 45 2 621 95 2 90

1 89 2 72

1 74 2 45

1 110 2 78

1 75 2 45

1 84 2 76

Dependent variable: Sales

Grouping variable: Day of the Week (1 = Weekend, 2 = Weekdays)

Answer

Null Hypothesis:There is no significant difference between the average sales during weekdays and

weekends

Alternate Hypothesis:There is Significant Difference between the average sales during weekdays and

weekends

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INTERPRETATION

From the first table, the mean sales under the promotion and non-promotion are 81.7 and 62.6,

respectively.

The test statistic, t, for this observed difference is 2.49(t= 2.493). The p-value for this t-statistic is

0.023(Sig. (2-tailed) =0.023). Since p-value (0.023) is less than 0.05, we reject the null hypothesis and

conclude that theres a significant difference in average sales between when firms offer price

promotion and when they offer just regular prices.

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4. CORRELATION

From the data of 70 employees of an organisation in respect to their DOB, Gender, Education level,

employment category, Previous Experience, Salary, Job time.

Is there any relationship between the educational levels and current salary?

Answer

There is a positive, medium-strong and significant (Sig. =0.000) relationship between the Educational

Level & and current Salary.

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5. LINEAR REGRESSION

To see whether Sales Promotions affects the sales of a Shirt Brand

SALES (Y) SALES PROMOTION (x1)$97000 45

$95000 47

$94000 40

$92000 36

$90000 35

$85000 37

$83000 32

$76000 30

$73000 25

$71000 27

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INTERPRETATION

(1)

From the last table, estimated regression coefficients are: Bo (Constant) = 42509 and B1

(coefficient for X1) = 1217.262.

(2)The p-value for testing Ho: b1 = 0 is 0.000. Therefore, we reject the null hypothesis and we

conclude that sales(Y) is significantly affected by Sales Promotion Techniques(X1). Based on

the estimated regression equation Y=42509.5+1217.262*X1, we expect that the sales(Y) will

increase by 1217.262 units if we increase Promotion(X1) by one unit.

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6. CROSS TABULATION & CHI-SQUARE

To see whether the preferred brands (brand A, brand B, and brand C) are associated with the

locations (Denver and Salt Lake City); Is there any difference in brand preference between the two

locations?

The selected 40 people in each city and measured what their preferred brands were.

If the preferred brand is A, the favourite brand =1.

If the preferred brand is B, the favourite brand =2.

If the preferred brand is C, the favourite brand =3.

Null Hypothesis: There is no difference in brand preference between the two locations.

Alternate Hypothesis:There is significant difference in brand preference between the two locations.

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CROSS TABULATION

From the second table, it is found that among 40 people in Denver (location=1), 10, 7, and

23 people prefer the brand A, B, and C, respectively.

On the other hand, 19, 16, and 5 out of 40 people in Salt Lake City (location=2) like brand

A, B, and C, respectively.

From the third table, the chi-square value is 17.89(Chi-Square = 17.886) and the associated p-

value for this chi-square value is 0.00(Sig. = 0.000) , which is less than 0.05. Therefore, we

conclude that people in different city prefer the different brand or that consumers favorite

brand is associated with where they live in.

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SPSS problems solved