statistics assignment
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hi_its_keny.zipSPSS Projects homework.pdf
SPSS MINI PROJECTS
• A teacher asked 10 of her students how many books they had read in the last 12 months. Their answers were as follows: 12, 23, 19, 6, 10, 7, 15, 25, 21, 12 a. Prepare a Frequency Distribution table for the data. b. Briefly describe the distribution. c. How many percent of students read 19 books or less in the last 12 month?
• Twenty Ohio University students were asked, "How many phone calls did you receive
last night?" The numbers below are their answers. 10 7 4 6 5 2 3 0 1 11 7 6 4 4 5 3 2 2 0 3 a. Complete the grouped frequency distribution. Interval Mid-point Frequency Cumulative FrequencRelative % 0-1 2-3 4-5 6-7 8-9 10-11 b. What percentage of OU students received between 2 and 3 phone calls? c. How many people received less than 9 phone calls? d. What is the percentile rank of a student who has received 3 phone calls? Interpret the outcome. e. What is the percentile rank of a student who has received 11 phone calls? Interpret the outcome. f. Draw a bar chart. g. Draw a histogram with normal curve. • Give two sets of four numbers that have the same mean but different median.
• Give two sets of four numbers that have the same median but different means.
• Give two sets of four numbers that have the same mean but different standard deviation.
• Give two sets of four numbers that have the same standard deviation but different mean.
• The following grades were obtained on the first statistics exam of Urban Studies Program of Rutgers University, during the Fall 2005. There were 32 students attending the course.
87 78 75 65 69 80 81 94 66 85
a) Mean of the observations is --------------------------------------------- b) Mode of the observations is --------------------------------------------- c) Median of the observations is ------------------------------------------- d) Range of the observations is ---------------------------------------------
e) Inter-quartile range of the observations is ----------------------------- f) Inter-quartile deviation of the observations is -------------------------
g) Estimate the percent of students who received a grade of 75 or more. h) Variance of the observations is -----------------------------------------------------------
i) Standard deviation of the observations is -------------------------------------------- • The number of requests for information and the actual enrollment for the past six years at SABA university are: Request for Information (100,000) Actual Enrollment (10,000) 3.0 4.0 4.0 5.0 4.0 6.0 5.0 6.0 5.0 7.0 6.0 9.0 a) Draw a scatter diagram. b) Using the scatter plot explain the relationship between request for information and enrollment at SABA university. c) Calculate correlation of coefficient and explain how strongly these two variables are related to each other?
d) Is the correlation between these two variables significantly more than 2%? e) Calculate coefficient of determination and explain what does it show? f) Calculate coefficient of non-determination and explain what does it show? g) Find the least-squares regression equation. h) Interpret the values of a for the above question. i) Interpret the values of b for the above question. j) Predict the number of enrollment if the number of requests for information reaches 4,000.
stats_spss_card.pdf
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Introduction to SPSS
Scatterplot
Descriptive Statistics, Histogram and Boxplot, Assessing Normality, and Generating Confidence Intervals (continued) 3. Click on the Statistics button. Ensure that the Descriptives
option is selected. Enter the confidence level required for the confidence interval. Select Continue.
4. Click on the Plots button. Ensure that the first Boxplot option is selected, ensure that the Histogram option is selected, and ensure that the Normality plots with tests option is selected. Select Continue. Then select OK. (Note: To generate side- by-side boxplots or to compare the distribution of the variable in question by different values of a categorical variable, sim- ply assign a categorical variable to the Factor List in the pre- vious screen shown.)
5. Typical results are shown below:
Regression and Residuals Plots. FROM THE DATA VIEW Use the following procedure to generate a linear regression equation and the associated residual plots:
Correlation FROM THE DATA VIEW Use the following procedure to generate the correlation coefficient for two quantitative variables:
1. Select Analyze>Correlate>Bivariate.
2. From the variable list, select the two quantitative variables of interest. Select OK.
Generating Random Numbers FROM THE DATA VIEW. Use the following procedure to generate random numbers:
When you launch SPSS, you will see the following: This process will import your dataset into SPSS. Your SPSS inter- face will look like this:
FROM THE DATA VIEW Use the following procedure to generate a scatterplot of two quantitative variables:
1. Select Graphs>Legacy Dialogs>Scatter/Dot>Simple Scatter>Define. This will produce the screen to the right:
2. Click on a quantitative variable and click on the arrow associ- ated with the y-axis. Click on a second quantitative variable and click on the arrow associated with the x-axis. Select OK.
1. Select Analyze>Regression> Linear. This will produce the screen to the right:
2. From the list of variables on the left, select an appropriate quantitative variable as the dependent variable. Click on the arrow next to the Dependent box. Select an appropriate second (or multiple) variable(s) from the list. Click on the arrow next to the Independent(s) box.
3. Select the Statistics button. Identify the required statistics. At a minimum, ensure that the Estimates option is selected and the Model Fit option is selected. Select Continue.
4. Select the Plots button. To check for linearity and equality of variance, select to plot ZPRED (standardized predictions) against ZRESID (standardized residuals). Select Continue.
5. If you need to save the predictions in the dataset, select the Save button and identify what needs to be retained. Select Continue.
6. Select OK. Typical results are shown below:
1. Select Transform>Compute Variable. This will produce the screen to the right:
2. In the Target Variable box, type the name of the random number variable — like random.
3. In the Function group box, scroll down to the Random Numbers option and then in the Functions and Special Variables box, scroll down to the Rv.Uniform option (notice that SPSS provides many distribution options for random numbers). Double click. This will populate the Numeric Expression box, as circled, with the RV.UNIFORM(?,?) function. Replace the ?’s with a 0 (min value) and a 1 (max value), respectively. Select OK.
4. There should now be a column of random numbers on the right side of your dataset in the Data View.
Sampling FROM THE DATA VIEW Use the following procedure to generate a simple random sample:
1. Select Data>Select Cases. Then check the option Random sample of cases. This will produce the screen to the right:
2. From the options provided, select the third option — Random sample of cases. Click on the Sample button. This will produce the following screen:
3. If you require a percentage of cases, select the first option. If you require a specific number of cases, select the second option (enter the total number of cases in the second box). Select Continue>OK.
Descriptive Statistics, Histogram and Boxplot, Assessing Normality, and Generating Confidence Intervals
FROM THE DATA VIEW Use the following procedures to find the complete description of a quantitative variable, including the mean, median, and standard deviation, histogram and box- plot, assess the variable’s degree of normality and generate confidence intervals:
1. Select Analyze>Descriptive Statistics>Explore. This will produce the screen to the left:
2. From the list of variables on the left, click on the quantitative variable of interest, and then click on the arrow as circled.
ISBN-13: ISBN-10:
978-0-321-58979-8 0-321-58979-3
9 7 8 0 3 2 1 5 8 9 7 9 8
9 0 0 0 0
When testing normality, the H 0
(null hypothesis) is that the data is approxi- mately normal. So, low p-values (such as these) would indicate that the data is not normal.
Note that this is the regression equation — the values under the B are the coefficients for each variable and the values under the Sig. column are the p-values. These results would indicate that both coefficients are statistically significant and not 0.
From this screen, you can open almost any type of file. If you have an existing file — such as an Excel file — ensure that the option button, circled above, is checked and select OK. You will then see the following screen:
If your Excel file has multiple worksheets, they will all be listed in the Worksheet box as circled above. Identify the worksheet that you want to analyze and click OK.
Notice that there are two tabs at the bottom — Data View and Variable View. The Data View tab is shown above and will resem- ble an Excel spreadsheet interface. The Variable View tab contains information about the individual variables. The Variable View provides information regarding how SPSS is reading the individual variables — specifically if the variables are read as Nominal (categorical) or Scale (quantitative). There is a third option — Ordinal, which is a type of qualitative data. This information can be found in the Measure column on the right. It is important that SPSS reads the data correctly, since some analytical executions are specific to quantitative or categorical data. If SPSS has misinterpreted a variable, feel free to change this information as necessary. This can be done by clicking inside the cell and selecting a different option.
IBM® SPSS® Statistics Student Version
J E N N I F E R L E W I S P R I E S T L E Y, P H . D.
IBM_SPSS_StatsStudentVersion.qxp:SPSS 9/24/10 11:00 AM Page 1
IBM® SPSS® Statistics Student Version
4 5 6
Finding Inverse Normality (Finding z -Scores Given an Area) and the Area Under the Normal Curve FROM THE DATA VIEW. Use the following procedure to convert quantitative values into their associated z-scores and their probability of occurrence given a normal distribution:
1. To convert the observations of a specific quantitative variable into z-scores (a process called standardizing), select Transform>Compute Variable. This will produce the screen to the right:
2. Give the standardized variable a name in the Target Variable box — like placing a Z in front of the variable name. Click on the variable of interest from the list of variables and click on the arrow, as circled. The variable of interest should now appear in the Numeric Expression box. After the variable name, type a minus sign, followed by the value of the mean of the variable. Place this expression inside paren- theses. Type a backslash (the sign that appears under the asterisk and above the dou- ble asterisks in the screen). Type the value of the standard deviation for the variable. This process executed the formula for a z-score [(x-mean)/stddev]. Select OK. This process will create a new variable in the Data View that provides the z-score for the specified variable for each observation of interest. (Note: The mean and standard deviation can be found by following the procedure Analyze>Descriptive Statistics>Explore.)
Hypothesis Test for Proportion FROM THE DATA VIEW Use the following procedure to generate a hypothesis test for a proportion:
Hypothesis Tests for Two Independent Sample Means and Associated Confidence Interval FROM THE DATA VIEW Use the following procedure to determine if a statistical difference exists between two independent sample means: 1. Select Analyze>Compare Means>Independent Samples T
Test. This will produce the following screen: 2. From the list of variables, select the quantitative variable of
interest. Click on the first arrow. From the list of variables, select the binary categorical variable that includes the two group values. Click on the second arrow. Once the grouping variable is assigned, the variable will appear in the box as above, with two ?’s. Click on the Define Groups button. This will pro- duce the screen to the right:
Sampling (continued) 4. The Data View will now have a number of observations with
a diagonal slash through the row indicator, as circled:
5. This slash indicates that the observation will not be included in any analysis — those observations without slashes are part of the sample. Notice that a new variable has been created on the right — filter_$. The observations with a value of 1 are part of the sample. The observations with a value of 0 are not part of the sample and will be excluded from analysis. To reset the data to have all of the observations available for analysis, select Data>Select Cases>All Cases (Note that the filter variable will remain, which can be used to re-create the sample as needed).
1. Select Analyze>Non-Parametric Tests>Legacy Dialogs> Binomial. This will produce the screen to the right:
2. The variable selected will need to be read as a scale variable — it will be shown with a ruler icon. If the categorical variable is described using words or non-numerical labels — like Male and Female — it will have to be transformed to numerical values. Click on the binary variable of interest, and click on the arrow. Type the required test proportion in the box. Select OK.
3. Typical results are shown below:
4. If a variable needs to be transformed or recoded, this can be done by selecting Transform>Recode into Same Variables. From the list, select the variable of interest. Click on the arrow. Select the button Old and New Values. This will produce the screen shown above:
5. Under Old Value, type the original value that needs to be transformed in the Value box. Under New Value, type the new value for the variable. For example, if Male needs to be recoded as 1, Male would be entered into the first box and 1 would be entered into the second box. Select the Add button. Continue this process until all values have been recoded. Select Continue>OK.
3. Enter the name of each group (there should only be two) as it appears in the Grouping Variable box. Select Continue.
4. This test will generate a 95% confidence interval. If a 90% or 99% interval is required, this can be achieved by clicking on the Options button and entering the required value. Select Continue>OK.
5. Typical results are shown to the right:
Hypothesis Tests for One Sample Mean and Associated Confidence Interval FROM THE DATA VIEW Use the following procedure to determine if a statistical difference exists between a single sample mean and a specified value: 1. Select Analyze>Compare Means>One Sample T Test.
2. Select the quantitative vari- able of interest from the list on the left. Click on the arrow button, as circled, to assign the variable. Enter the value to be tested against the sample mean. Click OK.
3. The test will generate a 95% confidence interval. If a 90% or 99% interval is required, this can be achieved by clicking on the Options button and entering the required value. Select Continue>OK.
Hypothesis Test for the Mean of Paired Differences FROM THE DATA VIEW Use the following procedure to determine if a statistical difference exists between paired sample means:
1. Select Analyze>Compare Means>Paired Sample T Test. This will produce the screen to the right:
2. From the list of variables on the left, select the first quantitative variable (like a prescore). Click inside the Variable 1 column on the right. Click the arrow, as circled. This will assign the first variable of the pair. Select the second quantitative variable (like a postscore). Click inside the Variable 2 column on the right. Click on the arrow. Select OK.
3. Typical results are shown to the right:
Finding Inverse Normality (Finding z -Scores Given an Area) and the Area Under the Normal Curve (continued) 3. To generate the percent of the normal curve that sits to the left (less than) an observation of interest, follow the Transform>Compute
Variable again. From the Function Group, select All. Then from the Functions and Special Variables box, select Cdf.Normal. Double click on this option. This will place the function in the Numeric Expression box, followed by three ?’s.
4. The first ? should be replaced with the quantitative variable of interest from the variables on the left. Click on the variable and then click on the arrow. The second ? should be replaced with the variable mean value (see note in step 2). The third ? should be replaced with the variable standard deviation. Finally, give the variable a name in the Target Variable box. Select OK. This pro- cess will create a new variable in the Data View that provides the expected area/percent under the normal curve for the specified variable for each observation of interest.
One-Way ANOVA FROM THE DATA VIEW Use the following procedure to execute a one-way ANOVA:
1. Select Analyze>Compare Means>One Way Anova. This will produce the following screen:
2. Click on the quantitative variable of interest. Click on the arrow next to the Dependent List box. Click on the cate- gorical variable of interest (it must have at least three val- ues). Click on the arrow next to the Factor box. (Note that to use this function in SPSS, the categorical or factor vari- able must be numeric and read as a scale variable. This means that a variable with three groups such as High, Medium, and Low need to be recoded as 1, 2, 3. Ensure that the Variable View indicates that this variable has Type = Numeric and Measure = Scale). Select OK.
3. If the p-value was low enough to reject the null hypothesis, it is typically helpful to understand which groups are statis- tically significant from each other. This can be determined by selecting the Post Hoc button and selecting one of the many options (e.g., Tukey, LSD, Bonferroni).
Chi-square Test of Independence (and Homogeneity) FROM THE DATA VIEW Use the following procedure to execute a chi-square test of independence:
1. Select Analyze>Descriptive Statistics>Crosstabs. This will produce the following screen:
2. From the list of variables, click on a categorical variable and click on the arrow next to the Row(s) box. Click on a second categorical variable and click on the arrow next to the Column(s) box.
3. Select the Statistics button. Select the chi-square option. Select Continue>OK.
4. Note that a chi-squared test of independence and a chi- squared test of homogeneity are executed the same way in SPSS, but the results are interpreted differently. A test of independence tests the null hypothesis that there is no asso- ciation between the row and column variable, which come from the same population. A test of homogeneity tests the null hypothesis that different populations have the same proportions of some variable.
Displays of Categorical Data (e.g., pie charts, and bar charts) FROM THE DATA VIEW Use the following procedure to generate a graphical display of categorical data:
1. Select Graphs>Legacy Dialogs>Bar. This will produce the screen to the right:
2. Ensure that the first option is selected. Click on the Define button. From the list of variables on the left, select a cat- egorical variable of interest. Click the arrow next to the box labeled Category Axis. Select OK.
3. Typical results are shown to the right:
4. Note that a similar process is used to generate pie charts. Follow the same process, but assign the relevant cate- gorical variable to the box labeled Define slices by.
IBM_SPSS_StatsStudentVersion.qxp:SPSS 9/24/10 11:00 AM Page 2
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