Formulas Flashcards
What does it mean, Descriptive statistics for demographic characteristic will be computed.
Frequency table
It means that basic statistical analyses will be carried out on the demographic information collected from participants. This involves calculating measures like averages, standard deviations, and ranges for age, as well as counts and percentages for categorical data such as gender, ethnicity, education level, and other demographic factors. These statistics provide a summary of the study population’s characteristics, helping to understand the sample’s composition and diversity.
Frequency table
explain:
Means, standard deviations, minimum scores, and maximum scores will then be computed for each DUREL question and for the SWLS measure”
For example, if participants respond to a Duke University Religion Index (DUREL) question about their frequency of prayer on a scale from 1 (Never) to 5 (Daily), the mean (average) score might indicate the overall level of prayer frequency among participants. Standard deviation would show how much variation exists from the average, revealing if responses are clustered or spread out. Minimum and maximum scores would highlight the lowest and highest levels of prayer frequency reported. Similarly, for the Satisfaction with Life Scale (SWLS), calculating these statistics would provide an overview of participants’ overall life satisfaction.
explain this “Given that the data points are ordinal and quantitative in nature, they may violate assumptions of normality. “
The data collected in this study are ranked (ordinal) and involve numbers, but they might not spread out in a way that’s evenly centered around the middle value, like a bell curve. This means some statistical methods that assume data is shaped like a bell curve might not work well with this data.
explain “Thus, non-parametric inferential statistical methods are an apt fit for analysis.”
Since the study’s data doesn’t neatly fit a bell curve, it’s better to use statistical methods that don’t assume data is spread this way. Non-parametric methods are great for this situation because they can handle data that ranks or categorizes without requiring a specific distribution pattern, making them more flexible for analyzing the study’s unique types of data.
give an example of non-parametric inferential statistical methods
An example of non-parametric inferential statistical methods is the Spearman’s rank correlation coefficient. This method is used to measure the strength and direction of the association between two ranked variables. It’s particularly useful when the data do not meet the normal distribution assumption required by parametric tests like Pearson’s correlation coefficient. Spearman’s rank is ideal for analyzing ordinal data or data that do not adhere to a normal distribution, offering a way to identify relationships between variables without assuming a specific data distribution pattern.
Explain how the hypothesis is going to be tested
To test if more frequent prayer and religious service attendance correlate with better well-being among college students, the study will use two Spearman’s rank correlation tests. This statistical method assesses how well the relationship between two variables can be described using a monotonic function, without assuming the data follows a normal distribution. If the correlation coefficient (Rs) for either prayer frequency or service attendance with subjective well-being is over 0.7 and the p-value is less than 0.05, it indicates a strong positive relationship, suggesting that higher engagement in these religious practices is associated with greater well-being.
Explain what is a point of exploratory analysis
To understand if the relationship between religious activities and well-being is straight-line (linear) or has a different pattern but still goes in one direction (monotonic), both Pearson’s and Spearman’s correlation coefficients will be calculated. Pearson’s is used when data is evenly spread and fits a bell curve, while Spearman’s doesn’t need the data to spread this way. By comparing the two, researchers can see if the relationship is direct or if it varies but still trends in the same direction, helping to clarify the nature of the connection between religious activities and well-being.
Why there are two linear regression models?
This passage explains that two linear regression models will be used to see if religious activities (like attending services or praying) can predict how well people feel about their lives. The first model looks at how going to religious services affects life satisfaction scores, while the second checks if prayer frequency does the same. The models will be carefully checked to make sure they fit the data well, using statistical tests to confirm if the findings are reliable. The aim is to see if more religious activity relates to higher satisfaction with life, but the analysis will be cautious because of the data’s nature.
Explain the scatterplots
This description outlines a method for visually analyzing the relationship between religious practices (prayer and service attendance) and subjective well-being using scatterplots. The x-axis represents the frequency of these religious activities, scored from 1 to 5, while the y-axis shows subjective well-being scores, ranging from 1 to 7. Linear regression lines on these plots predict how changes in religious activity frequency might affect well-being. The slope of these lines indicates the relationship’s direction, helping to understand if the relationship is linear or might better fit a nonlinear model, such as one represented by a LOWESS curve for more nuanced insights.
explain “The model will be assessed for fit, checking assumptions of linearity, independence, homoscedasticity, and normality of residuals.
This means that the linear regression model used in the analysis will be evaluated to ensure it accurately represents the data. “Linearity” checks if the relationship between variables is straight-line. “Independence” ensures that the data points do not influence each other. “Homoscedasticity” means the spread of the residuals (differences between observed and predicted values) is consistent across all levels of the independent variables. “Normality of residuals” tests whether the residuals are distributed in a bell-shaped curve. Meeting these assumptions validates the model’s reliability.
