How Do I Calculate Z-Scores and Create Frequency Distributions in SPSS?

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In summary, the conversation is about a student seeking help with using SPSS for a paper assigned by their university professor. The paper involves analyzing a survey on attitudes towards same-sex marriage, with questions on age, sex, opinions on same-sex marriage, education level, place of upbringing, and marital status. The student is stuck on constructing a frequency distribution and calculating appropriate measures of central tendency and dispersion. They also have questions about setting the standard deviation in SPSS for calculating z-scores.
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superstats
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My university professor has assigned us a paper and we are just beginning to learn how to use SPSS. I am stuck on one particular question and am not sure how to proceed. This is the question:

2) "A survey measuring attitudes toward same-sex marriage was administered to 1000 people. The survey asked the following questions:

1) What is your age?
2) What is your sex?
i) Male
ii) Female

3) Marriages between people of the same sex do not work out and should be banned by law.
i) Strongly agree
ii) Agree
iii) Undecided
iv) Disagree
v) Strongly disagree

4) How many years of schooling have you completed?
5) Which category below best describes the place where you grew up?
i) Large city
ii) Medium-size city
iii) Suburbs of a city
iv) Small town
v) Rural area

6) What is your martial status?
i) Married
ii) Separated or divorced
iii) Widowed
iv) Never married

The scores of 20 respondents are reproduced below:

Case / Age / Sex / Attitude On same-sex marriage / Years of school / Area / Marital Status
[the 20 cases and data is here]

a) For each variable, construct a frequency distribution and select and calculate an appropriate measure of central tendency and measure of dispersion. Summarize each variable in a sentence.

b) For all 1000 respondents, the mean age was 34.70 with a standard deviation of 3.4 years. Assuming the distribution of age is approximately normal, compute Z scores for each of the first 10 respondents above and determine the percentage of the area below (younger than) each respondent."

For a), how do I go about constructing a frequency distribution from my 20 cases?
For b), what confuses me is how do I set the standard deviation of 3.4 years in SPSS? Or am I thinking this question out incorrectly? Much thanks if you can guide me with SPSS!
 
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  • #2
Hey superstats.

For a frequency distribution go to the descriptives, then explore and you'll get the option to produce a histogram as well as the other descriptive statistics with a normality plot.

For b you need to consider the standard error of the mean and not the standard deviation: they are related but not the same. This is again an option in SPSS in one of the descriptives (forget which one).
 

1. What is a z-score and how is it calculated?

A z-score, also known as a standard score, is a statistical measure that indicates how many standard deviations a data point is from the mean of a data set. It is calculated by subtracting the mean from the data point and then dividing by the standard deviation.

2. Why are z-scores important in statistical analysis?

Z-scores are important because they allow for the comparison of data points from different data sets by standardizing the data. This makes it easier to identify outliers and understand the distribution of the data.

3. How is a z-score interpreted?

A z-score of 0 indicates that the data point is equal to the mean of the data set. Positive z-scores indicate that the data point is above the mean, while negative z-scores indicate that the data point is below the mean. Higher absolute values of z-scores indicate that the data point is further from the mean.

4. Can z-scores be used for non-normal distributions?

Yes, z-scores can be used for any distribution as long as the data is numerical and continuous. However, the interpretation of z-scores may be limited for non-normal distributions.

5. How do z-scores relate to p-values and significance levels?

Z-scores can be used to calculate p-values, which determine the probability of obtaining a certain result by chance. A significance level, typically set at 0.05, is used to determine if a p-value is low enough to reject the null hypothesis. Z-scores can also be used to compare the results of different statistical tests.

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