BU422 Final Test Cheat Sheet

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Wilfrid Laurier University *

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422

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Statistics

Date

Jan 9, 2024

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docx

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Uploaded by MajorDanger13006

Descriptive and Frequency Analysis ● Frequency test → nominal (categorical questions i.e yes/no, gender) ○ Questions with three coloured circles on SPSS indicate nominal ○ Can run one frequency test for all nominal values ● Descriptive test → interval, scale, ratio ○ Questions with ruler icon on SPSS indicate interval ○ Can run one descriptive test for all interval values - Example Question: Conduct a descriptive and frequency analysis for the following variables: Online Store, Certificates, Number of Certificates,YouTube, Instagram, Average Price, Revenue, and Production. Interpret the results of this analysis. Steps to Conduct Frequency Test on SPSS Click descriptive statistics → frequencies → add in the variable, → hit statistics → click mode and continue → select ok **doesn't really matter if you don't select mode How Analyze Results of a Frequency Test ● Analyze values in the “Valid Percentage” column (answers of those with valid responses) ● How to interpret → report basic findings (ex: majority of respondents i.e 80% do not have certificates)

Steps to Conduct a Descriptive Test on SPSS Click descriptive measures → discrepancies → select variables → select options → click median, minimum, maximum and standard deviation → select ok How Analyze Results of a Descriptive Test ● Analyze values in the mean column ○ How to interpret → the average is… (ex: average revenue of respondents is $220,033) ● Greater std deviations means greater variability in responses

Cross Tabulation ● Association between 2 variables (with percentages) - both variables are categorical ● Can calculate individual binaries or all from running test with no percentages ● If you’re determining binaries for all 4 conditions → can select total in SPSS - Example question: what % of wineries w certificate have fb and what % of wineries without certificate have fb → 2 binary example - In this case make certificates rows and facebook columns and u would calculate horizontally - Utilize an appropriate statistical test to determine the percentages of wineries that a) have both a certificate and an online store, b) have a certificate but no online store, c) do not have a certificate but have an online store, and d) have neither a certificate nor an online store → all 4 binary example Steps to Conduct Cross Tabulation Test on SPSS Analyze > Descriptive > Crosstabs> input one variable in rows and How to Analyze Cross Tabulations ● REQUIRE CALCULATING PERCENTAGES ● How to read the table ○ ● Example Question: determine the percentages of wineries that a) have both a certificate and an online store, b) have a certificate but no online store, c) do not have a certificate but have an online store, and d) have neither a certificate nor an online store **ignore

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● Given that certificate is mentioned first these totals should be calculated horizontal/rows, if it were asking people have an online store and certificate then calculate vertical/columns a) 63/105 = 60% ● How to answer: 60% of wineries with certificates also have an online store b) 42/105 = 40% ● How to answer: 40% of wineries w certificates do not have an online store c) 254/418 = ● How to answer: approximately 61% of wineries without certificates have an online store d) 164/418 = ● How to answer: aprox 39% of wineries without certificates also don't have an online store

Correlation ● Finding associations among continuous variables ● Looking for correlations amongst variables How to Calculate Correlation in SPSS Analyze > correlate > bivariate> input variables > ok How to Analyze Correlations (with more than 2 categorical variables) ● Pearson correlation column: Only look at numbers with * or ** → indicates a significant correlation exists ● If sig is < 0.05 it is statistically significant at 95% confidence level ● If sig is < 0.01 it is statistically significant at 99% confidence level ● Positive correlations → binaries move in the same direction ● Negatively correlated → binaries move in opposite direction ○ Example question: explore the association between winery size (acreage), production, average price, and revenue. Interpret the findings of this analysis. ■ Acre and production have a significant positive correlations: larger binaries have higher productions ■ Significant Negative correlation between avg price and production: binaries with higher production have a lower prices ● How to answer: ○ There is a positive correlation between acres and production suggesting that wineries that have a greater amount of acres, have higher production ○ There is a positive correlation between acres and revenues suggesting that wineries with greater amount of acres, experience higher revenues ○ There is a negative correlation between production and average price

suggesting that wineries with high production have lower average prices Independent Sample t-Test ● Comparing means of two groups

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● A scale variable requires comparing means ○ ex: 1 to 5, level of satisfaction male vs female ○ Interval, ratio ● null hypothesis states that there is no difference between the means being compared ● Reject null hypothesis: significant or true difference between the means How to Calculate t-Test on SPSS ● Test variable → level of something/scale ● Grouping variable → category (yes/no) (male/female) How to Analyze Output of Independent-Sample t Test ● Can first observe means but not enough to make a conclusion ● Look at the One sided or two-sided P (doesn't matter) ○ IF Sig. is < 0.05 → Look at the one-sided p-value in equal variances not assumed (just means that there is significant variances in responses) ■ If Sig>0.05 → look at one-sided p-value in equal variance

assumed ○ Can also choose to analyse at any one of the 4 p value numbers ○ If sig level is smaller than 0.05 → difference is statistically significant, reject null hypothesis ■ We can reject at the null hypothesis at 95% confidence level ○ If sig level is greater than 0.05 → no statistically significant difference, can’t reject null hypothesis, means are the same ● Example: investigate whether wineries with certificates have a higher number of followers on Instagram compared to those without certificates ● How to answer: the equal variances not assumed one-sided p value is greater than 0.05 meaning there is no statistically significant difference between the average number of instagram followers a winery with a certificate has and the number of followers a winery without a certificate has. Suggesting that wineries with certificates do not necessarily have more followers compared to those without. ONE-WAY ANOVA ● Comparing means of 2+ groups ● Interval scale

How to Calculate on SPSS ● Post Hoc → Duncan is essential because it tells us exactly where the differences are in each category ● The factor is the variable with 2 groups How to Analyze Output of ANOVA Test ● The Sig. value in the ANOVA table indicates the level of significance ● Sig < 0.05 indicates a statistically significant differences in at least one pair of means ○ Indicates there are differences among the group ○ If Sig > 0.05 shouldn’t analyze results because we accept the null hypothesis

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● Post Hoc Test can indicate which category had the highest and lowest means ○ Ex: individuals 60 and older have a higher degree of desirability toward the card model, ages 20-29 have lowest degree of desirability ● Ignore the middle table that they provide and focus on the two above Regression Analysis ● allows you to examine the relationship between two or more variables of interest How to Calculate Regression on SPSS

Analyze> regression>linear> dependent variable > add all independent variables > click statistics > collinearity diagnosis > ok ● Assumption of regression → indiepend variables are not highly correlated (otherwise cant run regression) How to Analyze Regressions *note values for questions with only options for response (1,2) 1. look at Adjusted R square → indicates that certain % of which the dependent variable can be predicted by the independent variables 2. look at Sig in ANOVA table (if < 0,05 → significant) ○ If there's a sig statistical diff then this means the model is significant and the independent variable variances can be attributed to some of the dependent variables so can proceed further into the analysis 3. Look at the Coefficients table and start by looking at values in the Statistics VIF column ● If all values are < than 10 → continue with analysis ● If Statistics VIF > 10 → must remove variable from analysis 4. Look at sig values in the coefficients tables and t column ○ If sig < 0.05 → significant ○ Look at t-test column to determine if it is negative or positive sig diff ■ Note: if values are only (0,1) → negative sig dependence indicates that as the dependent variables increase, the value of the independent variable goes down 5. Rerun the test but remove the variables that are not significant ● Compare and draw conclusions of correlations based on sig and negative/positive t values

Significance of the Difference Between Two Percentages ● If the null hypothesis were true, we would expect 95% of the z scores computed from 100 samples to fall between +1.96 and -1.96 standard errors. ○ Or if we can see no diff in percentage number ● If the computed z value is greater than +1.96 or - 1.96, it is likely that there is a real statistical difference between the two percentages. Reject null hypothesis Example: According to the data, 25% of unmarried respondents and 40% of married respondents own a luxury car. The sample sizes are 110 for unmarried individuals and 890 for married individuals. Determine if this difference in luxury car ownership between unmarried and married respondents is statistically significant. p1 = 25% q1 = 75% p2 = 40% q2= 60% n1=110 n2=890 ● Sp1 - p2 = = 4.44 ● Z = (25 - 40) / 4.44 = - 3.38 ○ Since the 7 score -3.38 is greater than -1.96 this indicates there is a statistically significant difference in the percentages of the two groups Calculating Response Rate - → # eligible completed surveys / estimated eligible respondents in the sample

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1. Calculate # of those who didn't open the email/message (refusals/not reached): = # total sent out - # those who opened & clicked on survey link 2. Calculate # of ineligible: = # those who opened and clicked on survey link - # eligible respondents 3. Calculate eligibility rate : = # eligible respondent completions/ # clicked on survey link 4. Calculate estimated total # of eligible respondents in our sample: = # eligible respondent completions + (# didn't open the email x eligibility rate) 5. Calculate RESPONSE RATE: # eligible survey completed surveys / estimated eligible respondents in the sample Example: in a recent survey, emails were sent to 2,500 individuals. Out of these, 1,300 recipients opened the email and clicked on the provided link. Among these, 1,000 qualified for and completed the survey. Calculate the response rate for this study. 1. 2500 - 1300 =1200 2. 1300 -1000 =300 3. 1000/1300 = 77% 4. 1000 + (1200 x 0.77) = 1924 5. 1000/1924 = 52% → refusals + not reached = # who did not open

BU422 Final Test Cheat Sheet

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