Personality, Nerdiness, and Attitudes Towards Statistics.

The study was run in the tutorials of Week 2, Semester 1, 2022. A total of 418 people participated, consisting of first year psychology students from PSYC1040. To make the computations more manageable, the initial sample was reduced to 130. Participation in the experiment was voluntary but students were encouraged to participate to better prepare for writing their research report.

Data organization, exploration and description

Raw data are in the Excel file, PSYC1040_SEM1_2022_Report_Raw_Data. The data are arranged in columns in the file in the following order:

Column A lists the participant numbers (Participant #)

Column B lists participant gender (Gender: 1 = Male; 2 = Female; 3 = Prefer not to say)

Column C lists each participant’s age (Age)

Column D lists individual total Extroversion scores from the Big Five Personality Scale

Column E lists individual total Agreeableness scores from the Big Five Personality Scale

Column F lists individual total Conscientiousness scores from the Big Five Personality Scale

Column G lists individual total Neuroticism scores from the Big Five Personality Scale

Column H lists individual total Openness scores from the Big Five Personality Scale

Column I lists individual total Scores from the Nerdy Personality Attributes Scale

Column J lists individual total Test & Class Anxiety from the Statistics Anxiety Rating Scale (STARS)

Column K lists individual total Interpretation Anxiety scores from STARS

Column L lists individual total Asking for help: Anxiety associated with asking for help scores from STARS

Column M lists individual total Worth of Statistics scores from STARS

Column N lists individual total Fear of Statistics Teachers from STARS

Column O lists individual total Self (ability to cope with calculations and math in stats) scores from STARS

Column P lists individual responses from the PSYC1040 Question: I feel like I am going to have a positive experience and successful semester in PSYC1040

Understanding the Data Set

Before you conduct any data analyses, make sure you are clear about what you are expecting and predicting.

As explained in your textbook, in the context of correlation, it doesn’t matter which variable is plotted on which axis in a scatterplot. However, we generally have an idea which variable is assumed to predict or influence the other and which variable is being predicted or influenced. The predictor variable goes on the x-axis and the predicted variable goes on the y-axis.

We can think of our Big Five Personality measures and the measure of the Nerdy Personality Attributes Scale as the predictor or influencer variables. We can think of the Statistics Anxiety Rating Scale (STARS) measures and the PSYC1040 question as the variables that are being predicted or influenced.

Expected Values

Recall from when you completed the questionnaire online, each item invited a response on a 5-point Likert scale indicating the degree to which you agreed or disagreed with the statement. The questionnaire software automatically codes the responses so that lower values indicate disagreement and higher values indicate agreement. Now we need to be careful when interpreting the values because we need to keep in mind what each scale was measuring:

The Big Five Personality Scale

Each of the subscales on this measure (Extroversion, Agreeableness, Conscientiousness, Neuroticism, and Openness) consist of ten items. Some of the items in each scale are positively scaled and some are negatively scaled. For example, a positively scaled item on the Extroversion scale states “I am the life of the party”. So, a high score on that item reflects a high level of extroversion. An example of a negatively scaled item on this scale might state “I have little to say”. If you responded with a high score to the first item, you would likely respond with a low score to the second one. Therefore, we need to recode the negatively scored items so that the numbers reflect the personality trait being measured.

So, for positively scaled items the scores map in the following way:

Very Inaccurate = 1

Moderately Inaccurate = 2

Neither Inaccurate nor Accurate = 3

Moderately Accurate = 4

Very Accurate = 5

And for negatively scaled items the scores map the opposite way:

Very Inaccurate = 5

Moderately Inaccurate = 4

Neither Inaccurate nor Accurate = 3

Moderately Accurate = 2

Very Accurate = 1

These mappings are done automatically by the questionnaire software. To arrive at an individual score on each of the measures, we just sum all the values from the ten items. These totals are what appear in Columns D-H in the data file. Here is how to interpret the scores on each of the five personality measures:

Extroversion (E) is the personality trait of seeking fulfillment from sources outside the self or in community. High scorers tend to be very social while low scorers prefer to work on their projects alone.

Example item: Please rate how accurately the following statement reflects who you are:

I am the life of the party.

Agreeableness (A) reflects how much individuals adjust their behaviour to suit others. High scorers are typically polite and like people. Low scorers are more blunt and tend to ‘tell it like it is’.

Example item: Please rate how accurately the following statement reflects who you are:

I am interested in other people.

Conscientiousness (C) is the personality trait of being honest and hardworking. High scorers tend to follow rules and prefer clean homes. Low scorers may be messy and cheat others.

Example item: Please rate how accurately the following statement reflects who you are:

I pay attention to details.

Neuroticism (N) is the personality trait of being emotional.

Example item: Please rate how accurately the following statement reflects who you are:

I get stressed out easily.

Openness to Experience (O) is the personality trait of seeking new experience and intellectual pursuits. High scores are curious and may seek adventure. Low scorers may be more conservative.

Example item: Please rate how accurately the following statement reflects who you are:

I am quick to understand things.

So, what is the range of values we should expect in Columns D-H? Well, each number represents the sum of the ten responses to each scale. Each response could take a value of between 1 and 5 as per the positive and negative scale mappings above. So, if someone responded “1” to all ten items, what would their total be? If they responded. “5” to all ten items, what would their total be? Answering these two questions tells us what the expected range of values on these scales is. Any observations outside that range would be impossible scores and they would need to be removed from the data set prior to computing the correlation.

Nerdy Personality Attributes Scale

This scale consisted of 50 items that reflect nerdy personality traits. Each item invites participants to rate how accurately a statement reflects who they are. For example:

Example item: Please rate how accurately the following statement reflects who you are:

I would rather read a book than go to a party.

Like the Big Five Personality Scale, The Nerdy Personality Attributes Scale is also positively and negatively scaled. After automatically adjusting for these mappings, the scores in Column I of the data file represent the total of the 50 items on this scale. To work out the expected range of values for this scale, what is the total if a participant responded “1” to all 50 items? What would the total be if they responded “5” to all 50 items? Any observations outside that range would be impossible scores and they would need to be removed from the data set prior to computing the correlation.

Statistics Anxiety Rating Scale (STARS)

Like the Big Five Personality Scale, this scale has six subscales: Test and Class Anxiety, Interpretation Anxiety, Anxiety Associated with Asking For Help, Worth of Statistics, Fear of Statistics Teachers, and Self (ability to cope with calculations in math in stats).

Each subscale consists of a different number of items. Like the other two scales, each item is scored on a scale of 1 to 5. Therefore, to work out the range of expected values, we need to take into account the number of items for each subscale individually:

Test and Class Anxiety: 8 items on this scale.

Higher values on this scale indicate greater anxiety during statistics tests and classes.

Example item:

Please rate how much anxiety you would experience in the following situation:

Walking into the room to take a statistics test

Interpretation Anxiety: 11 items on this scale.

Higher values on this scale indicate greater anxiety when interpreting statistics.

Example item:

Please rate how much anxiety you would experience in the following situation:

Walking into the room to take a statistics test

Ask for help (anxiety associated with asking for help): 4 items on this scale.

Higher values on this scale indicate greater anxiety when asking for help about statistics.

Example item:

Please rate how much anxiety you would experience in the following situation:

Asking one of your lecturers for help understanding the output of a statistics program

Worth of statistics: 16 items on this scale. (Warning: this is a tricky one)

Higher values on this scale indicate a more negative attitude towards statistics. That is, higher values correspond to the attitude that statistics is worth LESS.

Example item:

Please indicate your level of agreement with the following statements:

Statistics takes more time than it is worth

Fear of Statistics Teachers: 5 items on this scale.

Higher values on this scale indicate greater fear of statistics teachers.

Example item:

Please indicate your level of agreement with the following statements:

Most statistics teachers are not human

Self (confidence with calculations and math in statistics): 7 items on this scale. (Warning: this is a tricky one)

Higher values on this scale indicate LESS confidence when working through calculations in statistics.

Example item:

Please indicate your level of agreement with the following statements:

Since I never enjoyed maths I don’t see how I can enjoy statistics

PSYC1040 Question: One item on this scale.

On a scale of 1-100, with 1 being completely disagree and 100 being completely agree, participants respond to the following statement:

“I feel like I am going to have a positive experience and successful semester in PSYC1040.”

Your Hypotheses:

We have collected quite a bit of data with these questionnaires and so there are many different hypotheses that we can test. Below are six candidate relationships for your report. You are required to select three from this list for your report:

Neuroticism vs Test and Class Anxiety

Neuroticism vs Interpretation Anxiety

Extroversion vs Asking

Openness vs Worth

Nerdiness vs Worth

Nerdiness vs PSYC1040

For each of the three relationships you choose, you need to state a clear hypothesis about that relationship. It should indicate 1) which variable is the predictor/influencer and which is the predicted/influenced variable, and 2) the direction (sign) of the expected relationship. Here is an example statement using the relationship between Conscientiousness and PSYC1040 (this is not one of the six relationships you are examining):

Example – Conscientiousness vs PSYC1040:

From the description above, the personality trait of Conscientiousness reflects an individual’s tendency to work hard and follow rules. These attributes seem to complement the requirements of PSYC1040. Therefore, Hypothesis 1 is I expect to find a positive correlation between Conscientiousness scores and PSYC1040 scores.

Use the above example as a guide to formulate your own hypotheses about your chosen three relationships from the above list. There is no right or wrong hypothesis – you will evaluate your prediction after you have completed your analyses.

Data Screening

Once you have chosen the three relationships you want to evaluate, a key procedure in your preliminary analysis is to screen the data for unusual/impossible observations. Screen your data on the relevant variables and note any impossible scores. A researcher needs to be keenly aware of the range of possible values on each measure. Therefore, data screening can result in the removal of observations because they are impossible scores, among other reasons.

Statistical Computations:

Refer to the Report Template (below) for all the required graphs and computations.

Below are steps for calculating Pearson’s r and shared variance (remember to show the formula for correlation, the critical values and the final answer, rounded two the appropriate decimal place in an appendix:

1) Screen your data for impossible scores (if any).

Based on your knowledge of the possible responses to the variables for the three relationships you are evaluating, screen each variable for impossible scores. If you find an impossible score, you need to remove that participant for that specific analysis. That subject may stay in for other analyses if their other scores are within the acceptable range for the relevant variables.

Note: if you remove any impossible scores, you must recalculate the mean and standard deviation (without the impossible scores) for the relevant variable(s) in order to use the definitional formula to compute the Pearson’s r.

2) Compute the linear correlation for your first chosen relationship.

3) Compute the shared variance between the variables in the first relationship.

4) Compute the linear correlation for your second chosen relationship.

5) Compute the shared variance between the variables in the second relationship.

6) Compute the linear correlation for your third chosen relationship.

7) Compute the shared variance between the variables in the third relationship.

8) Assess the sign and strength of each of the three relationships. Did the results support your hypotheses?

Research Report Instructions:

These are your research report instructions. You must adhere to APA 7th Edition style and formatting practices for a research report. Here are some guidelines for each of the sections in the order that they will appear in your report (note that you will not write them in this order).

Title Page (Title is to be no more than 40 words maximum)

Also include your name

A running head:

Your tutor’s name.

Abstract (150 words maximum)

This is to be written by you.

The abstract appears by itself on a single page.

You need to summarize the study in one brief paragraph, stating the research design, the research question in terms of the variables measured, methodology, analysis, findings, and conclusion.

Introduction

You do not need to write a formal introduction.

This section can be organized with three headings:

Hypothesis 1:

You need to write one or two sentences stating your hypothesis for the first relationship you are evaluating. You need to indicate which is the predictor variable and which one is being predicted and you need to state the direction (sign) of the expected relationship.

Hypothesis 2:

Same as above but for the second relationship you are evaluating.

Hypothesis 3:

Same as above but for the third relationship you are evaluating.

Method (400 words Maximum)

This entire section is to be written by you.

You need to describe the participants in the study (number, demographic details (if any), method of recruitment, reason for participation); identify the research design; describe the measures, scoring, and variables – referring to the appendices where required; the procedure including how the measurements were acquired (random order; random assignment?). In sum, the method should enable a person completely unfamiliar with the study to replicate exactly what you did.

Results (300 words Maximum)

This section is to be written by you.

You need to describe the data including that they were explored graphically through bivariate scatterplots; state whether or not any data were excluded and give the reason why each item was excluded. Include a table of the means and standard deviations for the variables you used, label it and described it in the text. The means and standard deviations should summarize the data AFTER any impossible scores are removed. Report each of the three correlations correctly and describe them in terms of the variables that are summarized; report and describe the percentage of shared variance correctly.

Discussion

This section can be organized with three headings:

Hypothesis 1:

Indicate whether or not your hypothesis stated in the Introduction was supported. Was the result in the expected direction? Was the relationship as strong as you expected? Use shared variance to comment on the strength of relationship.

Hypothesis 2:

Same as above but for the second relationship you are evaluating.

Hypothesis 3:

Same as above but for the third relationship you are evaluating.

Appendices

This section is to be written by you.

You need to include:

Sample of the questionnaires. Although we completed the questionnaires online, a sample questionnaire document is in the Report folder on Blackboard.

Raw Data

Three Bivariate scatterplots for responses for the three relationships you choose to evaluate (identification of impossible observations, if any).

Three sets of Full workings of Pearson’s r

This means you should provide the specific values for the formula for Pearson’s r :

You should provide the values for numerator () and the denominator (N) of this formula. You don’t need to provide all the z scores or the cross products.

Three sets of Full workings of the percentage of shared variance between indicated variables.

Remember that anything you put in an appendix must be referred to in the body of the text.