Descriptive Statistics Worksheet

Directions: Answer each question completely, showing all your work. Refer to the SPSS tutorials as needed (see all attachments). Copy and Paste the SPSS output into the word document for the calculations portion of the problems. (Please remember to answer the questions you must interpret the SPSS output).

1. A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a personâ€™s life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest).

Participant

Hours of Exercise

Life Satisfaction

1

3

1

2

14

2

3

14

4

4

14

4

5

3

10

6

5

5

7

10

3

8

11

4

9

8

8

10

7

4

11

6

9

12

11

5

13

6

4

14

11

10

15

8

4

16

15

7

17

8

4

18

8

5

19

10

4

20

5

4

2. Find the mean hours of exercise per week by the participants.

3. Find the variance of the hours of exercise per week by the participants.

4. Determine if there is a linear relationship between the hours of exercise per week and the life satisfaction by using the correlation coefficient.

5. Describe the amount of variation in the life satisfaction ranking that is due to the relationship between the hours of exercise per week and the life satisfaction.

6. Develop a model of the linear relationship using the regression line formula.

SPSS Tutorial

01

Kruskal-Wallis Test

The Kruskal-Wallis Test is used when you want to test to see if there is a significant difference between two or more samples but the assumption for the One-Way ANOVA are not met, either the data is not normally distributed or the data is at an ordinal level of measurement. To explore this technique in SPSS, letâ€™s look at the following example.

Example:

A study was done to see if music type (1 = Country, 2 = Classic, 3 = Rock, and 4 = Jazz) had an effect on students perception of their performance on an in-class exam when students listened while taking the exam. A class of 40 students were given an exam and were asked to listen to one of four types of music with head phones during the exam. Ten students listened to each type of music. They were ask to rate how well they thought they performed on the exam at the end on a scale of 1 to 5 with 1 being the worst and 5 being the best. Us- ing the data below, we want to determine if there is a statistically significant effect on students perception of their performance due to the type of music listened to.

The first step to performing the analysis in SPSS is to enter the data. The data is en- tered in two columns, one for Music Type and one for Perception. Please review the data entry tutorial for questions on data entry.

The Kruskal-Wallis Test requires the assignment of the level of measurement be assigned for each of the variables in the Measure column in the variable view tab. Music Type is at the nominal scale and Perception is Interval but in SPSS both Interval and Ratio are called scale.

02

Once the measure is set, the analysis is run by selecting Analyze â€“ Nonparametric â€“ Independent Samples.

The Nonparametric Tests Two or More Independent Samples box will open. There are three tabs at the top of the box. Objective is the first and the default setting of Automatically compare distributions across groups will be selected.

03

Select the second tab, Fields. In this tab move Perception to the Test Fields box and the Music Type to the Groups box.

The last tab is the Settings tab. In this tab, first select Customize Test and then Kru- skal-Wallis 1-way ANOVA K samples. Then click Run.

The Hypothesis Test Summary is displayed in the output window. To get a detailed view for interpretation, double click on the Hypothesis Test Summary.

A pop-up output window will open with the results of the test.

The left side of the screen is the Hypothesis Test Summary and the right is a more detailed look at the test.

04

The p-value (Asymptotic Sig. (2-sided test) = .004) shows there is a statistically signif- icant effect on the perception of student performance due to the type of music listened to. To see which levels of the inde- pendent variables are significantly differ- ent from each other, the Pairwise Compar- isons will need to be selected under View at the bottom of the pop-up window.

The detailed report allows us to see which types of music are statistically different. The p-values for Rock â€“ Country and Rock â€“ Jazz show significant findings (they are less than .05). This implies that there is a statistically significant difference between student perception on exams when listen- ing to Rock and Country and Rock and Jazz music.

A separate pop-up window will open, the right side of the screen will have the detailed report.

05

SPSS Tutorial

Wilcoxon Signed- Ranks Test

The Wilcoxon Signed-Ranks test is used to test if there is a dif- ference in the levels of an independent variable when the same participant received both treatments (within-groups), but the data does not meet the normality assumption needed for the matched pairâ€™s t-test or the data is at the ordinal level of measurement. To explore the analysis technique in SPSS, we will work through the following example.

01

Example:

A study was done on studentâ€™s opinions of group work at the beginning and end of the semester. Students were ask to rate the following statement at the beginning of the semester and at the end after the group projects were completed.

Working in groups is the best way to accomplish research. Students were asked to rate according to the following scale. Strongly Disagree â€“ Disagree â€“ Neither Disagree nor Agree â€“ Agree â€“ Strongly Agree The goal was to determine if there was a significant change in at- titude toward working in groups from the beginning of the semes- ter to the end. The following data was collected from a class of 20 students.

The first step to the analysis in SPSS is to enter the data into the Data Editor in SPSS. The data is entered in two columns, one for the Beginning rating and one for the rating at the End of the class. Please review the Data entry tutorial for questions.

02

During the data entry portion, in the vari- able view window, ensure that both vari- ables are set to a Scale level of measure under the Measure column.

Start your analysis by clicking on Analyze â€“ Nonparametric Tests â€“ Related Samples.

The Nonparametric Tests window will open. It has three tabs at the top. It will start in the Objective tab, the default of Automatically compare observed data to hypothesize will be selected and does not need to be changed.

03

Go to the Fields tab. In this tab, move both the variables into the Test Fields box. Finally, select Run.

The output will be displayed in the output viewer. Double click on the Hypothesis Test Summary in the output window, and a pop- up window will open with results that are more detailed.

The right side of the screen gives the results to be interpreted.

04

The p-value = .609 (Sig.) is greater than 0.05; therefore, according to the Wilcoxon Signed-Rank test, there is not a statistically significant difference in the rating before or after the class on the studentsâ€™ opinion on group assignments.

SPSS Tutorial

Two-Way Analysis of Variance (ANOVA) â€“ Between Groups

01

A two-way ANOVA is used to test the equality of two or more means when there are two factors of interest. When two factors are of interest, an interaction effect is possible as well. There is an interaction between two factors if the effect of one of the factors

changes for different categories of the other factor. There are two different options: between groups and within groups. In be- tween-groups experiments, researchers randomly assign partic- ipants to independent groups and then expose one group to one level of the independent variable and the others to the other levels To explore the two-way ANOVA in SPSS we will use the following example from the Visual Learner Media Piece.

Example:

A professor at a local University believes there is a relationship between head size, the major of the students, and the gender of students in her biostatistics classes. She takes a random sample from her three classes. The data is in the following table. Notice that the sample size for each set of categories is the same. (i.e., female and Pre Med had 4 data values as does male and Pre Med)

02

A two way ANOVA essentially does three different hypothesis test. First test for interaction effect then effect from each of the two factors if there is no interaction effect.

The first step is to enter the data into SPSS. The two-way ANOVA has two factors and one response variables. This is how the data is entered into SPSS. One column for each factor, gender and major. A third column for the response, head size. The factors must be quantitative, so we need to assign numerical values to each level. For Gender, let Female = 1 and Male = 2. For Major, let Pre Med = 1, Pre PT = 2, Nursing = 3, and Health Car Admin = 4. You can use any values that you choose but make sure you are consistent and you note the values assigned.

Once the data is entered, the analysis is performed by selecting Analyze â€“ General linear Mode â€“ Univariate.

03

In the Univariate popup box, the factors, Gender and Major need to be put in Fixed Factor(s). The response, Head_Size is put in the Dependent Variable box.

There is an option for selection of Post_Hoc test on the right of the screen that gives several options for different Post_Hoc test that can be performed.

Remember that a Post_Hoc test is only need if there is significant difference found. Therefore, the two-way ANOVA should be run first. Select continue, then interpret the output in the output window.

The fist output box gives the sample size for each of the factors.

The second output box gives the two-way ANOVA table. Remember to test for inter- action, looking at Gender*Major first. Then, if there is no significant effect, go on to look for a significant effect due to Gender and Major separately.

Putting all the statistical conclusions together we can see that there is no effect from the interaction of gender and major on the head circumference and there is no effect on head circumference due to major but there is an effect due to gender on head circumference at a statistically significant level of 0.05.

SPSS Tutorial

01

Multiple Linear Regression

Regression begins to explain behavior by demonstrating how dif- ferent variables can be used to predict outcomes. Multiple regres- sion gives you the ability to control a third variable when investi- gating association claims. To explore Multiple Linear Regression, letâ€™s work through the following example.

Example:

A researcher is interested in studying four different variables: GPA, motivational score, IQ, and hours of study. The following data was collected on a simple random sample of students.

The researcher wants to examine the re- lationship between the dependent variable GPA and the independent variables of Moti- vational score, IQ, and hours of study.

To begin the analysis, enter the data into SPSS. There are four variables, so we need four columns. For questions entering data, please review the data entry tutorial.

Once the data are entered, click on Ana- lyze â€“ Regression â€“ Linear.

02

The Linear Regression pop-up window will open. Move GPA to the Dependent box and the other three variables to the Indepen- dent box. Then click OK.

03

The output will be displayed in the output window.

There are four boxes of output. The first is a description of the variables entered.

The second box is the Model Summary. This gives the correlation coefficient r, the coefficient of determination r2, ad- justed r2, and the standard error of the estimate. The correlation coefficient tells the strength and direction of the linear relationship. Since r = .968, it is a strong positive relationship (a positive number and close to one). The coefficient of deter- mination tells the proportion of variation that is account for by the linear relation- ship between the dependent and indepen- dent variables.

The third box gives an analysis to show if there is a statistically significant linear relationship between the dependent and independent variables. The p-value of .000 (Sig.) indicates a statistically significant linear relationship since it is less than 0.05.

04

The last output box gives an individual look at each of the independent variables as predictors of GPA.

To interpret this review the p-value (Sig.) for each of the variables. We can see that Motivation Score and IQ are statistically significant predictors of GPA (with p-value 0.05). From these results, we see that collectively these three predictor variables explain

a significant amount of variability in GPA, and individ- ually, because the slope values are all positive (the B column in the output table), motivation, and IQ signifi- cantly predict GPA (as motivation and IQ increase, so does GPA).

SPSS Tutorial

01

Chi-Square Goodness-of-Fit Test

The chi-square goodness-of-fit test is used to determine if a distri- bution of scores for one nominal variable meets expectations. The data collected is counts or frequency of occurrence at a particu- lar level of the nominal variable. To explore this test, consider the following example.

Example:

Sickness is claimed to be a random event, thus one would expect that the proportion of sick days taken would be equally spread throughout the work week. We would like to test this claim for a particular company in Phoenix, Arizona. The following is a sam- ple of the number of individuals who called in on the different days last year.

The analysis can be performed in SPSS. To do this, first we must enter the data into the data editor. You will need two columns. One for the nominal variable, Day, and one for the count, Call_Ins.

When frequencies are entered into SPSS such as the case here with the number of call_ins per day of the week, you must tell SPSS that are being entered rather than raw data. To do this the Weight Case command must be used. Click on Data then Weight Cases.

02

In the pop up window, select weight cases by and then move the Call_Ins variable over to Frequency variable. Then click OK.

03

Now the analysis can begin by selecting Analysis â€“ Nonparametric Tests â€“ One Sample.

There are three tabs in the One-sample Nonparametric Tests window. Select the Fields tab.

Ensure that Day is in the Test Fields box and then select the Settings tab.

04

Select Customize tests. Choose Compare observed probabilities to hypothesized (Chi-Square test). Then click on the options box.

The default is All categories have equal probability. This is what is needed for this test, as we are interested in determining if the number of call-ins is the same for each day of the week. Click OK and then Run.

05

The output window will populate with the results of the test.

Double click on the Hypothesis Test Sum- mary to get a more detailed output.

06

The chi-square test statistic is 6.662 with a p-value of .156. Since this p-value is greater than the assumed level of significance of 0.05, this is not a significant result. This suggest there is not a statistically signifi- cant difference in the number of call_ins on the different days of the week at a level of significance of 0.05.

SPSS Tutorial

01

Mann-Whitney U Test

The Mann-Whitney U test is used to test for a significant differ- ence between two samples but the data either does not meet the normality assumption needed for the independent samples t-test or the variables are ordinal.

Example:

A group of students are interested in discovering if music with or without words has an impact on student rating of class experience. During class work, students in one class were played music with no words and students in the other class were played music with words. Students were asked to rate their class experience on a scale of 1 to 5 with 1 being the worst and 5 being the best. The following data was collected where 1 is for music without words and 2 is for music with words.

To perform the Mann-Whitney U test in SPSS, first enter the data. Review the data entry tutorial if there are any questions about data entry. The data is entered in two columns.

It is important to note that in the variable view tab, you need to set the Measure (scale of measurement) for the two vari- ables. Music Type is nominal (it is a name or label) and the Class Rating is scale (specifi- cally it is the ordinal level of measurement, review the visual learner media piece).

02

Once the data is entered, the analysis is run by going to Analyze â€“ Nonparametric Tests â€“ Independent Samples.

The Nonparametric Tests Two or More Independent Samples window will open.

There are three tabs at the top of the win- dow. It will start on the Objective tab. The default setting of Automatically compare distributions across groups should be selected. Then go to the Fields tab.

03

In the Fields tab move the Class_Rating to the Test Fields box and Musics_Type to the Groups box. Select Run.

The output window will open with the Hypothesis Test Summary. To get the detailed output, you will need to double click on the Hypothesis Test Summary.

A pop-up output window will open when you double click.

04

The left hand side of the viewer displays the Hypothesis Test Summary and the right- hand side provides more detailed informa- tion.

According to the Mann-Whitney U test, there is a statistically significant difference based on the p-value (Exact Sig. (2 sided test)) = .013. Group 1, which listened to the music with no words (Mean Rank of 19.43), reported a higher rating of the class than the group that listened to music with words (Mean Rank of 11.57). According to the Mann-Whitney U test, there is a

statistically significant difference based on the p-val- ue (Exact Sig. (2 sided test)) = .013. Group 1, which listened to the music with no words (Mean Rank of 19.43), reported a higher rating of the class than the group that listened to music with words (Mean Rank of 11.57).

SPSS Tutorial

01

Multiple Analysis of Variance (MANOVA)

A MANOVA test is used to model two or more dependent variables that are continuous with one or more categorical predictor vari- ables. To explore this analysis in SPSS, letâ€™s look at the following example.

Example:

An instructor was interested to learn if there was an academic difference in stu- dents from different states. She randomly selected 20 students from each of three states; California, Arizona, and Colorado who were a part of the entering freshman class at the University. She assessed them based on their English and math placement tests. The independent variable is the state and the dependent variables are the scores on the two placement tests. The results are as follows.

The first step is to enter the data into the SPSS data editor. You will need three col- umns for the three variables. The first is state, second Math scores, and finally English scores.

02

To begin the analysis click on Analyze â€“ General Linear Model â€“ Multivariate.

In the Multivariate Window move Math and English to the Dependent Variable box and State to Fixed Factor(s).

Then select Options.

03

Move State to the Display Means for box and put a check next to Descriptive Statis- tics, Estimates of effect size, and Ob- served power. Then Click Continue.

Click Continue in the Multivariate window and the output will be displayed in the out- put viewer.

04

There are multiple boxes of information provided by this analysis. The first box sim- ply states how many samples there were for each level of the independent variable.

The Descriptive Statistics box provides the mean and standard deviation for the two different dependent variables which have been split by the independent variables levels.

05

The next box is the Multivariate tests. This is where we find the actual results of the one-way MANOVA. We want to look at the second effect labeled State and the Wilksâ€™ Lambda row. The Sig column gives the p-value and we can determine if the results were statistically

significant. Since the p-value = .223 then we see that there is not a statistically significant difference in the students academics from different states.

06

To determine how the dependent variables differ for the independent variables, we need to look at the Tests of Betweenâ€“Subjects Effects. Based on the p-values (Sig.) for Math and English, which are greater than

0.05, State does not have a significant effect on Math or English results.

The post SPSS tutorials appeared first on Versed Writers.