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I am very new to statistics and is currently performing binary logistic regression analysis to test null hypothesis for my dissertation.

First, both my independent variables and dependent variable are dichotomous (0, 1).

The dependent variable for the analysis is whether or not the respondents got attacked by cyberstalkers.

As you can see from the figure below, I have selected all variables as the covariates, and the significance levels show are .66 and .016 respectively for AcceptStrangerFR and PublicPrivacySetting.

enter image description here

However, when I insert them individually, the significance level changes to MORE SIGNIFICANT, example as follows: enter image description here

My question is why does the significance level differ when I insert the independent variables individually and as a group?

Also, which is the correct way to analyse these data? Should I compare the independent variables against the dependent variable individually or should I include them all at once and test them against the dependent variable?

This is important because the significance level is >0.05 when tested in group and is <0.05 when tested individually.

Hope you guys understand what I mean, thank you all very much in advance!

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It would be better to work at this from the ground up. First, study the statistical principles involved. Then see how those principles are used as a foundation for the analysis while you insert heavy subject matter knowledge. In the vast majority of cases it is best to proceed something like this:

  1. Make sure the measurements are valid
  2. Formulate a model based on subject matter knowledge, being cognizant of causal pathways and what is measured when
  3. Check that the number of parameters in the model can be supported by an adequate number of observations (a common rule of thumb is to have at least $15p$ as many observations in the least frequent $Y$ category where $p$ is the number of parameters required to fit the predictors)
  4. Fit the single model
  5. Interpret the model

In other words, don't think of this as a "let's try different models on the same data" exercise.

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