1. Basics of Data Analysis

Transcription

1

2 Cal Poly Pomona Department of Political Science Statistics Boot-Camp Table of Contents 1. Basics of Data Analysis... 1 a. What is SPSS?. 1 b. Variables and cases Hypotheses...2 a. Independent and dependent variables..3 b. The Causal Mechanism 3 c. What happens if my hypothesis is wrong? Data View vs. Variable View in SPSS Levels of Measurement 5 5. Descriptive Statistics 6 a. Determining the Appropriate Descriptive Statistic Single Variable Graphs 7 a. Bar Graphs... 7 b. Histograms Computing Variables Transforming Existing Variables Determining the Appropriate Test T-Test ANOVA Crosstabulations. 16 a. Chi-square Correlation Regression Basics of Data Analysis Data analysis is centered around a dataset. A dataset is housed in a spreadsheet program. A dataset can contain information about many different things, but we usually call these observations or cases. We collect information about these observations or cases as characteristics we call variables. Overall, we use datasets to draw conclusions about the connections between these variables. 1a. What is SPSS? SPSS is predictive analysis software that is heavily used within the social sciences, but has broad applications in the private sector. Predictive analysis software is another way of way to describe a computer program that is able to evaluate the complexities of a dataset like ours. SPSS looks and feels a lot like Microsoft Excel, a spreadsheet program that is available within Microsoft s software package. SPSS does what Excel does and 1

3 more! With SPSS, we have a lot of options with the drop-down menu, but we only use a small number of these options for this class. 1b. Variables and cases Variables and cases are the basic elements of a SPSS worksheet. Variables are represented in the columns of your worksheet, while cases (observations) are represented by the rows of your worksheet. You should read the SPSS worksheet as such: In the example above, each case (or row) represents a state. In the example, the case highlighted is the first state in the dataset: Alabama. We have information about each of these 50. We can look at this information in the variables. Columns in the SPSS worksheet represent variables. In the example above, the variable selected is population. In the worksheet, each state has an entry for population. For Alabama, this is 4,447. To get a full explanation for variables in a dataset, there usually is a codebook. A codebook is a PDF or DOC file that just gives you information about these variables and how that information is collected. If you are constructing your own dataset, you should consider keeping a codebook to be organized. 2. Hypotheses When forming a hypothesis, you are attempting to establish a relationship between two variables. When establishing a hypothesis, you are proposing that one variable causes a direct change in another variable. You should look at your variables and think sensibly about which variables are connected to one another. SPSS is a great tool for the social sciences because it can help us evaluate the truth to our hypotheses. A hypothesis 2

4 typically only has two variables: an independent and dependent variable. These are explained below. 2a. Independent and dependent variables The independent and dependent variable distinguishes which a) variable is causing the change and b) the variable that is being changed. When discussing the independent variable, we are referring to the variable that is causing the change. For example, if I am hypothesizing that an increase in police spending will decrease the murder rate in a state police spending is considered the independent variable. Police spending is causing a change in the murder rate. When discussing the dependent variable, we are referring to the variable that is being changed. In the above example, murder rate would be the dependent variable. Murder rate is responding to an increase in police spending, thus it is being changed by another variable in the dataset. In establishing a hypothesis, you should also figure out which of the two variables are the independent and dependent variables. Doing so will help you identify the tests you need to conduct. 2b. The Causal Mechanism The casual mechanism is an important element of the hypothesis. The causal mechanism describes the logic in your hypothesis. Essentially, you are explaining the logic behind why you think one variable would cause a change in another variable. This logic should follow a reasonable way of thinking about the relationship you are proposing. An example of a poorly formulated causal mechanism would be: An increase in police spending would cause a decrease in the murder rate. This does not explain the logic between the connection of police spending and the murder rate. A more appropriate causal mechanism would be: An increase in police spending would bring about more resources for police departments including more officers, better equipment, and a stronger means to dealing with criminals. These increased resources would discourage citizens from committing crimes like murder, which would drop the murder rate within a state. Notice how the causal mechanism logically explains why police spending would cause a change in the murder rate by taking the reader through a hypothetical situation of what would happen within a state had police spending increased. c. What happens if my hypothesis is wrong? Nothing. In testing your hypotheses with SPSS, you may find that you were completely wrong. This is completely fine. Do not worry about it. As long as you are performing the test correctly and interpreting the test correctly, you should feel confident about including the test and hypothesis in your paper. As social scientists, we should publish and report null findings. 3

5 3. Data View vs. Variable View in SPSS At the bottom of the SPSS worksheet, you ll see two options to view your data: Data View and Variable View : Data View is the default in SPSS. You should open the dataset and see Data View. Data View functions very similar to an Excel worksheet. You ll see the rows and columns of your dataset: showing the cases and variables for your data. You can examine Data View to look at the individual entries in your dataset. Variable View allows you to add more detail to your dataset. Variable View looks remarkably similar to the SPSS worksheet with rows and columns. However, do not be fooled. This is not a functioning worksheet. Rather, in Variable View, each row represents one variable. Variable View allows you to add information to SPSS, telling the program more about that variable. In the first column, you see Name, which just tells you the name of each of the variables. The second column, Type, allows you to tell SPSS whether or not your variable is String or Numeric. A variable that has text in the individual entries under Data View is a string variable. Any variable that has numbers in the individual entries under Data View is a numeric variable. Skipping to the fifth column, Label, this field allows you to give more information about the variable by typing in more text, including non- alpha/numeric characters. If you wanted to add more information about each of the variables by looking at the codebook, you would add this information in the Label field. 4

6 The sixth column, Values, allow you to add value labels to categorical (nominal or ordinal) variables in the dataset. If you leave this values field unlabeled, SPSS will only show you numbers when conducting its tests. This can get pretty confusing, especially if you re presenting this data in a professional setting! Thus, you should use this Values field to label your variable values. Thus, instead of having 0 and 1 appear in your output, SPSS would attach a label to the 0 and 1 each time a test was used. Variable View in SPSS Finally, the tenth column, Measure, allows you to tell SPSS your level of measurement: nominal, ordinal, or scale. Please note that Scale is another way of saying Interval- Ratio. 4. Levels of Measurement You must use the levels of measurement to determine which graphs and tests to use in SPSS. Thus, in establishing a hypothesis, you must determine each variable s level of measurement. Nominal: Does not indicate the amount of the thing being measured; If numbers are chosen, they are done so arbitrarily. These are categorical, but they are non-rankable categories. There is no sense in how they should be organized from left to right, top to bottom. Example: Gender is a nominal variable (male = 0; female = 1) Ordinal: These are also categorical, except variable is measured, but the variable can be ranked ordered. The differences between values are not measureable. Example: Party identification is an ordinal variable (Democrat = 1; Independent = 2; Republican = 3). 5

7 Interval-Ratio: The variable is measured, but the differences between values are measured and equal. No absolute zero point. Examples: Any percentage would be considered interval-ratio; Percentage of people who voted for Donald Trump. 5. Descriptive Statistics Descriptive statistics refers to the basic descriptive information about the variables that you are interested in. Descriptive statistics include the following: n (number of cases), mean, median, mode, standard deviation, range, minimum, maximum, and percentiles. Descriptive statistics are simply used to give the reader a sense of what your variables look like. They cannot be used to compare one variable to another. To calculate descriptive statistics: Analyze > Descriptive Statistics > Frequencies Move the variables you want to calculate descriptive statistics for in the Variable(s) box. Click Statistics and indicate which descriptive statistics you want. After you select the descriptive statistics, click Continue. This will take you back to the above box, now click OK. Here s an example of what you might include in your final analysis: Table 1. Descriptive Statistics for State-Level Data Variable Mean Standard Range Minimum Maximum Deviation Area Black population Divorce Rate

8 5a. Determining the Appropriate Descriptive Statistics Depending on your level of measurement, you would perform specific descriptive statistics: Level of Measurement Central Tendency Variance Nominal Mode Standard deviation; range Ordinal Mode Standard deviation; range Mean if no outliers Interval-Ratio in variable Standard deviation; Median if outliers in range variable 6. Single Variable Graphs We draw single variable graphs to show what a variable looks like. This the same as calculating descriptive statistics, but just providing the reader with a visual of the single variable. Level of Measurement Nominal Ordinal Interval-Ratio Type of Graph Bar graph Bar graph Histogram 6a. Bar Graphs A bar graph will show you a graphical representation of a variable. A bar graph will only work for those variables that are nominal or ordinal. Bar graphs are best calculated for variables with distinct categories. To construct a bar graph, go to: Analyze > Descriptive Statistics > Frequencies Move the variables you want to calculate a bar graph for in the Variable(s) box. Click on Charts. 7

9 In this box, select Bar charts. It s up to you whether or not you want your bar graph to show frequencies or percentages in each of the bars. Click Continue, then click OK on the first dialog box. A bar graph will appear in your output. However, you can format the bar graph in multiple ways. Your presentation should always be professional, so to edit the bar graph, double click on the graph to open the editor. 1) Colors of the graph: To alter the colors of the graph, click on the element you want to change. You can change the colors of the bars or the background of the 8

10 graph. Once you ve clicked on the appropriate element, go to the color scheme found on [1]. You can change your colors to those which you deem appropriate. 2) Titles: You can change the name of each of the axes and title of the graph. To make this change, double click on the words. You will see a cursor appear where you can edit the text. You should definitely label the values of the bars. In the example above, you see it says 0 and 1. This is confusing. Change these to reflect what each bar represents. 3) Values: You can show the values on the bars themselves. To do this, right click on any bar and choose the option Show data labels. 4) Axes: You can change the scale on the axes. To do this, right click the numbers on the axes and select Properties Window : Make sure that you are on the Scale tab at the top of the window. Here, you ll see that you can change the minimum, maximum, and increments of the axis. If you make these changes, make sure to uncheck all the boxes. 6b. Histograms A histogram will show you a graphical representation of a variable. A histogram will only work for those variables that are interval or ratio. To construct a histogram, go to: 9

11 Analyze > Descriptive Statistics > Frequencies Move the variables you want to calculate a histogram for in the Variable(s) box. Click on Charts. In this box, select histograms. Click Continue, then click OK on the first dialog box. A histogram will appear in your output. However, you should format the histogram in the same way you format the bar graph. Your presentation should always be professional, so to edit the histogram, double click on the graph to open the editor. 7. Computing Variables SPSS allows you to create completely new variables from those on the dataset. You can add, subtract, multiply, and divide variables to create completely new variables. If you want to create new variables in SPSS, go to: Transform > Compute Variables 10

12 Target Variable: To create the new variable, type in your new variables name in this box. This name should be short with no symbols or spaces. Numeric Expression: This is the box where you write in your transformation. The numeric expression box works a little bit like a calculator. In an example hypothetical dataset, to calculate a new variable density by multiplying population by 1000, and then dividing that value by area. To recreate that equation, you would type in the following to the numeric expression box: (populationx1000)/area Adding variables is done by using +, subtracting variables is done by using -, multiplying variables is done by using x, and dividing variables is done by using /. Once you have indicated your numeric expression, click OK. Your new variable will be included in your spreadsheet. 8. Transforming Existing Variables SPSS allows you to take existing variables and re-categorize and change its values. We did this in Assignment #2 as well. Transforming existing variables is necessary when you want a simplified version of a variable. Simplifying variables is needed when calculating a crosstab. There are two options to transform existing variables: 11

13 Transform > Recode Into Same Variable Transform > Recode Into Different Variable These two options are identical to one another. The only exception is that if you choose Same Variable, SPSS will replace the original variable with your new transformation. If you choose Different Variable, SPSS will add a new transformed variable to the dataset, while keeping your original variable. As a matter of safety, you should always Recode Into Different Variable. Choose the variable you want to transform by finding it in the drop down list. Once it is highlighted, click the arrow to move it over to the Input Variable -> Output Variable box. When you first do this, you will see a?. You need to name your new variable. You do this in the box labeled Output Variable/Name. You can also give it a label, but it is not necessary to do so. After you have followed those steps, click on Old and New Values. Old and New Values will be grayed out until you choose the variable you want to transform and give the new variable a name. 12

14 The above dialog will show after clicking Old and New Values. Here, you are indicating how you want to transform your old values. The first column of this dialogue asks you about your old values, the second column is where you indicate how these values will be transformed. Once you have indicated your changes, make sure to click Add for each individual transformation. You should account for all of the values of your variables. Click Continue once you have completely transformed your entire variable. A new variable will be added to the dataset with your transformation. 9. Determining the Appropriate Test To actually test a hypothesis, you need to determine the levels of measurement for both your independent and dependent variable. Independent Dependent Appropriate Test Nominal (bivariate) Nominal/Ordinal/Interval-Ratio T-Test Nominal/Ordinal Nominal/Ordinal Chi-square Nominal/Ordinal Interval-Ratio ANOVA Interval-Ratio Nominal/Ordinal Recode your independent variable to nominal; Chi-square Interval-Ratio Interval-Ratio Correlation & Regression 13

15 10. T-Test In comparing the relationship between an independent variable that only has two categories and a dependent variable that can be any level of measurement. To conduct a T-Test, go to: Analyze > Descriptive Statistics > Independent Samples T-Test Here, you would put the dependent variable in your Test Variable(s) box. Your independent variable would go in the Grouping Variable box. When you put the independent variable in the Grouping Variable box, you should click the Define Groups button. Here you are going to be asked to specify the values for Group 1 and Group 2. These are the values of your independent variable, whatever they are. Often, they are 0 and 1. Once you ve done that, click Continue and then click OK. 14

16 The above T-Test will appear on your output. You should include an appropriate version of this output on your paper. Do not include SPSS output on your final paper. Table 1. T-Test for Death Penalty and Policy Liberalness Value T value Significance Value.013 This table is much easier to read and a professional presentation that is appropriate for the paper. You must make one interpretation from this table and that is this significance value. T value: The T value for the relationship between death penalty and policylib is Significance: The significance value tells you if the relationship between your two variables exists in the first place. You are looking for a significance value that is lower than.05. Anything above.05 indicates that this relationship is not significant. The significance value indicates the probability that the relationship between the two variables is due to chance. This is why we want this value to below.05 or 5%. In Table 1, the significance value indicates that there is a 1.3% probability that this relationship is due to chance. This means that there is indeed a relationship between death penalty and policy liberalness, since it is below the statistical cutoff of 5 percent. 11. ANOVA In comparing the relationship between an independent variable that is nominal or ordinal and a dependent variable that is interval-ratio. To conduct an ANOVA, go to: Analyze > Compare Means > One-Way ANOVA 15

17 Here, you would put your independent variable in the Factor box. Remember, this would be a nominal or ordinal variable. You would put your dependent variable in the Dependent List box. Once you have selected your variables, click OK. The above ANOVA test will appear on your output. You should include an appropriate version of this output on paper. Do not include SPSS output on your final paper. Table 1. ANOVA for Death Penalty and Murder Value F value Significance Value.006 This table is much easier to read and a professional presentation that is appropriate for the paper. You must make one interpretation from this table and that is this significance value. F value: The F value for the relationship between death penalty and murder is Significance: The significance value tells you if the relationship between your two variables exists in the first place. You are looking for a significance value that is lower than.05. Anything above.05 indicates that this relationship is not significant. The significance value indicates the probability that the relationship between the two variables is due to chance. This is why we want this value to below.05 or 5%. In Table 1, the significance value indicates that there is a 0.6% probability that this relationship is due to chance. This means that there is indeed a relationship between death penalty and murder, since it is below the statistical cutoff of 5 percent. 12. Crosstabulations Crosstabulations compare the relationship between two variables. For this class, we simply used crosstabulations to show these differences on a table. It is important to have manageable categories in your crosstabulations. You cannot calculate a crosstab for variables like area or population. To do so, you would need to first transform those variables to a number of manageable categories. (For example, creating a new variable for population states with a population under 1,000,000 and states with a population over 1,000,000.) 16

18 To calculate a crosstabulation, go to: Analyze > Descriptive Statistics > Crosstab You must indicate which two variables you want to include in your crosstabulation. In hypothesizing a relationship between two variables, you have a cause and effect. You are hypothesizing that one variable causes an effect in another second variable. Typically, the outcome (the dependent, the effect) variable should be placed in your column. Your cause (the independent) variable should be placed in your row. Once you have placed the variables in the appropriate boxes, click on Cells. With this Cells box, make sure to tell SPSS that you want to calculate percentages. You can calculate percentages based on the row, the column, or for the total (everything). Choose whatever option is appropriate, but you should have percentages in your final crosstabulation. Click continue. On the original dialog box, click OK. You will get a crosstabulation in your output. You should not copy and paste this crosstabulation into your final report, it should look professional. An example that might be included in your final paper may look like: 17

19 Culture Table 1. Culture & Death Penalty. Death Penalty States without the States with the Death Penalty Death Penalty 7 9 Traditionalistic (14.0%) (18.0%) 5 13 Moralistic (10.0%) (26.0%) 1 15 Individualistic (2.0%) (30.0%) 12a. Chi-square Chi-square tests are tied to crosstabulations (review the previous section). Chi-squares also typically tests a hypothesis between two nominal variables. If you are being tasked with performing a chi-square, you need to draw a crosstabulation first. In fact, a chisquare is a simple option that you toggle with a crosstabulation. To calculate the chi-square, perform a crosstabulation: Analyze > Descriptive Statistics > Crosstab As discussed in the previous section, place your variables in the appropriate boxes. However, to calculate a chi-square, click on the Statistics button on the right side of the crosstabulation dialog box. The following dialogue box will then pop up on your screen: 18

20 Simply toggle the Chi-square box at the top of the box. Click Continue. Once you return to the first dialogue box, you are done. Click OK. 19

21 In addition to the crosstabulation, the chi-square test on the previous page will appear on your output. You should include an appropriate version of this output on your paper. Do not include SPSS output on your final paper. Table 1. Chi-Square for Culture and Death Penalty Value Chi-square value Significance Value.053 This table is much easier to read and a professional presentation that is appropriate for the paper. You must make one interpretation from this table and that is this significance value. Chi-square value: The chi-square value for the relationship between culture and death penalty is Significance: You must interpret the significance value separately from the chi-square value. The significance value tells you if the relationship between your two variables exists in the first place. You are looking for a significance value that is lower than.05. Anything above.05 indicates that this relationship is not significant. The significance value indicates the probability that the relationship between the two variables is due to chance. This is why we want this value to below.05 or 5%. In Table 1, the significance value indicates that there is a 5.3% probability that this relationship is due to chance. This means that there is not a relationship between political culture and death penalty, since it is above the statistical cutoff of 5 percent. 13. Correlations In comparing the relationship between two interval-ratio variables, we utilized correlation tests and regressions together. To conduct a correlation test, go to: Analyze > Correlate > Bivariate 20

22 Here, what you ll do is select the two variables you want to conduct the correlation test for and move them into the Variables box. You should make two changes: 1) For the Test of significance, make sure that one-tailed is selected. 2) Click Options. Make sure that Exclude cases listwise is selected. Once you have selected your variables and made the two changes, click OK. 21

23 The output on the previous page shows your SPSS output. You should include an appropriate version of this for your final policy project. It should be formatted professionally, like below: Table 1. Pearson Correlation for Christians and Murder Value Pearson Correlation Significance Value.340 This table is much easier to read and professionally presentable. You must make three interpretations with this table. Strength: Strength is interpreted by looking at the size of your Pearson Correlation. You should take the absolute value of your Pearson Correlation in interpreting the strength, meaning this interpretation holds the same for whether or not the value is positive or negative. For any value that falls between 0 and.29, this is a weak relationship. For any value that falls between.30 and.59, this is a moderate relationship. For any value that falls between.60 and 1.00, this is a strong relationship. In Table 1, the Pearson Correlation Value of is a weak effect. Direction: This is looking at the number sign, whether or not your Pearson Correlation is positive or negative. In Table 1, the Pearson Correlation Value is negative. This means as values on christians increase, the values of murder decrease. Had this value been positive, this would be the inverse: As values of one variable increases, the values of the other variable also increases. Significance: You must interpret the significance value separately from the Pearson Correlation. The significance value tells you if the relationship between your two variables exists in the first place. You are looking for a significance value that is lower than.05. Anything above.05 indicates that this relationship is not significant. The significance value indicates the probability that the relationship between the two variables is due to chance. This is why we want this value to below.05 or 5%. In Table 2, the significance value indicates that there is a 34.0% probability that this relationship is due to chance. This means that there is not a relationship between christians and murder, since it is above the statistical cutoff of 5 percent. 14. Regression Regressions are the most sophisticated tests that we conducted in this class. Regressions tell you quite a bit about the relationships between two interval-ratio variables. We calculate regressions in conjunction with correlations. To calculate a regression, go to the following: Analyze > Regression > Linear 22

24 Here, you only have to select the variables that you want to compare to each other. Whenever you hypothesize a relationship, you have a cause and effect. The Dependent box will always contain the variable that is the outcome. The Independent(s) variable will contain the variable that is the cause. In addition, you can hold additional variables constant with a regression. Perhaps you are concerned that another variable might affect your original hypothesis. If you want to make sure that this third or additional variables do not have an effect, you can include them in your Independent(s) box. The regression will then take that variable into account when estimating a model testing your original hypothesis. Once you select your variables, click OK. In the example, I will show below, my original hypothesis is that the amount of christians in a state will affect support for gay marriage. However, I want to control for the liberalness of the states themselves, with policylib. 23

25 You will get four charts in the SPSS output. For our purposes, you only need the charts labeled Model Summary and Coefficients. To include these charts in your final paper would be a relatively unprofessional presentation, make sure to present this information in a clear and concise way: Table 3. Regression Model on the Effect of Support of Gay Marriage in the States. Beta Coefficient Significance Value Percentage of Christians in a state R-Square.120 You have to interpret three numbers for each regression that you conduct. 24

26 Beta Coefficient: The beta coefficient tells you both the strength and direction of your relationship. For my original relationship between christians and marriage, my beta coefficient is This value tells me that: For every unit increase in the percentage of Christians in a state, there is a corresponding.290 unit decrease in the support for gay marriage in a state. Given that support for gay marriage ranges from 0 to 100, a.117 decrease is not a huge effect. Significance: Much like correlation, you must interpret the significance value separately from the beta coefficient. The significance value tells you if the relationship between your two variables exists in the first place. You are looking for a significance value that is lower than.05. Anything above.05 indicates that this relationship is not significant. The significance value indicates the probability that the relationship between the two variables is due to chance. This is why we want this value to below.05 or 5%. In Table 3, the significance value indicates that there is a 1.4% probability that this relationship is due to chance. This means that there is indeed a relationship between Christians and gay marriage support, since it is below the statistical cutoff of 5 percent. R-Square: R-square tells you how good of a job your model is doing at predicting your dependent variable. We are trying to predict gay marriage support in this regression. As a rule of thumb, a good model is anything above.60. This means that our model s variables predict more than 60% of the variation in the dependent variable. We would hope our model has strong predictive power! In Table 3, our R-square value is.120. This means that the model (christians, policylib) predict 12.0% of the variation in my dependent variable (marriage). Since this is below 60%, we know this model is a poor predictor of gay marriage support. 25