要实现Android对话框改变Activity的变量，可以使用接口回调的方式。以下是一个示例代码：

在Activity中定义一个接口，用于在对话框中更改变量的回调：

public interface DialogCallback {
    void onVariableChanged(String newValue);
}

在Activity中实现该接口：

public class MainActivity extends AppCompatActivity implements DialogCallback {

    private TextView textView;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        textView = findViewById(R.id.text_view);

        Button button = findViewById(R.id.button);
        button.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View v) {
                showDialog();
            }
        });
    }

    private void showDialog() {
        MyDialogFragment dialog = new MyDialogFragment();
        dialog.setCallback(this);
        dialog.show(getSupportFragmentManager(), "dialog");
    }

    @Override
    public void onVariableChanged(String newValue) {
        textView.setText(newValue);
    }
}

创建一个自定义的对话框Fragment：

public class MyDialogFragment extends DialogFragment {

    private DialogCallback callback;

    public void setCallback(DialogCallback callback) {
        this.callback = callback;
    }

    @NonNull
    @Override
    public Dialog onCreateDialog(@Nullable Bundle savedInstanceState) {
        AlertDialog.Builder builder = new AlertDialog.Builder(getActivity());
        builder.setTitle("Change Variable")
                .setMessage("Enter new value:")
                .setPositiveButton("OK", new DialogInterface.OnClickListener() {
                    @Override
                    public void onClick(DialogInterface dialog, int which) {
                        EditText editText = getDialog().findViewById(R.id.edit_text);
                        String newValue = editText.getText().toString();
                        callback.onVariableChanged(newValue);
                    }
                })
                .setNegativeButton("Cancel", null);

        return builder.create();
    }
}

在对话框的点击事件中，通过回调将新值传递给Activity，并在回调方法中更新变量的值。